LMFDB - Embedded newform 230.2.j.a.179.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

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

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			179.11
Character	$\chi$	$=$	230.179
Dual form			230.2.j.a.9.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.281733 - 0.959493i) q^{2} +(1.62154 + 1.40507i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-1.50506 - 1.65372i) q^{5} +(1.80499 - 1.16000i) q^{6} +(4.06165 - 1.85489i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(0.228216 + 1.58728i) q^{9} +O(q^{10})$	\(q+(0.281733 - 0.959493i) q^{2} +(1.62154 + 1.40507i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-1.50506 - 1.65372i) q^{5} +(1.80499 - 1.16000i) q^{6} +(4.06165 - 1.85489i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(0.228216 + 1.58728i) q^{9} +(-2.01076 + 0.978188i) q^{10} +(-2.71299 + 0.796606i) q^{11} +(-0.604486 - 2.05869i) q^{12} +(4.55837 + 2.08174i) q^{13} +(-0.635457 - 4.41970i) q^{14} +(-0.116917 - 4.79628i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.557281 + 0.867146i) q^{17} +(1.58728 + 0.228216i) q^{18} +(-2.21722 - 1.42492i) q^{19} +(0.372068 + 2.20490i) q^{20} +(9.19236 + 2.69912i) q^{21} +2.82752i q^{22} +(-2.84316 + 3.86218i) q^{23} -2.14560 q^{24} +(-0.469587 + 4.97790i) q^{25} +(3.28165 - 3.78723i) q^{26} +(1.61982 - 2.52049i) q^{27} +(-4.41970 - 0.635457i) q^{28} +(-6.14851 + 3.95141i) q^{29} +(-4.63494 - 1.23909i) q^{30} +(-1.21119 - 1.39778i) q^{31} +(0.989821 - 0.142315i) q^{32} +(-5.51850 - 2.52021i) q^{33} +(0.989025 - 0.290404i) q^{34} +(-9.18049 - 3.92511i) q^{35} +(0.666161 - 1.45869i) q^{36} +(-5.30635 + 0.762938i) q^{37} +(-1.99187 + 1.72596i) q^{38} +(4.46657 + 9.78043i) q^{39} +(2.22041 + 0.264194i) q^{40} +(0.379411 - 2.63886i) q^{41} +(5.17957 - 8.05957i) q^{42} +(-7.97658 - 6.91175i) q^{43} +(2.71299 + 0.796606i) q^{44} +(2.28144 - 2.76636i) q^{45} +(2.90473 + 3.81609i) q^{46} +9.52621i q^{47} +(-0.604486 + 2.05869i) q^{48} +(8.47232 - 9.77757i) q^{49} +(4.64396 + 1.85300i) q^{50} +(-0.314749 + 2.18913i) q^{51} +(-2.70927 - 4.21571i) q^{52} +(6.13122 - 2.80004i) q^{53} +(-1.96204 - 2.26431i) q^{54} +(5.40058 + 3.28759i) q^{55} +(-1.85489 + 4.06165i) q^{56} +(-1.59319 - 5.42592i) q^{57} +(2.05911 + 7.01270i) q^{58} +(-3.67827 + 8.05429i) q^{59} +(-2.49471 + 4.09810i) q^{60} +(0.962688 + 1.11100i) q^{61} +(-1.68239 + 0.768323i) q^{62} +(3.87117 + 6.02365i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-3.41800 - 10.6714i) q^{65} +(-3.97287 + 4.58494i) q^{66} +(-3.95010 + 13.4528i) q^{67} -1.03078i q^{68} +(-10.0369 + 2.26784i) q^{69} +(-6.35256 + 7.70279i) q^{70} +(5.75091 + 1.68862i) q^{71} +(-1.21192 - 1.05014i) q^{72} +(0.315595 - 0.491075i) q^{73} +(-0.762938 + 5.30635i) q^{74} +(-7.75575 + 7.41205i) q^{75} +(1.09488 + 2.39744i) q^{76} +(-9.54159 + 8.26783i) q^{77} +(10.6426 - 1.53018i) q^{78} +(4.90969 - 10.7507i) q^{79} +(0.879053 - 2.05603i) q^{80} +(10.7840 - 3.16647i) q^{81} +(-2.42508 - 1.10750i) q^{82} +(8.64400 - 1.24282i) q^{83} +(-6.27385 - 7.24041i) q^{84} +(0.595276 - 2.22669i) q^{85} +(-8.87904 + 5.70621i) q^{86} +(-15.5221 - 2.23173i) q^{87} +(1.52868 - 2.37867i) q^{88} +(0.803321 - 0.927082i) q^{89} +(-2.01155 - 2.96840i) q^{90} +22.3759 q^{91} +(4.47987 - 1.71195i) q^{92} -3.96836i q^{93} +(9.14033 + 2.68384i) q^{94} +(0.980629 + 5.81126i) q^{95} +(1.80499 + 1.16000i) q^{96} +(5.00839 + 0.720098i) q^{97} +(-6.99459 - 10.8838i) q^{98} +(-1.88359 - 4.12448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.281733	−	0.959493i	0.199215	−	0.678464i
$2$	0.281733	−	0.959493i	0.199215	−	0.678464i
$3$	1.62154	+	1.40507i	0.936195	+	0.811217i	0.982222	−	0.187723i	$-0.0601107\pi$
$3$	1.62154	+	1.40507i	0.936195	+	0.811217i	−0.0460273	+	0.998940i	$0.514656\pi$
$4$	−0.841254	−	0.540641i	−0.420627	−	0.270320i
$5$	−1.50506	−	1.65372i	−0.673083	−	0.739567i
$5$	−1.50506	−	1.65372i	−0.673083	−	0.739567i
$6$	1.80499	−	1.16000i	0.736886	−	0.473568i
$7$	4.06165	−	1.85489i	1.53516	−	0.701083i	0.544666	−	0.838653i	$-0.316657\pi$
$7$	4.06165	−	1.85489i	1.53516	−	0.701083i	0.990492	+	0.137570i	$0.0439293\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	0.228216	+	1.58728i	0.0760722	+	0.529093i
$10$	−2.01076	+	0.978188i	−0.635858	+	0.309330i
$11$	−2.71299	+	0.796606i	−0.817997	+	0.240186i	−0.663853	−	0.747863i	$-0.731080\pi$
$11$	−2.71299	+	0.796606i	−0.817997	+	0.240186i	−0.154144	+	0.988048i	$0.549262\pi$
$12$	−0.604486	−	2.05869i	−0.174500	−	0.594292i
$13$	4.55837	+	2.08174i	1.26426	+	0.577370i	0.930847	−	0.365410i	$-0.119071\pi$
$13$	4.55837	+	2.08174i	1.26426	+	0.577370i	0.333417	+	0.942780i	$0.391798\pi$
$14$	−0.635457	−	4.41970i	−0.169833	−	1.18122i
$15$	−0.116917	−	4.79628i	−0.0301879	−	1.23840i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	0.557281	+	0.867146i	0.135160	+	0.210314i	0.902236	−	0.431244i	$-0.141925\pi$
$17$	0.557281	+	0.867146i	0.135160	+	0.210314i	−0.767075	+	0.641557i	$0.778289\pi$
$18$	1.58728	+	0.228216i	0.374126	+	0.0537911i
$19$	−2.21722	−	1.42492i	−0.508666	−	0.326900i	0.261008	−	0.965337i	$-0.415945\pi$
$19$	−2.21722	−	1.42492i	−0.508666	−	0.326900i	−0.769674	+	0.638437i	$0.779581\pi$
$20$	0.372068	+	2.20490i	0.0831970	+	0.493030i
$21$	9.19236	+	2.69912i	2.00594	+	0.588996i
$22$			2.82752i			0.602830i
$23$	−2.84316	+	3.86218i	−0.592839	+	0.805321i
$23$	−2.84316	+	3.86218i	−0.592839	+	0.805321i
$24$	−2.14560			−0.437969
$25$	−0.469587	+	4.97790i	−0.0939174	+	0.995580i
$26$	3.28165	−	3.78723i	0.643585	−	0.742736i
$27$	1.61982	−	2.52049i	0.311734	−	0.485068i
$28$	−4.41970	−	0.635457i	−0.835245	−	0.120090i
$29$	−6.14851	+	3.95141i	−1.14175	+	0.733758i	−0.967980	−	0.251028i	$-0.919231\pi$
$29$	−6.14851	+	3.95141i	−1.14175	+	0.733758i	−0.173771	+	0.984786i	$0.555595\pi$
$30$	−4.63494	−	1.23909i	−0.846221	−	0.226226i
$31$	−1.21119	−	1.39778i	−0.217535	−	0.251049i	0.636485	−	0.771289i	$-0.280388\pi$
$31$	−1.21119	−	1.39778i	−0.217535	−	0.251049i	−0.854020	+	0.520240i	$0.825842\pi$
$32$	0.989821	−	0.142315i	0.174977	−	0.0251579i
$33$	−5.51850	−	2.52021i	−0.960648	−	0.438713i
$34$	0.989025	−	0.290404i	0.169616	−	0.0498038i
$35$	−9.18049	−	3.92511i	−1.55179	−	0.663464i
$36$	0.666161	−	1.45869i	0.111027	−	0.243115i
$37$	−5.30635	+	0.762938i	−0.872359	+	0.125426i	−0.563931	−	0.825822i	$-0.690712\pi$
$37$	−5.30635	+	0.762938i	−0.872359	+	0.125426i	−0.308427	+	0.951248i	$0.599803\pi$
$38$	−1.99187	+	1.72596i	−0.323123	+	0.279988i
$39$	4.46657	+	9.78043i	0.715224	+	1.56612i
$40$	2.22041	+	0.264194i	0.351077	+	0.0417728i
$41$	0.379411	−	2.63886i	0.0592541	−	0.412121i	−0.938508	−	0.345257i	$-0.887792\pi$
$41$	0.379411	−	2.63886i	0.0592541	−	0.412121i	0.997762	−	0.0668639i	$-0.0212993\pi$
$42$	5.17957	−	8.05957i	0.799226	−	1.24362i
$43$	−7.97658	−	6.91175i	−1.21642	−	1.05403i	−0.996920	−	0.0784189i	$-0.975013\pi$
$43$	−7.97658	−	6.91175i	−1.21642	−	1.05403i	−0.219497	−	0.975613i	$-0.570442\pi$
$44$	2.71299	+	0.796606i	0.408999	+	0.120093i
$45$	2.28144	−	2.76636i	0.340097	−	0.412384i
$46$	2.90473	+	3.81609i	0.428279	+	0.562652i
$47$			9.52621i			1.38954i	0.719232	+	0.694770i	$0.244494\pi$
$47$			9.52621i			1.38954i	−0.719232	+	0.694770i	$0.755506\pi$
$48$	−0.604486	+	2.05869i	−0.0872500	+	0.297146i
$49$	8.47232	−	9.77757i	1.21033	−	1.39680i
$50$	4.64396	+	1.85300i	0.656755	+	0.262054i
$51$	−0.314749	+	2.18913i	−0.0440737	+	0.306539i
$52$	−2.70927	−	4.21571i	−0.375708	−	0.584613i
$53$	6.13122	−	2.80004i	0.842188	−	0.384614i	0.0528720	−	0.998601i	$-0.483162\pi$
$53$	6.13122	−	2.80004i	0.842188	−	0.384614i	0.789316	+	0.613987i	$0.210435\pi$
$54$	−1.96204	−	2.26431i	−0.266999	−	0.308134i
$55$	5.40058	+	3.28759i	0.728214	+	0.443299i
$56$	−1.85489	+	4.06165i	−0.247870	+	0.542760i
$57$	−1.59319	−	5.42592i	−0.211024	−	0.718680i
$58$	2.05911	+	7.01270i	0.270375	+	0.920812i
$59$	−3.67827	+	8.05429i	−0.478870	+	1.04858i	0.503903	+	0.863760i	$0.331897\pi$
$59$	−3.67827	+	8.05429i	−0.478870	+	1.04858i	−0.982773	+	0.184819i	$0.940830\pi$
$60$	−2.49471	+	4.09810i	−0.322066	+	0.529063i
$61$	0.962688	+	1.11100i	0.123260	+	0.142249i	0.814025	−	0.580830i	$-0.197272\pi$
$61$	0.962688	+	1.11100i	0.123260	+	0.142249i	−0.690766	+	0.723079i	$0.742726\pi$
$62$	−1.68239	+	0.768323i	−0.213664	+	0.0975772i
$63$	3.87117	+	6.02365i	0.487721	+	0.758909i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−3.41800	−	10.6714i	−0.423951	−	1.32362i
$66$	−3.97287	+	4.58494i	−0.489026	+	0.564367i
$67$	−3.95010	+	13.4528i	−0.482581	+	1.64352i	0.254024	+	0.967198i	$0.418246\pi$
$67$	−3.95010	+	13.4528i	−0.482581	+	1.64352i	−0.736605	+	0.676323i	$0.763572\pi$
$68$		−	1.03078i		−	0.125000i
$69$	−10.0369	+	2.26784i	−1.20830	+	0.273016i
$70$	−6.35256	+	7.70279i	−0.759276	+	0.920659i
$71$	5.75091	+	1.68862i	0.682507	+	0.200402i	0.604565	−	0.796556i	$-0.293347\pi$
$71$	5.75091	+	1.68862i	0.682507	+	0.200402i	0.0779421	+	0.996958i	$0.475165\pi$
$72$	−1.21192	−	1.05014i	−0.142826	−	0.123760i
$73$	0.315595	−	0.491075i	0.0369376	−	0.0574760i	−0.822294	−	0.569063i	$-0.807306\pi$
$73$	0.315595	−	0.491075i	0.0369376	−	0.0574760i	0.859231	+	0.511587i	$0.170942\pi$
$74$	−0.762938	+	5.30635i	−0.0886898	+	0.616851i
$75$	−7.75575	+	7.41205i	−0.895557	+	0.855869i
$76$	1.09488	+	2.39744i	0.125591	+	0.275005i
$77$	−9.54159	+	8.26783i	−1.08736	+	0.942207i
$78$	10.6426	−	1.53018i	1.20504	−	0.173259i
$79$	4.90969	−	10.7507i	0.552384	−	1.20955i	−0.403276	−	0.915078i	$-0.632129\pi$
$79$	4.90969	−	10.7507i	0.552384	−	1.20955i	0.955660	−	0.294473i	$-0.0951441\pi$
$80$	0.879053	−	2.05603i	0.0982811	−	0.229871i
$81$	10.7840	−	3.16647i	1.19822	−	0.351830i
$82$	−2.42508	−	1.10750i	−0.267805	−	0.122303i
$83$	8.64400	−	1.24282i	0.948802	−	0.136417i	0.349497	−	0.936938i	$-0.386353\pi$
$83$	8.64400	−	1.24282i	0.948802	−	0.136417i	0.599305	+	0.800520i	$0.295444\pi$
$84$	−6.27385	−	7.24041i	−0.684533	−	0.789993i
$85$	0.595276	−	2.22669i	0.0645668	−	0.241519i
$86$	−8.87904	+	5.70621i	−0.957451	+	0.615317i
$87$	−15.5221	−	2.23173i	−1.66414	−	0.239267i
$88$	1.52868	−	2.37867i	0.162957	−	0.253567i
$89$	0.803321	−	0.927082i	0.0851519	−	0.0982705i	−0.711575	−	0.702610i	$-0.752018\pi$
$89$	0.803321	−	0.927082i	0.0851519	−	0.0982705i	0.796727	+	0.604340i	$0.206563\pi$
$90$	−2.01155	−	2.96840i	−0.212036	−	0.312897i
$91$	22.3759			2.34563
$92$	4.47987	−	1.71195i	0.467059	−	0.178483i
$93$		−	3.96836i		−	0.411500i
$94$	9.14033	+	2.68384i	0.942753	+	0.276817i
$95$	0.980629	+	5.81126i	0.100610	+	0.596223i
$96$	1.80499	+	1.16000i	0.184221	+	0.118392i
$97$	5.00839	+	0.720098i	0.508525	+	0.0731148i	0.391802	−	0.920050i	$-0.371852\pi$
$97$	5.00839	+	0.720098i	0.508525	+	0.0731148i	0.116723	+	0.993164i	$0.462761\pi$
$98$	−6.99459	−	10.8838i	−0.706560	−	1.09943i
$99$	−1.88359	−	4.12448i	−0.189308	−	0.414526i
$100$	3.08630	−	3.93380i	0.308630	−	0.393380i
$101$	−1.15006	−	7.99884i	−0.114435	−	0.795914i	−0.963516	−	0.267651i	$-0.913753\pi$
$101$	−1.15006	−	7.99884i	−0.114435	−	0.795914i	0.849081	−	0.528263i	$-0.177156\pi$
$102$	2.01178	+	0.918748i	0.199196	+	0.0909696i
$103$	1.14159	+	3.88789i	0.112484	+	0.383086i	0.996422	−	0.0845189i	$-0.0269353\pi$
$103$	1.14159	+	3.88789i	0.112484	+	0.383086i	−0.883938	+	0.467604i	$0.845117\pi$
$104$	−4.80823	+	1.41182i	−0.471486	+	0.138441i
$105$	−9.37146	−	19.2639i	−0.914561	−	1.87997i
$106$	−0.959249	−	6.67173i	−0.0931705	−	0.648015i
$107$	3.74153	−	3.24205i	0.361707	−	0.313421i	−0.454980	−	0.890502i	$-0.650354\pi$
$107$	3.74153	−	3.24205i	0.361707	−	0.313421i	0.816687	+	0.577081i	$0.195808\pi$
$108$	−2.72536	+	1.24463i	−0.262248	+	0.119765i
$109$	−0.845706	+	0.543502i	−0.0810040	+	0.0520581i	−0.580516	−	0.814249i	$-0.697149\pi$
$109$	−0.845706	+	0.543502i	−0.0810040	+	0.0520581i	0.499512	+	0.866307i	$0.333513\pi$
$110$	4.67594	−	4.25560i	0.445833	−	0.405755i
$111$	−9.67643	−	6.21866i	−0.918446	−	0.590249i
$112$	3.37454	+	2.92405i	0.318864	+	0.276297i
$113$	4.20081	−	14.3067i	0.395179	−	1.34586i	−0.486365	−	0.873756i	$-0.661678\pi$
$113$	4.20081	−	14.3067i	0.395179	−	1.34586i	0.881545	−	0.472101i	$-0.156504\pi$
$114$	−5.65498			−0.529638
$115$	10.6661	−	1.11103i	0.994619	−	0.103604i
$116$	7.30875			0.678601
$117$	−2.26400	+	7.71049i	−0.209307	+	0.712835i
$118$	6.69174	+	5.79843i	0.616025	+	0.533789i
$119$	3.87194	+	2.48834i	0.354940	+	0.228106i
$120$	3.22926	+	3.54823i	0.294790	+	0.323907i
$121$	−2.52805	+	1.62468i	−0.229823	+	0.147698i
$122$	1.33722	−	0.610687i	0.121066	−	0.0552890i
$123$	4.32302	−	3.74592i	0.389793	−	0.337758i
$124$	0.263216	+	1.83071i	0.0236375	+	0.164402i
$125$	8.93882	−	6.71547i	0.799512	−	0.600650i
$126$	6.87029	−	2.01730i	0.612054	−	0.179715i
$127$	1.38874	+	4.72960i	0.123230	+	0.419684i	0.997881	−	0.0650704i	$-0.0207272\pi$
$127$	1.38874	+	4.72960i	0.123230	+	0.419684i	−0.874650	+	0.484754i	$0.838909\pi$
$128$	−0.909632	−	0.415415i	−0.0804009	−	0.0367178i
$129$	−3.22284	−	22.4153i	−0.283755	−	1.97356i
$130$	−11.2021	+	0.273069i	−0.982489	+	0.0239498i
$131$	−9.10304	−	19.9329i	−0.795337	−	1.74154i	−0.660701	−	0.750649i	$-0.729741\pi$
$131$	−9.10304	−	19.9329i	−0.795337	−	1.74154i	−0.134635	−	0.990895i	$-0.542986\pi$
$132$	3.27993	+	5.10367i	0.285481	+	0.444217i
$133$	−11.6486	−	1.67482i	−1.01007	−	0.145226i
$134$	11.7950	+	7.58018i	1.01893	+	0.654828i
$135$	−6.60611	+	1.11476i	−0.568564	+	0.0959430i
$136$	−0.989025	−	0.290404i	−0.0848082	−	0.0249019i
$137$		−	8.25702i		−	0.705445i	−0.935728	−	0.352723i	$-0.885256\pi$
$137$		−	8.25702i		−	0.705445i	0.935728	−	0.352723i	$-0.114744\pi$
$138$	−0.651751	+	10.2693i	−0.0554807	+	0.874179i
$139$	−19.5418			−1.65751			−0.828755	−	0.559611i	$-0.810950\pi$
$139$	−19.5418			−1.65751			−0.828755	+	0.559611i	$0.810950\pi$
$140$	5.60105	+	8.26536i	0.473375	+	0.698550i
$141$	−13.3850	+	15.4471i	−1.12722	+	1.30088i
$142$	3.24044	−	5.04222i	0.271931	−	0.423134i
$143$	−14.0251	−	2.01651i	−1.17284	−	0.168629i
$144$	−1.34904	+	0.866973i	−0.112420	+	0.0722478i
$145$	15.7884	+	4.22082i	1.31116	+	0.350520i
$146$	−0.382270	−	0.441163i	−0.0316369	−	0.0365109i
$147$	27.4763	−	3.95050i	2.26621	−	0.325832i
$148$	4.87646	+	2.22701i	0.400843	+	0.183059i
$149$	−0.509619	+	0.149638i	−0.0417496	+	0.0122588i	−0.302541	−	0.953136i	$-0.597835\pi$
$149$	−0.509619	+	0.149638i	−0.0417496	+	0.0122588i	0.260791	+	0.965395i	$0.416017\pi$
$150$	4.92676	+	9.52980i	0.402268	+	0.778105i
$151$	−3.50395	+	7.67259i	−0.285148	+	0.624386i	−0.996954	−	0.0779893i	$-0.975150\pi$
$151$	−3.50395	+	7.67259i	−0.285148	+	0.624386i	0.711807	+	0.702376i	$0.247877\pi$
$152$	2.60879	−	0.375087i	0.211601	−	0.0304236i
$153$	−1.24922	+	1.08246i	−0.100994	+	0.0875115i
$154$	5.24475	+	11.4844i	0.422634	+	0.925440i
$155$	−0.488636	+	4.10671i	−0.0392482	+	0.329859i
$156$	1.53018	−	10.6426i	0.122512	−	0.852093i
$157$	−1.44727	+	2.25200i	−0.115505	+	0.179729i	−0.894192	−	0.447683i	$-0.852249\pi$
$157$	−1.44727	+	2.25200i	−0.115505	+	0.179729i	0.778688	+	0.627412i	$0.215886\pi$
$158$	−8.93203	−	7.73964i	−0.710594	−	0.615733i
$159$	13.8762	+	4.07443i	1.10046	+	0.323124i
$160$	−1.72509	−	1.42270i	−0.136380	−	0.112474i
$161$	−4.38396	+	20.9606i	−0.345505	+	1.65192i
$162$		−	11.2393i		−	0.883040i
$163$	2.27325	−	7.74198i	0.178055	−	0.606399i	−0.821301	−	0.570496i	$-0.806751\pi$
$163$	2.27325	−	7.74198i	0.178055	−	0.606399i	0.999355	−	0.0359028i	$-0.0114307\pi$
$164$	−1.74586	+	2.01483i	−0.136329	+	0.157332i
$165$	4.13794	+	12.9191i	0.322138	+	1.00575i
$166$	1.24282	−	8.64400i	0.0964615	−	0.670904i
$167$	7.29581	+	11.3525i	0.564567	+	0.878483i	0.999761	−	0.0218536i	$-0.00695677\pi$
$167$	7.29581	+	11.3525i	0.564567	+	0.878483i	−0.435195	+	0.900336i	$0.643320\pi$
$168$	−8.71467	+	3.97986i	−0.672351	+	0.307053i
$169$	7.93189	+	9.15389i	0.610145	+	0.704145i
$170$	−1.96879	−	1.19850i	−0.150999	−	0.0919204i
$171$	1.75574	−	3.84454i	0.134265	−	0.294000i
$172$	2.97356	+	10.1270i	0.226732	+	0.772177i
$173$	−4.58148	−	15.6031i	−0.348323	−	1.18628i	−0.928358	−	0.371688i	$-0.878779\pi$
$173$	−4.58148	−	15.6031i	−0.348323	−	1.18628i	0.580034	−	0.814592i	$-0.303039\pi$
$174$	−6.51440	+	14.2645i	−0.493855	+	1.08139i
$175$	7.32617	+	21.0895i	0.553806	+	1.59422i
$176$	−1.85164	−	2.13690i	−0.139572	−	0.161075i
$177$	−17.2813	+	7.89210i	−1.29894	+	0.593207i
$178$	−0.663207	−	1.03197i	−0.0497095	−	0.0773495i
$179$	−0.162396	+	1.12949i	−0.0121381	+	0.0844222i	−0.994990	−	0.0999743i	$-0.968124\pi$
$179$	−0.162396	+	1.12949i	−0.0121381	+	0.0844222i	0.982852	+	0.184396i	$0.0590330\pi$
$180$	−3.41488	+	1.09377i	−0.254530	+	0.0815248i
$181$	−5.39162	+	6.22226i	−0.400756	+	0.462497i	−0.919879	−	0.392203i	$-0.871713\pi$
$181$	−5.39162	+	6.22226i	−0.400756	+	0.462497i	0.519123	+	0.854700i	$0.326259\pi$
$182$	6.30401	−	21.4695i	0.467284	−	1.59142i
$183$			3.15417i			0.233163i
$184$	−0.380478	−	4.78072i	−0.0280492	−	0.352439i
$185$	9.24807	+	7.62696i	0.679931	+	0.560745i
$186$	−3.80761	−	1.11802i	−0.279188	−	0.0819769i
$187$	−2.20267	−	1.90863i	−0.161075	−	0.139573i
$188$	5.15026	−	8.01396i	0.375621	−	0.584478i
$189$	1.90390	−	13.2419i	0.138488	−	0.963208i
$190$	5.85214	+	0.696315i	0.424559	+	0.0505160i
$191$	−8.46851	−	18.5434i	−0.612760	−	1.34176i	−0.920670	−	0.390341i	$-0.872357\pi$
$191$	−8.46851	−	18.5434i	−0.612760	−	1.34176i	0.307911	−	0.951415i	$-0.400370\pi$
$192$	1.62154	−	1.40507i	0.117024	−	0.101402i
$193$	24.6261	−	3.54069i	1.77262	−	0.254865i	0.822952	−	0.568112i	$-0.192326\pi$
$193$	24.6261	−	3.54069i	1.77262	−	0.254865i	0.949672	+	0.313247i	$0.101417\pi$
$194$	2.10195	−	4.60264i	0.150912	−	0.330450i
$195$	9.45165	−	22.1066i	0.676846	−	1.58309i
$196$	−12.4135	+	3.64494i	−0.886680	+	0.260353i
$197$	9.46829	+	4.32402i	0.674588	+	0.308074i	0.723095	−	0.690749i	$-0.242719\pi$
$197$	9.46829	+	4.32402i	0.674588	+	0.308074i	−0.0485069	+	0.998823i	$0.515446\pi$
$198$	−4.48807	+	0.645288i	−0.318954	+	0.0458586i
$199$	−2.93954	−	3.39241i	−0.208379	−	0.240482i	0.641934	−	0.766760i	$-0.278132\pi$
$199$	−2.93954	−	3.39241i	−0.208379	−	0.240482i	−0.850312	+	0.526278i	$0.823587\pi$
$200$	−2.90494	−	4.06956i	−0.205410	−	0.287761i
$201$	−25.3073	+	16.2640i	−1.78504	+	1.14718i
$202$	−7.99884	−	1.15006i	−0.562796	−	0.0809179i
$203$	−17.6436	+	27.4541i	−1.23834	+	1.92690i
$204$	1.44832	−	1.67144i	0.101402	−	0.117025i
$205$	−4.93498	+	3.34421i	−0.344674	+	0.233570i
$206$	4.05203			0.282318
$207$	−6.77922	−	3.63147i	−0.471189	−	0.252405i
$208$			5.01122i			0.347466i
$209$	7.15040	+	2.09955i	0.494604	+	0.145229i
$210$	−21.1239	+	3.56457i	−1.45768	+	0.245979i
$211$	17.6999	+	11.3750i	1.21851	+	0.783088i	0.982062	−	0.188557i	$-0.0603810\pi$
$211$	17.6999	+	11.3750i	1.21851	+	0.783088i	0.236446	+	0.971645i	$0.424017\pi$
$212$	−6.67173	−	0.959249i	−0.458216	−	0.0658815i
$213$	6.95268	+	10.8186i	0.476390	+	0.741277i
$214$	−2.05662	−	4.50336i	−0.140587	−	0.307843i
$215$	0.575134	+	23.5936i	0.0392238	+	1.60907i
$216$	0.426391	+	2.96561i	0.0290122	+	0.201785i
$217$	−7.51214	−	3.43068i	−0.509958	−	0.232890i
$218$	0.283224	+	0.964571i	0.0191823	+	0.0653290i
$219$	1.20174	−	0.352864i	0.0812062	−	0.0238443i
$220$	−2.76585	−	5.68547i	−0.186474	−	0.383314i
$221$	0.735121	+	5.11288i	0.0494496	+	0.343930i
$222$	−8.69293	+	7.53246i	−0.583431	+	0.505546i
$223$	−15.6662	+	7.15450i	−1.04908	+	0.479101i	−0.863932	−	0.503609i	$-0.832005\pi$
$223$	−15.6662	+	7.15450i	−1.04908	+	0.479101i	−0.185153	+	0.982710i	$0.559278\pi$
$224$	3.75632	−	2.41404i	0.250980	−	0.161295i
$225$	−8.00849	+	0.390672i	−0.533899	+	0.0260448i
$226$	−12.5436	−	8.06130i	−0.834390	−	0.536230i
$227$	−8.90509	−	7.71631i	−0.591052	−	0.512149i	0.307192	−	0.951648i	$-0.400611\pi$
$227$	−8.90509	−	7.71631i	−0.591052	−	0.512149i	−0.898243	+	0.439498i	$0.855156\pi$
$228$	−1.59319	+	5.42592i	−0.105512	+	0.359340i
$229$	6.65247			0.439607			0.219804	−	0.975544i	$-0.429458\pi$
$229$	6.65247			0.439607			0.219804	+	0.975544i	$0.429458\pi$
$230$	1.93896	−	10.5471i	0.127851	−	0.695452i
$231$	−27.0889			−1.78232
$232$	2.05911	−	7.01270i	0.135187	−	0.460406i
$233$	−12.4111	−	10.7543i	−0.813078	−	0.704536i	0.145503	−	0.989358i	$-0.453520\pi$
$233$	−12.4111	−	10.7543i	−0.813078	−	0.704536i	−0.958580	+	0.284822i	$0.908065\pi$
$234$	6.76032	+	4.34459i	0.441936	+	0.284015i
$235$	15.7537	−	14.3375i	1.02766	−	0.935277i
$236$	7.44884	−	4.78708i	0.484878	−	0.311612i
$237$	23.0668	−	10.5342i	1.49835	−	0.684272i
$238$	3.47840	−	3.01405i	0.225471	−	0.195372i
$239$	1.51948	+	10.5682i	0.0982868	+	0.683600i	0.978078	+	0.208239i	$0.0667732\pi$
$239$	1.51948	+	10.5682i	0.0982868	+	0.683600i	−0.879791	+	0.475360i	$0.842318\pi$
$240$	4.31428	−	2.09880i	0.278486	−	0.135477i
$241$	27.9611	−	8.21012i	1.80113	−	0.528861i	0.803357	−	0.595498i	$-0.203045\pi$
$241$	27.9611	−	8.21012i	1.80113	−	0.528861i	0.997777	+	0.0666376i	$0.0212271\pi$
$242$	0.846635	+	2.88337i	0.0544238	+	0.185350i
$243$	13.7597	+	6.28384i	0.882684	+	0.403108i
$244$	−0.209212	−	1.45510i	−0.0133934	−	0.0931534i
$245$	−28.9207	+	0.704990i	−1.84768	+	0.0450401i
$246$	−2.37625	−	5.20325i	−0.151504	−	0.331747i
$247$	−7.14060	−	11.1110i	−0.454345	−	0.706975i
$248$	1.83071	+	0.263216i	0.116250	+	0.0167142i
$249$	15.7628	+	10.1301i	0.998927	+	0.641972i
$250$	−3.92509	−	10.4687i	−0.248245	−	0.662099i
$251$	−6.83951	−	2.00826i	−0.431706	−	0.126760i	0.0586578	−	0.998278i	$-0.481318\pi$
$251$	−6.83951	−	2.00826i	−0.431706	−	0.126760i	−0.490364	+	0.871518i	$0.663136\pi$
$252$		−	7.16033i		−	0.451058i
$253$	4.63682	−	12.7429i	0.291514	−	0.801142i
$254$	4.92927			0.309290
$255$	4.09392	−	2.77426i	0.256371	−	0.173731i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	7.22143	−	11.2368i	0.450460	−	0.700930i	−0.539545	−	0.841956i	$-0.681404\pi$
$257$	7.22143	−	11.2368i	0.450460	−	0.700930i	0.990006	+	0.141026i	$0.0450402\pi$
$258$	−22.4153	−	3.22284i	−1.39552	−	0.200645i
$259$	−20.1373	+	12.9415i	−1.25127	+	0.804145i
$260$	−2.89399	+	10.8253i	−0.179478	+	0.671355i
$261$	−7.67519	−	8.85764i	−0.475082	−	0.548274i
$262$	−21.6901	+	3.11856i	−1.34002	+	0.192666i
$263$	5.28678	+	2.41439i	0.325997	+	0.148878i	0.571690	−	0.820470i	$-0.306288\pi$
$263$	5.28678	+	2.41439i	0.325997	+	0.148878i	−0.245693	+	0.969348i	$0.579015\pi$
$264$	5.82099	−	1.70920i	0.358257	−	0.105194i
$265$	−13.8583	−	5.92511i	−0.851311	−	0.363977i
$266$	−4.88878	+	10.7049i	−0.299751	+	0.656362i
$267$	2.60523	−	0.374576i	0.159438	−	0.0229237i
$268$	10.5962	−	9.18163i	0.647264	−	0.560857i
$269$	0.834171	+	1.82658i	0.0508603	+	0.111368i	0.933356	−	0.358952i	$-0.116866\pi$
$269$	0.834171	+	1.82658i	0.0508603	+	0.111368i	−0.882496	+	0.470320i	$0.844138\pi$
$270$	−0.791555	+	6.65258i	−0.0481725	+	0.404863i
$271$	−0.446016	+	3.10211i	−0.0270935	+	0.188440i	−0.998874	−	0.0474487i	$-0.984891\pi$
$271$	−0.446016	+	3.10211i	−0.0270935	+	0.188440i	0.971780	+	0.235889i	$0.0758000\pi$
$272$	−0.557281	+	0.867146i	−0.0337901	+	0.0525784i
$273$	36.2833	+	31.4396i	2.19596	+	1.90281i
$274$	−7.92256	−	2.32627i	−0.478619	−	0.140535i
$275$	−2.69144	−	13.8791i	−0.162300	−	0.836939i
$276$	9.66968	+	3.51854i	0.582046	+	0.211791i
$277$			16.5668i			0.995401i	0.867349	+	0.497700i	$0.165822\pi$
$277$			16.5668i			0.995401i	−0.867349	+	0.497700i	$0.834178\pi$
$278$	−5.50555	+	18.7502i	−0.330201	+	1.12456i
$279$	1.94226	−	2.24149i	0.116280	−	0.134194i
$280$	9.50855	−	3.04555i	0.568245	−	0.182006i
$281$	1.47670	−	10.2707i	0.0880924	−	0.612696i	−0.897175	−	0.441675i	$-0.854384\pi$
$281$	1.47670	−	10.2707i	0.0880924	−	0.612696i	0.985267	−	0.171021i	$-0.0547066\pi$
$282$	11.0504	+	17.1948i	0.658042	+	1.02393i
$283$	−25.4272	+	11.6122i	−1.51149	+	0.690274i	−0.986937	−	0.161105i	$-0.948494\pi$
$283$	−25.4272	+	11.6122i	−1.51149	+	0.690274i	−0.524551	+	0.851379i	$0.675767\pi$
$284$	−3.92504	−	4.52973i	−0.232908	−	0.268790i
$285$	−6.57510	+	10.8010i	−0.389475	+	0.639798i
$286$	−5.88616	+	12.8889i	−0.348056	+	0.762136i
$287$	−3.35377	−	11.4219i	−0.197967	−	0.674213i
$288$	0.451787	+	1.53865i	0.0266218	+	0.0906656i
$289$	6.62068	−	14.4973i	0.389451	−	0.852780i
$290$	8.49796	−	13.9597i	0.499017	−	0.819744i
$291$	7.10950	+	8.20480i	0.416766	+	0.480974i
$292$	−0.530990	+	0.242495i	−0.0310739	+	0.0141910i
$293$	13.0744	+	20.3442i	0.763816	+	1.18852i	0.977359	+	0.211588i	$0.0678634\pi$
$293$	13.0744	+	20.3442i	0.763816	+	1.18852i	−0.213543	+	0.976934i	$0.568500\pi$
$294$	3.95050	−	27.4763i	0.230398	−	1.60245i
$295$	18.8556	−	6.03936i	1.09781	−	0.351625i
$296$	3.51065	−	4.05151i	0.204053	−	0.235489i
$297$	−2.38672	+	8.12842i	−0.138492	+	0.471659i
$298$			0.531134i			0.0307678i
$299$	−21.0002	+	11.6865i	−1.21447	+	0.675850i
$300$	10.5318	−	2.04233i	0.608054	−	0.117914i
$301$	−45.2186	−	13.2774i	−2.60636	−	0.765295i
$302$	6.37462	+	5.52364i	0.366818	+	0.317850i
$303$	9.37406	−	14.5863i	0.538526	−	0.837962i
$304$	0.375087	−	2.60879i	0.0215127	−	0.149624i
$305$	0.388383	−	3.26414i	0.0222387	−	0.186904i
$306$	0.686664	+	1.50358i	0.0392540	+	0.0859542i
$307$	1.10648	−	0.958774i	0.0631504	−	0.0547201i	−0.622714	−	0.782450i	$-0.713970\pi$
$307$	1.10648	−	0.958774i	0.0631504	−	0.0547201i	0.685864	+	0.727730i	$0.259424\pi$
$308$	12.4968	−	1.79677i	0.712072	−	0.102381i
$309$	−3.61163	+	7.90837i	−0.205459	+	0.449892i
$310$	3.80270	+	1.62584i	0.215979	+	0.0923413i
$311$	−7.77000	+	2.28148i	−0.440596	+	0.129371i	−0.494504	−	0.869175i	$-0.664650\pi$
$311$	−7.77000	+	2.28148i	−0.440596	+	0.129371i	0.0539080	+	0.998546i	$0.482832\pi$
$312$	−9.78043	−	4.46657i	−0.553708	−	0.252870i
$313$	−30.0393	+	4.31899i	−1.69792	+	0.244124i	−0.922133	−	0.386872i	$-0.873555\pi$
$313$	−30.0393	+	4.31899i	−1.69792	+	0.244124i	−0.775786	+	0.630996i	$0.782646\pi$
$314$	1.75303	+	2.02311i	0.0989294	+	0.114171i
$315$	4.13510	−	15.4678i	0.232987	−	0.871511i
$316$	−9.94258	+	6.38971i	−0.559314	+	0.359449i
$317$	26.8501	+	3.86046i	1.50805	+	0.216825i	0.846222	−	0.532831i	$-0.178872\pi$
$317$	26.8501	+	3.86046i	1.50805	+	0.216825i	0.661828	+	0.749656i	$0.269781\pi$
$318$	7.81878	−	12.1663i	0.438456	−	0.682250i
$319$	13.5331	−	15.6181i	0.757711	−	0.874445i
$320$	−1.85108	+	1.25439i	−0.103479	+	0.0701226i
$321$	10.6223			0.592881
$322$	18.8764	+	10.1117i	1.05194	+	0.563501i
$323$		−	2.71674i		−	0.151163i
$324$	−10.7840	−	3.16647i	−0.599111	−	0.175915i
$325$	−12.5032	+	21.7135i	−0.693554	+	1.20445i
$326$	−6.78792	−	4.36233i	−0.375948	−	0.241607i
$327$	−2.13500	−	0.306967i	−0.118066	−	0.0169753i
$328$	1.44135	+	2.24278i	0.0795852	+	0.123837i
$329$	17.6701	+	38.6921i	0.974183	+	2.13316i
$330$	13.5616	−	0.330586i	0.746542	−	0.0181982i
$331$	1.21817	+	8.47258i	0.0669569	+	0.465695i	0.995522	+	0.0945265i	$0.0301337\pi$
$331$	1.21817	+	8.47258i	0.0669569	+	0.465695i	−0.928565	+	0.371169i	$0.878957\pi$
$332$	−7.94371	−	3.62777i	−0.435968	−	0.199100i
$333$	−2.42199	−	8.24855i	−0.132724	−	0.452018i
$334$	12.9481	−	3.80191i	0.708489	−	0.208031i
$335$	28.1923	−	13.7149i	1.54031	−	0.749326i
$336$	1.36344	+	9.48292i	0.0743816	+	0.517336i
$337$	−17.9010	+	15.5113i	−0.975130	+	0.844955i	−0.987920	−	0.154963i	$-0.950474\pi$
$337$	−17.9010	+	15.5113i	−0.975130	+	0.844955i	0.0127901	+	0.999918i	$0.495929\pi$
$338$	11.0178	−	5.03164i	0.599287	−	0.273685i
$339$	26.9136	−	17.2963i	1.46175	−	0.939408i
$340$	−1.70462	+	1.55138i	−0.0924460	+	0.0841356i
$341$	4.39942	+	2.82733i	0.238242	+	0.153109i
$342$	−3.19416	−	2.76776i	−0.172721	−	0.149663i
$343$	7.46935	−	25.4383i	0.403307	−	1.37354i
$344$	10.5545			0.569062
$345$	18.8565	+	13.1850i	1.01520	+	0.709858i
$346$	−16.2618			−0.874240
$347$	3.76003	−	12.8055i	0.201849	−	0.687435i	−0.794891	−	0.606753i	$-0.792472\pi$
$347$	3.76003	−	12.8055i	0.201849	−	0.687435i	0.996740	−	0.0806824i	$-0.0257100\pi$
$348$	11.8514	+	10.2693i	0.635302	+	0.550493i
$349$	−26.9613	−	17.3270i	−1.44321	−	0.927493i	−0.999510	−	0.0313170i	$-0.990030\pi$
$349$	−26.9613	−	17.3270i	−1.44321	−	0.927493i	−0.443698	−	0.896176i	$-0.646334\pi$
$350$	22.2992	−	1.08781i	1.19194	−	0.0581457i
$351$	12.6307	−	8.11727i	0.674178	−	0.433268i
$352$	−2.57201	+	1.17460i	−0.137088	+	0.0626062i
$353$	11.8927	−	10.3051i	0.632985	−	0.548484i	−0.278179	−	0.960529i	$-0.589731\pi$
$353$	11.8927	−	10.3051i	0.632985	−	0.548484i	0.911164	+	0.412045i	$0.135185\pi$
$354$	2.70371	+	18.8047i	0.143701	+	0.999460i
$355$	−5.86296	−	12.0519i	−0.311174	−	0.639647i
$356$	−1.17702	+	0.345603i	−0.0623817	+	0.0183169i
$357$	2.78219	+	9.47528i	0.147249	+	0.501485i
$358$	1.03799	+	0.474033i	0.0548593	+	0.0250534i
$359$	−0.876637	−	6.09714i	−0.0462671	−	0.321795i	−0.999790	−	0.0204754i	$-0.993482\pi$
$359$	−0.876637	−	6.09714i	−0.0462671	−	0.321795i	0.953523	−	0.301319i	$-0.0974271\pi$
$360$	0.0873829	+	3.58470i	0.00460548	+	0.188930i
$361$	−5.00721	−	10.9643i	−0.263538	−	0.577067i
$362$	4.45122	+	6.92624i	0.233951	+	0.364035i
$363$	−6.38212	−	0.917611i	−0.334974	−	0.0481621i
$364$	−18.8238	−	12.0973i	−0.986634	−	0.634071i
$365$	−1.28709	+	0.217192i	−0.0673694	+	0.0113683i
$366$	3.02641	+	0.888633i	0.158193	+	0.0464496i
$367$		−	8.40662i		−	0.438822i	−0.975633	−	0.219411i	$-0.929586\pi$
$367$		−	8.40662i		−	0.438822i	0.975633	−	0.219411i	$-0.0704136\pi$
$368$	−4.69426	−	0.981817i	−0.244705	−	0.0511808i
$369$	4.27521			0.222558
$370$	9.92349	−	6.72469i	0.515898	−	0.349600i
$371$	19.7091	−	22.7455i	1.02325	−	1.18089i
$372$	−2.14546	+	3.33840i	−0.111237	+	0.173088i
$373$	20.9647	+	3.01427i	1.08551	+	0.156073i	0.661767	−	0.749709i	$-0.269807\pi$
$373$	20.9647	+	3.01427i	1.08551	+	0.156073i	0.423743	+	0.905782i	$0.360716\pi$
$374$	−2.45188	+	1.57573i	−0.126784	+	0.0814788i
$375$	23.9303	+	1.67027i	1.23576	+	0.0862525i
$376$	−6.23834	−	7.19943i	−0.321718	−	0.371282i
$377$	−36.2530	+	5.21239i	−1.86712	+	0.268452i
$378$	−12.1691	−	5.55746i	−0.625913	−	0.285845i
$379$	−3.00851	+	0.883378i	−0.154537	+	0.0453761i	−0.358086	−	0.933689i	$-0.616571\pi$
$379$	−3.00851	+	0.883378i	−0.154537	+	0.0453761i	0.203549	+	0.979065i	$0.434752\pi$
$380$	2.31685	−	5.41891i	0.118852	−	0.277984i
$381$	−4.39353	+	9.62049i	−0.225087	+	0.492873i
$382$	−20.1782	+	2.90118i	−1.03240	+	0.148437i
$383$	−20.8576	+	18.0732i	−1.06577	+	0.923499i	−0.997247	−	0.0741504i	$-0.976376\pi$
$383$	−20.8576	+	18.0732i	−1.06577	+	0.923499i	−0.0685274	+	0.997649i	$0.521830\pi$
$384$	−0.891315	−	1.95171i	−0.0454847	−	0.0995976i
$385$	28.0334	+	3.33554i	1.42871	+	0.169995i
$386$	3.54069	−	24.6261i	0.180217	−	1.25343i
$387$	9.15050	−	14.2385i	0.465146	−	0.723781i
$388$	−3.82401	−	3.31352i	−0.194135	−	0.168219i
$389$	17.0188	+	4.99716i	0.862885	+	0.253366i	0.683086	−	0.730338i	$-0.260637\pi$
$389$	17.0188	+	4.99716i	0.862885	+	0.253366i	0.179799	+	0.983703i	$0.442455\pi$
$390$	−18.5483	−	15.2969i	−0.939230	−	0.774591i
$391$	−4.93351	−	0.313111i	−0.249498	−	0.0158347i
$392$			12.9376i			0.653447i
$393$	13.2462	−	45.1123i	0.668181	−	2.27562i
$394$	6.81640	−	7.86654i	0.343405	−	0.396311i
$395$	−25.1681	+	8.06123i	−1.26634	+	0.405604i
$396$	−0.645288	+	4.48807i	−0.0324269	+	0.225534i
$397$	1.19416	+	1.85815i	0.0599330	+	0.0932576i	0.869927	−	0.493181i	$-0.164166\pi$
$397$	1.19416	+	1.85815i	0.0599330	+	0.0932576i	−0.809994	+	0.586439i	$0.800530\pi$
$398$	−4.08316	+	1.86472i	−0.204670	+	0.0934698i
$399$	−16.5355	−	19.0829i	−0.827809	−	0.955342i
$400$	−4.72313	+	1.64074i	−0.236157	+	0.0820371i
$401$	5.22524	−	11.4417i	0.260936	−	0.571370i	−0.733138	−	0.680080i	$-0.761945\pi$
$401$	5.22524	−	11.4417i	0.260936	−	0.571370i	0.994073	+	0.108711i	$0.0346722\pi$
$402$	8.47533	+	28.8643i	0.422711	+	1.43962i
$403$	−2.61121	−	8.89298i	−0.130074	−	0.442991i
$404$	−3.35701	+	7.35082i	−0.167017	+	0.365717i
$405$	−21.4670	−	13.0680i	−1.06670	−	0.649354i
$406$	21.3712	+	24.6637i	1.06063	+	1.22404i
$407$	13.7883	−	6.29691i	0.683462	−	0.312126i
$408$	−1.19570	−	1.86055i	−0.0591961	−	0.0921109i
$409$	−0.369184	+	2.56773i	−0.0182550	+	0.126966i	−0.996911	−	0.0785388i	$-0.974975\pi$
$409$	−0.369184	+	2.56773i	−0.0182550	+	0.126966i	0.978656	+	0.205505i	$0.0658836\pi$
$410$	1.81840	+	5.67725i	0.0898044	+	0.280380i
$411$	11.6017	−	13.3891i	0.572269	−	0.660434i
$412$	1.14159	−	3.88789i	0.0562420	−	0.191543i
$413$			39.5365i			1.94546i
$414$	−5.39430	+	5.48151i	−0.265115	+	0.269402i
$415$	−15.0650	−	12.4242i	−0.739512	−	0.609882i
$416$	4.80823	+	1.41182i	0.235743	+	0.0692204i
$417$	−31.6877	−	27.4575i	−1.55175	−	1.34460i
$418$	4.02900	−	6.26925i	0.197065	−	0.306639i
$419$	−1.98268	+	13.7898i	−0.0968603	+	0.673678i	0.882315	+	0.470660i	$0.155984\pi$
$419$	−1.98268	+	13.7898i	−0.0968603	+	0.673678i	−0.979175	+	0.203018i	$0.934925\pi$
$420$	−2.53109	+	21.2724i	−0.123505	+	1.03799i
$421$	−8.60168	−	18.8351i	−0.419220	−	0.917965i	−0.994954	−	0.100328i	$-0.968011\pi$
$421$	−8.60168	−	18.8351i	−0.419220	−	0.917965i	0.575734	−	0.817637i	$-0.304716\pi$
$422$	15.9009	−	13.7782i	0.774042	−	0.670711i
$423$	−15.1208	+	2.17404i	−0.735197	+	0.105705i
$424$	−2.80004	+	6.13122i	−0.135982	+	0.297759i
$425$	−4.57826	+	2.36689i	−0.222078	+	0.114811i
$426$	12.3392	−	3.62310i	0.597834	−	0.175540i
$427$	5.97088	+	2.72681i	0.288951	+	0.131960i
$428$	−4.90036	+	0.704565i	−0.236868	+	0.0340565i
$429$	−19.9089	−	22.9761i	−0.961212	−	1.10930i
$430$	22.8000	+	6.09526i	1.09951	+	0.293940i
$431$	−14.8257	+	9.52791i	−0.714129	+	0.458943i	−0.846590	−	0.532245i	$-0.821348\pi$
$431$	−14.8257	+	9.52791i	−0.714129	+	0.458943i	0.132461	+	0.991188i	$0.457712\pi$
$432$	2.96561	+	0.426391i	0.142683	+	0.0205147i
$433$	−2.87236	+	4.46948i	−0.138037	+	0.214790i	−0.903389	−	0.428822i	$-0.858929\pi$
$433$	−2.87236	+	4.46948i	−0.138037	+	0.214790i	0.765352	+	0.643612i	$0.222565\pi$
$434$	−5.40813	+	6.24131i	−0.259599	+	0.299593i
$435$	19.6710	+	29.0280i	0.943150	+	1.39179i
$436$	1.00529			0.0481448
$437$	11.8072	−	4.51204i	0.564816	−	0.215840i
$438$		−	1.25248i		−	0.0598457i
$439$	20.3051	+	5.96212i	0.969110	+	0.284556i	0.727722	−	0.685872i	$-0.240579\pi$
$439$	20.3051	+	5.96212i	0.969110	+	0.284556i	0.241388	+	0.970429i	$0.422397\pi$
$440$	−6.23440	+	1.05203i	−0.297213	+	0.0501537i
$441$	17.4533	+	11.2165i	0.831108	+	0.534121i
$442$	5.11288	+	0.735121i	0.243195	+	0.0349661i
$443$	0.626481	+	0.974823i	0.0297650	+	0.0463152i	0.855817	−	0.517278i	$-0.173055\pi$
$443$	0.626481	+	0.974823i	0.0297650	+	0.0463152i	−0.826052	+	0.563594i	$0.809418\pi$
$444$	4.77827	+	10.4629i	0.226766	+	0.496549i
$445$	−2.74218	+	0.0668452i	−0.129992	+	0.00316877i
$446$	2.45102	+	17.0472i	0.116059	+	0.807210i
$447$	−1.03662	−	0.473407i	−0.0490303	−	0.0223914i
$448$	−1.25798	−	4.28428i	−0.0594339	−	0.202413i
$449$	−30.9405	+	9.08495i	−1.46017	+	0.428745i	−0.912891	−	0.408203i	$-0.866155\pi$
$449$	−30.9405	+	9.08495i	−1.46017	+	0.428745i	−0.547281	+	0.836949i	$0.684337\pi$
$450$	−1.88141	+	7.79416i	−0.0886903	+	0.367420i
$451$	1.07280	+	7.46145i	0.0505160	+	0.351346i
$452$	−11.2687	+	9.76439i	−0.530035	+	0.459278i
$453$	−16.4623	+	7.51809i	−0.773467	+	0.353230i
$454$	−9.91260	+	6.37044i	−0.465221	+	0.298980i
$455$	−33.6770	−	37.0034i	−1.57880	−	1.73475i
$456$	4.75727	+	3.05731i	0.222780	+	0.143172i
$457$	−0.141553	−	0.122656i	−0.00662156	−	0.00573761i	0.651544	−	0.758611i	$-0.274122\pi$
$457$	−0.141553	−	0.122656i	−0.00662156	−	0.00573761i	−0.658165	+	0.752874i	$0.728667\pi$
$458$	1.87422	−	6.38300i	0.0875764	−	0.298258i
$459$	3.08833			0.144151
$460$	−9.57356	−	4.83187i	−0.446370	−	0.225287i
$461$	12.4537			0.580028			0.290014	−	0.957022i	$-0.406340\pi$
$461$	12.4537			0.580028			0.290014	+	0.957022i	$0.406340\pi$
$462$	−7.63183	+	25.9916i	−0.355065	+	1.20924i
$463$	6.36485	+	5.51517i	0.295799	+	0.256312i	0.790098	−	0.612981i	$-0.210030\pi$
$463$	6.36485	+	5.51517i	0.295799	+	0.256312i	−0.494299	+	0.869292i	$0.664575\pi$
$464$	−6.14851	−	3.95141i	−0.285438	−	0.183440i
$465$	−6.56256	+	5.97262i	−0.304331	+	0.276974i
$466$	−13.8153	+	8.87853i	−0.639979	+	0.411290i
$467$	−34.1117	+	15.5783i	−1.57850	+	0.720878i	−0.995778	−	0.0917915i	$-0.970741\pi$
$467$	−34.1117	+	15.5783i	−1.57850	+	0.720878i	−0.582725	+	0.812670i	$0.698013\pi$
$468$	6.07321	−	5.26247i	0.280734	−	0.243258i
$469$	8.90958	+	61.9675i	0.411406	+	2.86139i
$470$	−9.31842	−	19.1549i	−0.429827	−	0.883550i
$471$	−5.51102	+	1.61818i	−0.253934	+	0.0745619i
$472$	−2.49459	−	8.49578i	−0.114823	−	0.391050i
$473$	27.1463	+	12.3973i	1.24819	+	0.570029i
$474$	−3.60887	−	25.1002i	−0.165761	−	1.15289i
$475$	8.13430	−	10.3680i	0.373227	−	0.475716i
$476$	−1.91198	−	4.18666i	−0.0876355	−	0.191895i
$477$	5.84369	+	9.09296i	0.267564	+	0.416338i
$478$	10.5682	+	1.51948i	0.483378	+	0.0694993i
$479$	−1.12834	−	0.725140i	−0.0515552	−	0.0331325i	0.514609	−	0.857425i	$-0.327937\pi$
$479$	−1.12834	−	0.725140i	−0.0515552	−	0.0331325i	−0.566165	+	0.824292i	$0.691573\pi$
$480$	−0.798310	−	4.73083i	−0.0364377	−	0.215932i
$481$	−25.7765	−	7.56867i	−1.17531	−	0.345102i
$482$		−	29.1416i		−	1.32736i
$483$	−36.5598	+	27.8286i	−1.66353	+	1.26624i
$484$	3.00510			0.136596
$485$	−6.34709	−	9.36627i	−0.288206	−	0.425300i
$486$	9.90585	−	11.4320i	0.449338	−	0.518564i
$487$	11.4246	−	17.7771i	0.517699	−	0.805556i	−0.479715	−	0.877424i	$-0.659260\pi$
$487$	11.4246	−	17.7771i	0.517699	−	0.805556i	0.997414	+	0.0718687i	$0.0228963\pi$
$488$	−1.45510	−	0.209212i	−0.0658694	−	0.00947059i
$489$	14.5642	−	9.35983i	0.658615	−	0.423266i
$490$	−7.47148	+	27.9478i	−0.337527	+	1.26256i
$491$	8.53136	+	9.84571i	0.385015	+	0.444331i	0.914865	−	0.403761i	$-0.132297\pi$
$491$	8.53136	+	9.84571i	0.385015	+	0.444331i	−0.529850	+	0.848091i	$0.677752\pi$
$492$	−5.66195	+	0.814065i	−0.255260	+	0.0367009i
$493$	−6.85290	−	3.12961i	−0.308639	−	0.140951i
$494$	−12.6727	+	3.72103i	−0.570170	+	0.167417i
$495$	−3.98583	+	9.32251i	−0.179150	+	0.419016i
$496$	0.768323	−	1.68239i	0.0344987	−	0.0755417i
$497$	26.4904	−	3.80874i	1.18825	−	0.170845i
$498$	14.1607	−	12.2703i	0.634556	−	0.549846i
$499$	3.85270	+	8.43623i	0.172470	+	0.377658i	0.976052	−	0.217537i	$-0.0698023\pi$
$499$	3.85270	+	8.43623i	0.172470	+	0.377658i	−0.803582	+	0.595195i	$0.797075\pi$
$500$	−11.1505	+	0.816727i	−0.498664	+	0.0365251i
$501$	−4.12063	+	28.6596i	−0.184096	+	1.28042i
$502$	−3.85382	+	5.99667i	−0.172005	+	0.267644i
$503$	10.3562	+	8.97373i	0.461762	+	0.400119i	0.854434	−	0.519559i	$-0.173904\pi$
$503$	10.3562	+	8.97373i	0.461762	+	0.400119i	−0.392672	+	0.919678i	$0.628449\pi$
$504$	−6.87029	−	2.01730i	−0.306027	−	0.0898576i
$505$	−11.4969	+	13.9406i	−0.511607	+	0.620349i
$506$	−10.9204	−	8.03910i	−0.485472	−	0.357381i
$507$			25.9882i			1.15418i
$508$	1.38874	−	4.72960i	0.0616152	−	0.209842i
$509$	4.20288	−	4.85039i	0.186290	−	0.214990i	−0.654921	−	0.755697i	$-0.727298\pi$
$509$	4.20288	−	4.85039i	0.186290	−	0.214990i	0.841210	+	0.540708i	$0.181844\pi$
$510$	−1.50849	−	4.70969i	−0.0667972	−	0.208549i
$511$	0.370943	−	2.57997i	0.0164096	−	0.114131i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	−7.18300	+	3.28037i	−0.317137	+	0.144832i
$514$	−8.74708	−	10.0947i	−0.385817	−	0.445257i
$515$	4.71133	−	7.73938i	0.207606	−	0.341038i
$516$	−9.40741	+	20.5994i	−0.414138	+	0.906836i
$517$	−7.58864	−	25.8445i	−0.333748	−	1.13664i
$518$	6.74392	+	22.9677i	0.296311	+	1.00914i
$519$	14.4944	−	31.7383i	0.636233	−	1.39316i
$520$	9.57144	+	5.82659i	0.419735	+	0.255513i
$521$	16.4281	+	18.9590i	0.719727	+	0.830609i	0.991274	−	0.131816i	$-0.0420809\pi$
$521$	16.4281	+	18.9590i	0.719727	+	0.830609i	−0.271548	+	0.962425i	$0.587535\pi$
$522$	−10.6612	+	4.86880i	−0.466628	+	0.213102i
$523$	−3.65423	−	5.68609i	−0.159788	−	0.248635i	0.752123	−	0.659023i	$-0.229030\pi$
$523$	−3.65423	−	5.68609i	−0.159788	−	0.248635i	−0.911911	+	0.410387i	$0.865394\pi$
$524$	−3.11856	+	21.6901i	−0.136235	+	0.947536i
$525$	−17.7526	+	44.4912i	−0.774785	+	1.94175i
$526$	3.80605	−	4.39241i	0.165952	−	0.191518i
$527$	0.537111	−	1.82923i	0.0233969	−	0.0796826i
$528$		−	6.06674i		−	0.264021i
$529$	−6.83292	−	21.9616i	−0.297083	−	0.954852i
$530$	−9.58945	+	11.6277i	−0.416539	+	0.505074i
$531$	−13.6239	−	4.00033i	−0.591225	−	0.173599i
$532$	8.89399	+	7.70668i	0.385603	+	0.334127i
$533$	7.22292	−	11.2391i	0.312859	−	0.486818i
$534$	0.374576	−	2.60523i	0.0162095	−	0.112739i
$535$	−10.9927	−	1.30796i	−0.475255	−	0.0565480i
$536$	−5.82442	−	12.7537i	−0.251577	−	0.550876i
$537$	−1.85035	+	1.60333i	−0.0798483	+	0.0691890i
$538$	1.98760	−	0.285774i	0.0856916	−	0.0123206i
$539$	−15.1964	+	33.2756i	−0.654557	+	1.43328i
$540$	6.16010	+	2.63374i	0.265088	+	0.113338i
$541$	25.0109	−	7.34386i	1.07530	−	0.315737i	0.304304	−	0.952575i	$-0.401576\pi$
$541$	25.0109	−	7.34386i	1.07530	−	0.315737i	0.770998	+	0.636838i	$0.219758\pi$
$542$	2.85080	+	1.30191i	0.122452	+	0.0559220i
$543$	−17.4854	+	2.51402i	−0.750371	+	0.107887i
$544$	0.675016	+	0.779010i	0.0289411	+	0.0333998i
$545$	2.17164	+	0.580558i	0.0930228	+	0.0248684i
$546$	40.3883	−	25.9560i	1.72846	−	1.11081i
$547$	−19.2693	−	2.77050i	−0.823894	−	0.118458i	−0.282543	−	0.959255i	$-0.591178\pi$
$547$	−19.2693	−	2.77050i	−0.823894	−	0.118458i	−0.541351	+	0.840797i	$0.682087\pi$
$548$	−4.46408	+	6.94625i	−0.190696	+	0.296729i
$549$	−1.54377	+	1.78160i	−0.0658865	+	0.0760370i
$550$	−14.0751	−	1.32777i	−0.600166	−	0.0566163i
$551$	19.2631			0.820635
$552$	6.10028	−	8.28670i	0.259645	−	0.352706i
$553$		−	52.7726i		−	2.24412i
$554$	15.8957	+	4.66740i	0.675344	+	0.198299i
$555$	4.27967	+	25.3616i	0.181662	+	1.07654i
$556$	16.4396	+	10.5651i	0.697193	+	0.448059i
$557$	−5.91272	−	0.850120i	−0.250530	−	0.0360207i	0.0159057	−	0.999873i	$-0.494937\pi$
$557$	−5.91272	−	0.850120i	−0.250530	−	0.0360207i	−0.266436	+	0.963853i	$0.585846\pi$
$558$	−1.60349	−	2.49509i	−0.0678813	−	0.105625i
$559$	−21.9718	−	48.1114i	−0.929306	−	2.03490i
$560$	−0.243313	−	9.98142i	−0.0102819	−	0.421792i
$561$	−0.889961	−	6.18981i	−0.0375742	−	0.261334i
$562$	−9.43859	−	4.31046i	−0.398143	−	0.181826i
$563$	−11.0799	−	37.7345i	−0.466961	−	1.59032i	−0.770459	−	0.637490i	$-0.779973\pi$
$563$	−11.0799	−	37.7345i	−0.466961	−	1.59032i	0.303498	−	0.952832i	$-0.401845\pi$
$564$	19.6115	−	5.75846i	0.825793	−	0.242475i
$565$	−29.9817	+	14.5854i	−1.26134	+	0.613612i
$566$	3.97816	+	27.6687i	0.167215	+	1.16300i
$567$	37.9273	−	32.8642i	1.59280	−	1.38017i
$568$	−5.45206	+	2.48987i	−0.228763	+	0.104473i
$569$	−17.0762	+	10.9742i	−0.715870	+	0.460062i	−0.847198	−	0.531277i	$-0.821712\pi$
$569$	−17.0762	+	10.9742i	−0.715870	+	0.460062i	0.131328	+	0.991339i	$0.458076\pi$
$570$	8.51109	+	9.35176i	0.356490	+	0.391702i
$571$	38.0729	+	24.4680i	1.59330	+	1.02395i	0.970353	+	0.241691i	$0.0777019\pi$
$571$	38.0729	+	24.4680i	1.59330	+	1.02395i	0.622949	+	0.782263i	$0.285934\pi$
$572$	10.7085	+	9.27895i	0.447744	+	0.387972i
$573$	12.3228	−	41.9677i	0.514794	−	1.75323i
$574$	−11.9041			−0.496867
$575$	−17.8905	−	15.9666i	−0.746083	−	0.665852i
$576$	1.60360			0.0668168
$577$	3.02905	−	10.3160i	0.126101	−	0.429461i	−0.872106	−	0.489317i	$-0.837246\pi$
$577$	3.02905	−	10.3160i	0.126101	−	0.429461i	0.998207	+	0.0598564i	$0.0190643\pi$
$578$	−12.0448	−	10.4368i	−0.500996	−	0.434115i
$579$	44.9070	+	28.8600i	1.86627	+	1.19938i
$580$	−11.0001	−	12.0866i	−0.456755	−	0.501870i
$581$	32.8036	−	21.0816i	1.36092	−	0.874611i
$582$	9.87543	−	4.50996i	0.409350	−	0.186944i
$583$	−14.4034	+	12.4806i	−0.596529	+	0.516895i
$584$	0.0830751	+	0.577800i	0.00343767	+	0.0239095i
$585$	16.1585	−	7.86072i	0.668070	−	0.325001i
$586$	23.2036	−	6.81320i	0.958533	−	0.281451i
$587$	−0.463798	−	1.57955i	−0.0191430	−	0.0651951i	0.949368	−	0.314167i	$-0.101725\pi$
$587$	−0.463798	−	1.57955i	−0.0191430	−	0.0651951i	−0.968511	+	0.248972i	$0.919907\pi$
$588$	−25.2504	−	11.5315i	−1.04131	−	0.475549i
$589$	0.693736	+	4.82504i	0.0285849	+	0.198812i
$590$	−0.482493	−	19.7933i	−0.0198639	−	0.814876i
$591$	9.27763	+	20.3152i	0.381631	+	0.835655i
$592$	−2.89833	−	4.50989i	−0.119121	−	0.185355i
$593$	28.9509	+	4.16251i	1.18887	+	0.170934i	0.708229	−	0.705983i	$-0.249494\pi$
$593$	28.9509	+	4.16251i	1.18887	+	0.170934i	0.480643	+	0.876917i	$0.340403\pi$
$594$	7.12675	+	4.58008i	0.292414	+	0.187923i
$595$	−1.71247	−	10.1482i	−0.0702046	−	0.416036i
$596$	0.509619	+	0.149638i	0.0208748	+	0.00612940i
$597$		−	9.63119i		−	0.394178i
$598$	5.29672	+	23.4420i	0.216599	+	0.958616i
$599$	25.0823			1.02483			0.512417	−	0.858737i	$-0.328750\pi$
$599$	25.0823			1.02483			0.512417	+	0.858737i	$0.328750\pi$
$600$	1.00755	−	10.6806i	0.0411329	−	0.436033i
$601$	18.0593	−	20.8416i	0.736656	−	0.850146i	−0.256548	−	0.966531i	$-0.582585\pi$
$601$	18.0593	−	20.8416i	0.736656	−	0.850146i	0.993204	+	0.116385i	$0.0371307\pi$
$602$	−25.4791	+	39.6463i	−1.03845	+	1.61586i
$603$	−22.2548	−	3.19976i	−0.906287	−	0.130304i
$604$	7.09583	−	4.56021i	0.288725	−	0.185552i
$605$	6.49164	+	1.73545i	0.263923	+	0.0705562i
$606$	−11.3545	−	13.1038i	−0.461245	−	0.532305i
$607$	27.7696	−	3.99267i	1.12714	−	0.162058i	0.446573	−	0.894747i	$-0.352644\pi$
$607$	27.7696	−	3.99267i	1.12714	−	0.162058i	0.680563	+	0.732690i	$0.261735\pi$
$608$	−2.39744	−	1.09488i	−0.0972291	−	0.0444030i
$609$	−67.1847	+	19.7272i	−2.72246	+	0.799387i
$610$	−3.02250	−	1.29227i	−0.122377	−	0.0523223i
$611$	−19.8311	+	43.4240i	−0.802279	+	1.75675i
$612$	1.63613	−	0.235241i	0.0661368	−	0.00950904i
$613$	−12.0625	+	10.4522i	−0.487198	+	0.422159i	−0.863509	−	0.504334i	$-0.831738\pi$
$613$	−12.0625	+	10.4522i	−0.487198	+	0.422159i	0.376311	+	0.926494i	$0.377193\pi$
$614$	−0.608205	−	1.33178i	−0.0245451	−	0.0537464i
$615$	−12.7011	−	1.51124i	−0.512158	−	0.0609389i
$616$	1.79677	−	12.4968i	0.0723940	−	0.503511i
$617$	−5.67040	+	8.82331i	−0.228282	+	0.355213i	−0.936432	−	0.350848i	$-0.885893\pi$
$617$	−5.67040	+	8.82331i	−0.228282	+	0.355213i	0.708151	+	0.706061i	$0.249530\pi$
$618$	6.57052	+	5.69338i	0.264305	+	0.229021i
$619$	−3.08043	−	0.904497i	−0.123813	−	0.0363548i	0.219239	−	0.975671i	$-0.429643\pi$
$619$	−3.08043	−	0.904497i	−0.123813	−	0.0363548i	−0.343052	+	0.939316i	$0.611461\pi$
$620$	2.63132	−	3.19061i	0.105676	−	0.128138i
$621$	5.12919	+	13.4222i	0.205827	+	0.538614i
$622$			8.09803i			0.324701i
$623$	1.54317	−	5.25555i	0.0618258	−	0.210559i
$624$	−7.04111	+	8.12588i	−0.281870	+	0.325295i
$625$	−24.5590	−	4.67512i	−0.982359	−	0.187005i
$626$	−4.31899	+	30.0393i	−0.172622	+	1.20061i
$627$	8.64463	+	13.4513i	0.345233	+	0.537194i
$628$	2.43505	−	1.11205i	0.0971689	−	0.0443755i
$629$	−3.61871	−	4.17621i	−0.144287	−	0.166516i
$630$	−13.6762	−	8.32538i	−0.544875	−	0.331691i
$631$	−2.07634	+	4.54655i	−0.0826577	+	0.180995i	−0.946448	−	0.322856i	$-0.895357\pi$
$631$	−2.07634	+	4.54655i	−0.0826577	+	0.180995i	0.863790	+	0.503852i	$0.168084\pi$
$632$	3.32973	+	11.3400i	0.132450	+	0.451082i
$633$	12.7183	+	43.3145i	0.505507	+	1.72160i
$634$	11.2686	−	24.6748i	0.447534	−	0.979963i
$635$	5.73131	−	9.41491i	0.227440	−	0.373619i
$636$	−9.47064	−	10.9297i	−0.375535	−	0.433391i
$637$	58.9742	−	26.9326i	2.33664	−	1.06711i
$638$	−11.1727	−	17.3851i	−0.442332	−	0.688282i
$639$	−1.36786	+	9.51368i	−0.0541117	+	0.376355i
$640$	0.682070	+	2.12950i	0.0269612	+	0.0841760i
$641$	10.8861	−	12.5633i	0.429976	−	0.496219i	−0.498874	−	0.866674i	$-0.666253\pi$
$641$	10.8861	−	12.5633i	0.429976	−	0.496219i	0.928850	+	0.370456i	$0.120798\pi$
$642$	2.99266	−	10.1921i	0.118111	−	0.402248i
$643$			37.1232i			1.46400i	0.681306	+	0.731999i	$0.261412\pi$
$643$			37.1232i			1.46400i	−0.681306	+	0.731999i	$0.738588\pi$
$644$	15.0202	−	15.2630i	0.591877	−	0.601446i
$645$	−32.2181	+	39.0661i	−1.26859	+	1.53823i
$646$	−2.60669	−	0.765393i	−0.102559	−	0.0301140i
$647$	32.0100	+	27.7369i	1.25844	+	1.09045i	0.991952	+	0.126611i	$0.0404100\pi$
$647$	32.0100	+	27.7369i	1.25844	+	1.09045i	0.266492	+	0.963837i	$0.414135\pi$
$648$	−6.07641	+	9.45507i	−0.238704	+	0.371430i
$649$	3.56302	−	24.7813i	0.139861	−	0.972753i
$650$	17.3114	+	18.1142i	0.679010	+	0.710496i
$651$	−7.36087	−	16.1181i	−0.288495	−	0.631717i
$652$	−6.09801	+	5.28395i	−0.238816	+	0.206936i
$653$	−3.89702	+	0.560307i	−0.152502	+	0.0219265i	−0.218143	−	0.975917i	$-0.570000\pi$
$653$	−3.89702	+	0.560307i	−0.152502	+	0.0219265i	0.0656408	+	0.997843i	$0.479091\pi$
$654$	−0.896032	+	1.96204i	−0.0350376	+	0.0767217i
$655$	−19.2628	+	45.0541i	−0.752660	+	1.76041i
$656$	2.55801	−	0.751099i	0.0998735	−	0.0293255i
$657$	0.851497	+	0.388866i	0.0332201	+	0.0151711i
$658$	42.1030	−	6.05350i	1.64135	−	0.235990i
$659$	−30.7016	−	35.4316i	−1.19597	−	1.38022i	−0.906053	−	0.423165i	$-0.860919\pi$
$659$	−30.7016	−	35.4316i	−1.19597	−	1.38022i	−0.289913	−	0.957053i	$-0.593626\pi$
$660$	3.50355	−	13.1054i	0.136376	−	0.510127i
$661$	−16.9223	+	10.8753i	−0.658201	+	0.423000i	−0.826655	−	0.562709i	$-0.809759\pi$
$661$	−16.9223	+	10.8753i	−0.658201	+	0.423000i	0.168453	+	0.985710i	$0.446123\pi$
$662$	8.47258	+	1.21817i	0.329296	+	0.0473456i
$663$	−5.99193	+	9.32362i	−0.232707	+	0.362099i
$664$	−5.71882	+	6.59987i	−0.221933	+	0.256125i
$665$	14.7622	+	21.7843i	0.572455	+	0.844760i
$666$	−8.59678			−0.333119
$667$	2.22012	−	34.9812i	0.0859633	−	1.35448i
$668$		−	13.4947i		−	0.522127i
$669$	−35.4558	−	10.4108i	−1.37080	−	0.402504i
$670$	−5.21667	−	30.9143i	−0.201538	−	1.19432i
$671$	−3.49679	−	2.24725i	−0.134992	−	0.0867542i
$672$	9.48292	+	1.36344i	0.365812	+	0.0525958i
$673$	−24.9339	−	38.7979i	−0.961132	−	1.49555i	−0.865974	−	0.500089i	$-0.833301\pi$
$673$	−24.9339	−	38.7979i	−0.961132	−	1.49555i	−0.0951582	−	0.995462i	$-0.530336\pi$
$674$	9.83970	+	21.5459i	0.379011	+	0.829918i
$675$	11.7861	+	9.24689i	0.453647	+	0.355913i
$676$	−1.72376	−	11.9890i	−0.0662986	−	0.461117i
$677$	18.3180	+	8.36555i	0.704018	+	0.321514i	0.735058	−	0.678004i	$-0.237155\pi$
$677$	18.3180	+	8.36555i	0.704018	+	0.321514i	−0.0310404	+	0.999518i	$0.509882\pi$
$678$	−9.01326	−	30.6964i	−0.346152	−	1.17889i
$679$	21.6780	−	6.36524i	0.831925	−	0.244275i
$680$	1.00829	+	2.07265i	0.0386663	+	0.0794823i
$681$	−3.59799	−	25.0246i	−0.137875	−	0.958943i
$682$	3.95227	−	3.42466i	0.151340	−	0.131137i
$683$	−18.2912	+	8.35330i	−0.699893	+	0.319630i	−0.733390	−	0.679809i	$-0.762063\pi$
$683$	−18.2912	+	8.35330i	−0.699893	+	0.319630i	0.0334969	+	0.999439i	$0.489336\pi$
$684$	−3.55554	+	2.28501i	−0.135950	+	0.0873695i
$685$	−13.6548	+	12.4273i	−0.521724	+	0.474823i
$686$	−22.3035	−	14.3336i	−0.851551	−	0.547259i
$687$	10.7872	+	9.34718i	0.411558	+	0.356617i
$688$	2.97356	−	10.1270i	0.113366	−	0.386088i
$689$	33.7773			1.28681
$690$	17.9634	−	14.3781i	0.683857	−	0.547364i
$691$	0.192592			0.00732653			0.00366326	−	0.999993i	$-0.498834\pi$
$691$	0.192592			0.00732653			0.00366326	+	0.999993i	$0.498834\pi$
$692$	−4.58148	+	15.6031i	−0.174162	+	0.593140i
$693$	−15.3009	−	13.2583i	−0.581234	−	0.503642i
$694$	−11.2275	−	7.21545i	−0.426189	−	0.273895i
$695$	29.4115	+	32.3166i	1.11564	+	1.22584i
$696$	13.1923	−	8.47815i	0.500051	−	0.321363i
$697$	2.49972	−	1.14158i	0.0946836	−	0.0432406i
$698$	−24.2210	+	20.9876i	−0.916779	+	0.794394i
$699$	−5.01454	−	34.8769i	−0.189667	−	1.31917i
$700$	5.23868	−	21.7024i	0.198003	−	0.820275i
$701$	−5.12787	+	1.50568i	−0.193677	+	0.0568687i	−0.377133	−	0.926159i	$-0.623090\pi$
$701$	−5.12787	+	1.50568i	−0.193677	+	0.0568687i	0.183455	+	0.983028i	$0.441272\pi$
$702$	−4.22998	−	14.4060i	−0.159650	−	0.543719i
$703$	12.8525	+	5.86954i	0.484741	+	0.221374i
$704$	0.402399	+	2.79874i	0.0151660	+	0.105482i
$705$	45.6904	−	1.11378i	1.72080	−	0.0419473i
$706$	−6.53710	−	14.3142i	−0.246027	−	0.538724i
$707$	−19.5081	−	30.3552i	−0.733678	−	1.14162i
$708$	18.8047	+	2.70371i	0.706725	+	0.101612i
$709$	−16.4950	−	10.6007i	−0.619482	−	0.398117i	0.192920	−	0.981214i	$-0.438204\pi$
$709$	−16.4950	−	10.6007i	−0.619482	−	0.398117i	−0.812402	+	0.583098i	$0.801841\pi$
$710$	−13.2155	+	2.23006i	−0.495968	+	0.0836928i
$711$	18.1849	+	5.33957i	0.681987	+	0.200249i
$712$			1.22671i			0.0459727i
$713$	8.84209	−	0.703706i	0.331139	−	0.0263540i
$714$	9.87530			0.369574
$715$	17.7739	+	26.2286i	0.664707	+	0.980895i
$716$	0.747266	−	0.862391i	0.0279266	−	0.0322291i
$717$	−12.3852	+	19.2717i	−0.462532	+	0.719714i
$718$	−6.09714	−	0.876637i	−0.227543	−	0.0327158i
$719$	2.92170	−	1.87767i	0.108961	−	0.0700251i	−0.485025	−	0.874500i	$-0.661190\pi$
$719$	2.92170	−	1.87767i	0.108961	−	0.0700251i	0.593986	+	0.804475i	$0.297553\pi$
$720$	3.46411	+	0.926083i	0.129100	+	0.0345131i
$721$	11.8483	+	13.6737i	0.441256	+	0.509236i
$722$	−11.9308	+	1.71539i	−0.444020	+	0.0638404i
$723$	56.8758	+	25.9743i	2.11523	+	0.965995i
$724$	7.89973	−	2.31957i	0.293591	−	0.0862061i
$725$	−16.7825	−	32.4622i	−0.623285	−	1.20562i
$726$	−2.67849	+	5.86508i	−0.0994082	+	0.217674i
$727$	−8.07215	+	1.16060i	−0.299379	+	0.0430443i	−0.290368	−	0.956915i	$-0.593778\pi$
$727$	−8.07215	+	1.16060i	−0.299379	+	0.0430443i	−0.00901164	+	0.999959i	$0.502869\pi$
$728$	−16.9105	+	14.6531i	−0.626747	+	0.543079i
$729$	−0.524277	−	1.14801i	−0.0194177	−	0.0425188i
$730$	−0.154221	+	1.29614i	−0.00570798	+	0.0479724i
$731$	1.54830	−	10.7686i	0.0572659	−	0.398293i
$732$	1.70528	−	2.65346i	0.0630288	−	0.0980747i
$733$	38.7239	+	33.5545i	1.43030	+	1.23936i	0.926900	+	0.375309i	$0.122463\pi$
$733$	38.7239	+	33.5545i	1.43030	+	1.23936i	0.503401	+	0.864053i	$0.332082\pi$
$734$	−8.06609	−	2.36842i	−0.297725	−	0.0874199i
$735$	−47.8866	−	39.4925i	−1.76632	−	1.45670i
$736$	−2.26457	+	4.22750i	−0.0834732	+	0.155828i
$737$		−	39.6440i		−	1.46030i
$738$	1.20446	−	4.10203i	0.0443370	−	0.150998i
$739$	−14.9540	+	17.2579i	−0.550093	+	0.634841i	−0.960905	−	0.276879i	$-0.910700\pi$
$739$	−14.9540	+	17.2579i	−0.550093	+	0.634841i	0.410812	+	0.911720i	$0.365245\pi$
$740$	−3.65652	−	11.4161i	−0.134416	−	0.419664i
$741$	4.03297	−	28.0499i	0.148155	−	1.03044i
$742$	−16.2715	−	25.3189i	−0.597344	−	0.929485i
$743$	42.9514	−	19.6153i	1.57574	−	0.719614i	0.580242	−	0.814444i	$-0.302958\pi$
$743$	42.9514	−	19.6153i	1.57574	−	0.719614i	0.995494	+	0.0948296i	$0.0302306\pi$
$744$	2.59872	+	2.99908i	0.0952738	+	0.109952i
$745$	1.01447	+	0.617554i	0.0371672	+	0.0226254i
$746$	8.79861	−	19.2663i	0.322140	−	0.705388i
$747$	3.94541	+	13.4368i	0.144355	+	0.491627i
$748$	0.821124	+	2.79649i	0.0300233	+	0.102250i
$749$	9.18311	−	20.1082i	0.335543	−	0.734738i
$750$	8.34457	−	22.4904i	0.304700	−	0.821234i
$751$	12.3052	+	14.2009i	0.449022	+	0.518199i	0.934458	−	0.356073i	$-0.115885\pi$
$751$	12.3052	+	14.2009i	0.449022	+	0.518199i	−0.485436	+	0.874272i	$0.661339\pi$
$752$	−8.66535	+	3.95733i	−0.315993	+	0.144309i
$753$	−8.26877	−	12.8665i	−0.301331	−	0.468880i
$754$	−5.21239	+	36.2530i	−0.189824	+	1.32026i
$755$	17.9620	−	5.75315i	0.653703	−	0.209378i
$756$	−8.76079	+	10.1105i	−0.318627	+	0.367715i
$757$	−8.67318	+	29.5381i	−0.315232	+	1.07358i	0.637671	+	0.770308i	$0.279898\pi$
$757$	−8.67318	+	29.5381i	−0.315232	+	1.07358i	−0.952904	+	0.303274i	$0.901920\pi$
$758$			3.13552i			0.113887i
$759$	25.4235	−	14.1481i	0.922814	−	0.513543i
$760$	−4.54668	−	3.74968i	−0.164925	−	0.136015i
$761$	8.87635	+	2.60633i	0.321768	+	0.0944795i	0.438628	−	0.898669i	$-0.355465\pi$
$761$	8.87635	+	2.60633i	0.321768	+	0.0944795i	−0.116860	+	0.993148i	$0.537283\pi$
$762$	7.99299	+	6.92597i	0.289556	+	0.250901i
$763$	−2.42682	+	3.77621i	−0.0878568	+	0.136708i
$764$	−2.90118	+	20.1782i	−0.104961	+	0.730020i
$765$	3.67024	+	0.436702i	0.132698	+	0.0157890i
$766$	11.4649	+	25.1046i	0.414242	+	0.907064i
$767$	−33.5338	+	29.0572i	−1.21084	+	1.04920i
$768$	−2.12376	+	0.305351i	−0.0766346	+	0.0110184i
$769$	−2.29563	+	5.02674i	−0.0827827	+	0.181269i	−0.946497	−	0.322713i	$-0.895405\pi$
$769$	−2.29563	+	5.02674i	−0.0827827	+	0.181269i	0.863714	+	0.503982i	$0.168132\pi$

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.281733 - 0.959493i) q^{2} +(1.62154 + 1.40507i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-1.50506 - 1.65372i) q^{5} +(1.80499 - 1.16000i) q^{6} +(4.06165 - 1.85489i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(0.228216 + 1.58728i) q^{9} +O(q^{10})\)	\(q+(0.281733 - 0.959493i) q^{2} +(1.62154 + 1.40507i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-1.50506 - 1.65372i) q^{5} +(1.80499 - 1.16000i) q^{6} +(4.06165 - 1.85489i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(0.228216 + 1.58728i) q^{9} +(-2.01076 + 0.978188i) q^{10} +(-2.71299 + 0.796606i) q^{11} +(-0.604486 - 2.05869i) q^{12} +(4.55837 + 2.08174i) q^{13} +(-0.635457 - 4.41970i) q^{14} +(-0.116917 - 4.79628i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.557281 + 0.867146i) q^{17} +(1.58728 + 0.228216i) q^{18} +(-2.21722 - 1.42492i) q^{19} +(0.372068 + 2.20490i) q^{20} +(9.19236 + 2.69912i) q^{21} +2.82752i q^{22} +(-2.84316 + 3.86218i) q^{23} -2.14560 q^{24} +(-0.469587 + 4.97790i) q^{25} +(3.28165 - 3.78723i) q^{26} +(1.61982 - 2.52049i) q^{27} +(-4.41970 - 0.635457i) q^{28} +(-6.14851 + 3.95141i) q^{29} +(-4.63494 - 1.23909i) q^{30} +(-1.21119 - 1.39778i) q^{31} +(0.989821 - 0.142315i) q^{32} +(-5.51850 - 2.52021i) q^{33} +(0.989025 - 0.290404i) q^{34} +(-9.18049 - 3.92511i) q^{35} +(0.666161 - 1.45869i) q^{36} +(-5.30635 + 0.762938i) q^{37} +(-1.99187 + 1.72596i) q^{38} +(4.46657 + 9.78043i) q^{39} +(2.22041 + 0.264194i) q^{40} +(0.379411 - 2.63886i) q^{41} +(5.17957 - 8.05957i) q^{42} +(-7.97658 - 6.91175i) q^{43} +(2.71299 + 0.796606i) q^{44} +(2.28144 - 2.76636i) q^{45} +(2.90473 + 3.81609i) q^{46} +9.52621i q^{47} +(-0.604486 + 2.05869i) q^{48} +(8.47232 - 9.77757i) q^{49} +(4.64396 + 1.85300i) q^{50} +(-0.314749 + 2.18913i) q^{51} +(-2.70927 - 4.21571i) q^{52} +(6.13122 - 2.80004i) q^{53} +(-1.96204 - 2.26431i) q^{54} +(5.40058 + 3.28759i) q^{55} +(-1.85489 + 4.06165i) q^{56} +(-1.59319 - 5.42592i) q^{57} +(2.05911 + 7.01270i) q^{58} +(-3.67827 + 8.05429i) q^{59} +(-2.49471 + 4.09810i) q^{60} +(0.962688 + 1.11100i) q^{61} +(-1.68239 + 0.768323i) q^{62} +(3.87117 + 6.02365i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-3.41800 - 10.6714i) q^{65} +(-3.97287 + 4.58494i) q^{66} +(-3.95010 + 13.4528i) q^{67} -1.03078i q^{68} +(-10.0369 + 2.26784i) q^{69} +(-6.35256 + 7.70279i) q^{70} +(5.75091 + 1.68862i) q^{71} +(-1.21192 - 1.05014i) q^{72} +(0.315595 - 0.491075i) q^{73} +(-0.762938 + 5.30635i) q^{74} +(-7.75575 + 7.41205i) q^{75} +(1.09488 + 2.39744i) q^{76} +(-9.54159 + 8.26783i) q^{77} +(10.6426 - 1.53018i) q^{78} +(4.90969 - 10.7507i) q^{79} +(0.879053 - 2.05603i) q^{80} +(10.7840 - 3.16647i) q^{81} +(-2.42508 - 1.10750i) q^{82} +(8.64400 - 1.24282i) q^{83} +(-6.27385 - 7.24041i) q^{84} +(0.595276 - 2.22669i) q^{85} +(-8.87904 + 5.70621i) q^{86} +(-15.5221 - 2.23173i) q^{87} +(1.52868 - 2.37867i) q^{88} +(0.803321 - 0.927082i) q^{89} +(-2.01155 - 2.96840i) q^{90} +22.3759 q^{91} +(4.47987 - 1.71195i) q^{92} -3.96836i q^{93} +(9.14033 + 2.68384i) q^{94} +(0.980629 + 5.81126i) q^{95} +(1.80499 + 1.16000i) q^{96} +(5.00839 + 0.720098i) q^{97} +(-6.99459 - 10.8838i) q^{98} +(-1.88359 - 4.12448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

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