LMFDB - Embedded newform 309.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,2,Mod(1,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("309.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	309.a (trivial)

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:	yes
Analytic conductor:	$2.46737742246$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.81509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 $ x^5 - x^4 - 5x^3 + 3x^2 + 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.21568$ of defining polynomial
Character	$\chi$	$=$	309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32829 q^{2} -1.00000 q^{3} +3.42092 q^{4} -0.354824 q^{5} +2.32829 q^{6} -0.931655 q^{7} -3.30831 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.32829 q^{2} -1.00000 q^{3} +3.42092 q^{4} -0.354824 q^{5} +2.32829 q^{6} -0.931655 q^{7} -3.30831 q^{8} +1.00000 q^{9} +0.826132 q^{10} -4.43135 q^{11} -3.42092 q^{12} +6.77349 q^{13} +2.16916 q^{14} +0.354824 q^{15} +0.860851 q^{16} +5.16058 q^{17} -2.32829 q^{18} -4.75779 q^{19} -1.21382 q^{20} +0.931655 q^{21} +10.3175 q^{22} -8.16058 q^{23} +3.30831 q^{24} -4.87410 q^{25} -15.7706 q^{26} -1.00000 q^{27} -3.18712 q^{28} -7.58823 q^{29} -0.826132 q^{30} -1.21382 q^{31} +4.61231 q^{32} +4.43135 q^{33} -12.0153 q^{34} +0.330574 q^{35} +3.42092 q^{36} -4.88180 q^{37} +11.0775 q^{38} -6.77349 q^{39} +1.17387 q^{40} -1.85513 q^{41} -2.16916 q^{42} -3.76962 q^{43} -15.1593 q^{44} -0.354824 q^{45} +19.0002 q^{46} +3.04427 q^{47} -0.860851 q^{48} -6.13202 q^{49} +11.3483 q^{50} -5.16058 q^{51} +23.1716 q^{52} -6.04366 q^{53} +2.32829 q^{54} +1.57235 q^{55} +3.08220 q^{56} +4.75779 q^{57} +17.6676 q^{58} -0.951861 q^{59} +1.21382 q^{60} -2.03608 q^{61} +2.82613 q^{62} -0.931655 q^{63} -12.4605 q^{64} -2.40340 q^{65} -10.3175 q^{66} +4.44336 q^{67} +17.6539 q^{68} +8.16058 q^{69} -0.769670 q^{70} +12.1150 q^{71} -3.30831 q^{72} -2.95123 q^{73} +11.3662 q^{74} +4.87410 q^{75} -16.2760 q^{76} +4.12849 q^{77} +15.7706 q^{78} -6.41005 q^{79} -0.305451 q^{80} +1.00000 q^{81} +4.31927 q^{82} +12.7318 q^{83} +3.18712 q^{84} -1.83110 q^{85} +8.77676 q^{86} +7.58823 q^{87} +14.6603 q^{88} +14.4836 q^{89} +0.826132 q^{90} -6.31056 q^{91} -27.9167 q^{92} +1.21382 q^{93} -7.08792 q^{94} +1.68818 q^{95} -4.61231 q^{96} -5.18853 q^{97} +14.2771 q^{98} -4.43135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 5 q^{3} + 2 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 5 * q^3 + 2 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 2 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 5 q^{9} - q^{10} - 12 q^{11} - 2 q^{12} + q^{13} - 8 q^{14} + 5 q^{15} - 4 q^{16} - 10 q^{17} - 2 q^{18} - 16 q^{19} - 13 q^{20} + 2 q^{21} + 4 q^{22} - 5 q^{23} + 6 q^{24} + 12 q^{25} - 10 q^{26} - 5 q^{27} + 7 q^{28} - 16 q^{29} + q^{30} - 13 q^{31} + 11 q^{32} + 12 q^{33} - 2 q^{34} - 22 q^{35} + 2 q^{36} + 4 q^{37} + 21 q^{38} - q^{39} + 11 q^{40} - 20 q^{41} + 8 q^{42} + 7 q^{43} + 2 q^{44} - 5 q^{45} + 8 q^{46} + 8 q^{47} + 4 q^{48} + 23 q^{49} + 13 q^{50} + 10 q^{51} + 31 q^{52} - 8 q^{53} + 2 q^{54} - 6 q^{55} + 5 q^{56} + 16 q^{57} + 20 q^{58} - 19 q^{59} + 13 q^{60} - 19 q^{61} + 9 q^{62} - 2 q^{63} - 16 q^{64} + q^{65} - 4 q^{66} + 11 q^{67} + 15 q^{68} + 5 q^{69} + 44 q^{70} - 10 q^{71} - 6 q^{72} + 20 q^{73} + 44 q^{74} - 12 q^{75} - 8 q^{76} + 8 q^{77} + 10 q^{78} - 14 q^{79} + 45 q^{80} + 5 q^{81} - 3 q^{82} - 11 q^{83} - 7 q^{84} + 12 q^{85} - 11 q^{86} + 16 q^{87} + 30 q^{88} + 22 q^{89} - q^{90} - 42 q^{91} - 21 q^{92} + 13 q^{93} - 6 q^{94} - 10 q^{95} - 11 q^{96} + 7 q^{97} - 11 q^{98} - 12 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 2 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 5 * q^9 - q^10 - 12 * q^11 - 2 * q^12 + q^13 - 8 * q^14 + 5 * q^15 - 4 * q^16 - 10 * q^17 - 2 * q^18 - 16 * q^19 - 13 * q^20 + 2 * q^21 + 4 * q^22 - 5 * q^23 + 6 * q^24 + 12 * q^25 - 10 * q^26 - 5 * q^27 + 7 * q^28 - 16 * q^29 + q^30 - 13 * q^31 + 11 * q^32 + 12 * q^33 - 2 * q^34 - 22 * q^35 + 2 * q^36 + 4 * q^37 + 21 * q^38 - q^39 + 11 * q^40 - 20 * q^41 + 8 * q^42 + 7 * q^43 + 2 * q^44 - 5 * q^45 + 8 * q^46 + 8 * q^47 + 4 * q^48 + 23 * q^49 + 13 * q^50 + 10 * q^51 + 31 * q^52 - 8 * q^53 + 2 * q^54 - 6 * q^55 + 5 * q^56 + 16 * q^57 + 20 * q^58 - 19 * q^59 + 13 * q^60 - 19 * q^61 + 9 * q^62 - 2 * q^63 - 16 * q^64 + q^65 - 4 * q^66 + 11 * q^67 + 15 * q^68 + 5 * q^69 + 44 * q^70 - 10 * q^71 - 6 * q^72 + 20 * q^73 + 44 * q^74 - 12 * q^75 - 8 * q^76 + 8 * q^77 + 10 * q^78 - 14 * q^79 + 45 * q^80 + 5 * q^81 - 3 * q^82 - 11 * q^83 - 7 * q^84 + 12 * q^85 - 11 * q^86 + 16 * q^87 + 30 * q^88 + 22 * q^89 - q^90 - 42 * q^91 - 21 * q^92 + 13 * q^93 - 6 * q^94 - 10 * q^95 - 11 * q^96 + 7 * q^97 - 11 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.32829	−1.64635	−0.823174	−	0.567790i	$-0.807799\pi$
$2$	−2.32829	−1.64635	−0.823174	+	0.567790i	$0.807799\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.42092	1.71046
$5$	−0.354824	−0.158682	−0.0793411	−	0.996848i	$-0.525282\pi$
$5$	−0.354824	−0.158682	−0.0793411	+	0.996848i	$0.525282\pi$
$6$	2.32829	0.950519
$7$	−0.931655	−0.352132	−0.176066	−	0.984378i	$-0.556337\pi$
$7$	−0.931655	−0.352132	−0.176066	+	0.984378i	$0.556337\pi$
$8$	−3.30831	−1.16966
$9$	1.00000	0.333333
$10$	0.826132	0.261246
$11$	−4.43135	−1.33610	−0.668051	−	0.744115i	$-0.732871\pi$
$11$	−4.43135	−1.33610	−0.668051	+	0.744115i	$0.732871\pi$
$12$	−3.42092	−0.987534
$13$	6.77349	1.87863	0.939315	−	0.343057i	$-0.111462\pi$
$13$	6.77349	1.87863	0.939315	+	0.343057i	$0.111462\pi$
$14$	2.16916	0.579732
$15$	0.354824	0.0916152
$16$	0.860851	0.215213
$17$	5.16058	1.25162	0.625812	−	0.779974i	$-0.284768\pi$
$17$	5.16058	1.25162	0.625812	+	0.779974i	$0.284768\pi$
$18$	−2.32829	−0.548782
$19$	−4.75779	−1.09151	−0.545756	−	0.837944i	$-0.683757\pi$
$19$	−4.75779	−1.09151	−0.545756	+	0.837944i	$0.683757\pi$
$20$	−1.21382	−0.271419
$21$	0.931655	0.203304
$22$	10.3175	2.19969
$23$	−8.16058	−1.70160	−0.850799	−	0.525491i	$-0.823882\pi$
$23$	−8.16058	−1.70160	−0.850799	+	0.525491i	$0.823882\pi$
$24$	3.30831	0.675306
$25$	−4.87410	−0.974820
$26$	−15.7706	−3.09288
$27$	−1.00000	−0.192450
$28$	−3.18712	−0.602308
$29$	−7.58823	−1.40910	−0.704549	−	0.709655i	$-0.748851\pi$
$29$	−7.58823	−1.40910	−0.704549	+	0.709655i	$0.748851\pi$
$30$	−0.826132	−0.150830
$31$	−1.21382	−0.218009	−0.109005	−	0.994041i	$-0.534766\pi$
$31$	−1.21382	−0.218009	−0.109005	+	0.994041i	$0.534766\pi$
$32$	4.61231	0.815348
$33$	4.43135	0.771399
$34$	−12.0153	−2.06061
$35$	0.330574	0.0558771
$36$	3.42092	0.570153
$37$	−4.88180	−0.802562	−0.401281	−	0.915955i	$-0.631435\pi$
$37$	−4.88180	−0.802562	−0.401281	+	0.915955i	$0.631435\pi$
$38$	11.0775	1.79701
$39$	−6.77349	−1.08463
$40$	1.17387	0.185605
$41$	−1.85513	−0.289722	−0.144861	−	0.989452i	$-0.546274\pi$
$41$	−1.85513	−0.289722	−0.144861	+	0.989452i	$0.546274\pi$
$42$	−2.16916	−0.334709
$43$	−3.76962	−0.574862	−0.287431	−	0.957801i	$-0.592801\pi$
$43$	−3.76962	−0.574862	−0.287431	+	0.957801i	$0.592801\pi$
$44$	−15.1593	−2.28535
$45$	−0.354824	−0.0528941
$46$	19.0002	2.80142
$47$	3.04427	0.444052	0.222026	−	0.975041i	$-0.428733\pi$
$47$	3.04427	0.444052	0.222026	+	0.975041i	$0.428733\pi$
$48$	−0.860851	−0.124253
$49$	−6.13202	−0.876003
$50$	11.3483	1.60489
$51$	−5.16058	−0.722626
$52$	23.1716	3.21332
$53$	−6.04366	−0.830160	−0.415080	−	0.909785i	$-0.636246\pi$
$53$	−6.04366	−0.830160	−0.415080	+	0.909785i	$0.636246\pi$
$54$	2.32829	0.316840
$55$	1.57235	0.212016
$56$	3.08220	0.411876
$57$	4.75779	0.630184
$58$	17.6676	2.31987
$59$	−0.951861	−0.123922	−0.0619609	−	0.998079i	$-0.519735\pi$
$59$	−0.951861	−0.123922	−0.0619609	+	0.998079i	$0.519735\pi$
$60$	1.21382	0.156704
$61$	−2.03608	−0.260694	−0.130347	−	0.991468i	$-0.541609\pi$
$61$	−2.03608	−0.260694	−0.130347	+	0.991468i	$0.541609\pi$
$62$	2.82613	0.358919
$63$	−0.931655	−0.117377
$64$	−12.4605	−1.55756
$65$	−2.40340	−0.298105
$66$	−10.3175	−1.26999
$67$	4.44336	0.542842	0.271421	−	0.962461i	$-0.412506\pi$
$67$	4.44336	0.542842	0.271421	+	0.962461i	$0.412506\pi$
$68$	17.6539	2.14085
$69$	8.16058	0.982418
$70$	−0.769670	−0.0919932
$71$	12.1150	1.43779	0.718895	−	0.695119i	$-0.244648\pi$
$71$	12.1150	1.43779	0.718895	+	0.695119i	$0.244648\pi$
$72$	−3.30831	−0.389888
$73$	−2.95123	−0.345416	−0.172708	−	0.984973i	$-0.555252\pi$
$73$	−2.95123	−0.345416	−0.172708	+	0.984973i	$0.555252\pi$
$74$	11.3662	1.32130
$75$	4.87410	0.562813
$76$	−16.2760	−1.86699
$77$	4.12849	0.470485
$78$	15.7706	1.78567
$79$	−6.41005	−0.721187	−0.360594	−	0.932723i	$-0.617426\pi$
$79$	−6.41005	−0.721187	−0.360594	+	0.932723i	$0.617426\pi$
$80$	−0.305451	−0.0341504
$81$	1.00000	0.111111
$82$	4.31927	0.476984
$83$	12.7318	1.39750	0.698749	−	0.715367i	$-0.253740\pi$
$83$	12.7318	1.39750	0.698749	+	0.715367i	$0.253740\pi$
$84$	3.18712	0.347743
$85$	−1.83110	−0.198610
$86$	8.77676	0.946422
$87$	7.58823	0.813543
$88$	14.6603	1.56279
$89$	14.4836	1.53526	0.767631	−	0.640892i	$-0.221436\pi$
$89$	14.4836	1.53526	0.767631	+	0.640892i	$0.221436\pi$
$90$	0.826132	0.0870820
$91$	−6.31056	−0.661526
$92$	−27.9167	−2.91052
$93$	1.21382	0.125868
$94$	−7.08792	−0.731064
$95$	1.68818	0.173203
$96$	−4.61231	−0.470742
$97$	−5.18853	−0.526815	−0.263408	−	0.964685i	$-0.584846\pi$
$97$	−5.18853	−0.526815	−0.263408	+	0.964685i	$0.584846\pi$
$98$	14.2771	1.44220
$99$	−4.43135	−0.445368
$100$	−16.6739	−1.66739
$101$	−18.1079	−1.80181	−0.900904	−	0.434019i	$-0.857095\pi$
$101$	−18.1079	−1.80181	−0.900904	+	0.434019i	$0.857095\pi$
$102$	12.0153	1.18969
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−22.4088	−2.19736
$105$	−0.330574	−0.0322607
$106$	14.0714	1.36673
$107$	−9.02002	−0.871998	−0.435999	−	0.899947i	$-0.643605\pi$
$107$	−9.02002	−0.871998	−0.435999	+	0.899947i	$0.643605\pi$
$108$	−3.42092	−0.329178
$109$	2.84184	0.272199	0.136099	−	0.990695i	$-0.456543\pi$
$109$	2.84184	0.272199	0.136099	+	0.990695i	$0.456543\pi$
$110$	−3.66088	−0.349051
$111$	4.88180	0.463360
$112$	−0.802016	−0.0757834
$113$	0.716737	0.0674250	0.0337125	−	0.999432i	$-0.489267\pi$
$113$	0.716737	0.0674250	0.0337125	+	0.999432i	$0.489267\pi$
$114$	−11.0775	−1.03750
$115$	2.89557	0.270013
$116$	−25.9587	−2.41021
$117$	6.77349	0.626210
$118$	2.21621	0.204018
$119$	−4.80788	−0.440737
$120$	−1.17387	−0.107159
$121$	8.63687	0.785170
$122$	4.74059	0.429193
$123$	1.85513	0.167271
$124$	−4.15240	−0.372896
$125$	3.50357	0.313369
$126$	2.16916	0.193244
$127$	−21.8438	−1.93833	−0.969163	−	0.246421i	$-0.920745\pi$
$127$	−21.8438	−1.93833	−0.969163	+	0.246421i	$0.920745\pi$
$128$	19.7870	1.74894
$129$	3.76962	0.331897
$130$	5.59580	0.490784
$131$	6.04668	0.528301	0.264151	−	0.964481i	$-0.414908\pi$
$131$	6.04668	0.528301	0.264151	+	0.964481i	$0.414908\pi$
$132$	15.1593	1.31945
$133$	4.43262	0.384356
$134$	−10.3454	−0.893707
$135$	0.354824	0.0305384
$136$	−17.0728	−1.46398
$137$	3.79801	0.324486	0.162243	−	0.986751i	$-0.448127\pi$
$137$	3.79801	0.324486	0.162243	+	0.986751i	$0.448127\pi$
$138$	−19.0002	−1.61740
$139$	−7.92009	−0.671773	−0.335886	−	0.941902i	$-0.609036\pi$
$139$	−7.92009	−0.671773	−0.335886	+	0.941902i	$0.609036\pi$
$140$	1.13087	0.0955756
$141$	−3.04427	−0.256373
$142$	−28.2073	−2.36710
$143$	−30.0157	−2.51004
$144$	0.860851	0.0717376
$145$	2.69249	0.223599
$146$	6.87132	0.568674
$147$	6.13202	0.505760
$148$	−16.7002	−1.37275
$149$	−18.2636	−1.49621	−0.748106	−	0.663579i	$-0.769037\pi$
$149$	−18.2636	−1.49621	−0.748106	+	0.663579i	$0.769037\pi$
$150$	−11.3483	−0.926585
$151$	15.1279	1.23109	0.615545	−	0.788102i	$-0.288936\pi$
$151$	15.1279	1.23109	0.615545	+	0.788102i	$0.288936\pi$
$152$	15.7402	1.27670
$153$	5.16058	0.417208
$154$	−9.61231	−0.774582
$155$	0.430694	0.0345942
$156$	−23.1716	−1.85521
$157$	17.0794	1.36308	0.681541	−	0.731779i	$-0.261310\pi$
$157$	17.0794	1.36308	0.681541	+	0.731779i	$0.261310\pi$
$158$	14.9244	1.18732
$159$	6.04366	0.479293
$160$	−1.63656	−0.129381
$161$	7.60284	0.599188
$162$	−2.32829	−0.182927
$163$	3.28714	0.257468	0.128734	−	0.991679i	$-0.458909\pi$
$163$	3.28714	0.257468	0.128734	+	0.991679i	$0.458909\pi$
$164$	−6.34624	−0.495558
$165$	−1.57235	−0.122407
$166$	−29.6433	−2.30077
$167$	9.76359	0.755529	0.377765	−	0.925902i	$-0.376693\pi$
$167$	9.76359	0.755529	0.377765	+	0.925902i	$0.376693\pi$
$168$	−3.08220	−0.237797
$169$	32.8802	2.52925
$170$	4.26332	0.326982
$171$	−4.75779	−0.363837
$172$	−12.8956	−0.983278
$173$	2.94307	0.223758	0.111879	−	0.993722i	$-0.464313\pi$
$173$	2.94307	0.223758	0.111879	+	0.993722i	$0.464313\pi$
$174$	−17.6676	−1.33938
$175$	4.54098	0.343266
$176$	−3.81473	−0.287546
$177$	0.951861	0.0715463
$178$	−33.7220	−2.52757
$179$	−14.6553	−1.09539	−0.547694	−	0.836679i	$-0.684494\pi$
$179$	−14.6553	−1.09539	−0.547694	+	0.836679i	$0.684494\pi$
$180$	−1.21382	−0.0904732
$181$	18.7548	1.39403	0.697016	−	0.717056i	$-0.254511\pi$
$181$	18.7548	1.39403	0.697016	+	0.717056i	$0.254511\pi$
$182$	14.6928	1.08910
$183$	2.03608	0.150512
$184$	26.9977	1.99030
$185$	1.73218	0.127352
$186$	−2.82613	−0.207222
$187$	−22.8683	−1.67230
$188$	10.4142	0.759533
$189$	0.931655	0.0677679
$190$	−3.93056	−0.285153
$191$	−2.37828	−0.172086	−0.0860430	−	0.996291i	$-0.527422\pi$
$191$	−2.37828	−0.172086	−0.0860430	+	0.996291i	$0.527422\pi$
$192$	12.4605	0.899258
$193$	3.15324	0.226976	0.113488	−	0.993539i	$-0.463798\pi$
$193$	3.15324	0.226976	0.113488	+	0.993539i	$0.463798\pi$
$194$	12.0804	0.867321
$195$	2.40340	0.172111
$196$	−20.9771	−1.49837
$197$	−4.66488	−0.332359	−0.166179	−	0.986096i	$-0.553143\pi$
$197$	−4.66488	−0.332359	−0.166179	+	0.986096i	$0.553143\pi$
$198$	10.3175	0.733230
$199$	10.1270	0.717886	0.358943	−	0.933359i	$-0.383137\pi$
$199$	10.1270	0.717886	0.358943	+	0.933359i	$0.383137\pi$
$200$	16.1250	1.14021
$201$	−4.44336	−0.313410
$202$	42.1605	2.96640
$203$	7.06961	0.496189
$204$	−17.6539	−1.23602
$205$	0.658244	0.0459738
$206$	2.32829	0.162219
$207$	−8.16058	−0.567199
$208$	5.83097	0.404305
$209$	21.0834	1.45837
$210$	0.769670	0.0531123
$211$	−10.9121	−0.751218	−0.375609	−	0.926778i	$-0.622566\pi$
$211$	−10.9121	−0.751218	−0.375609	+	0.926778i	$0.622566\pi$
$212$	−20.6749	−1.41996
$213$	−12.1150	−0.830108
$214$	21.0012	1.43561
$215$	1.33755	0.0912203
$216$	3.30831	0.225102
$217$	1.13087	0.0767682
$218$	−6.61662	−0.448134
$219$	2.95123	0.199426
$220$	5.37888	0.362644
$221$	34.9551	2.35134
$222$	−11.3662	−0.762851
$223$	11.7889	0.789446	0.394723	−	0.918800i	$-0.370841\pi$
$223$	11.7889	0.789446	0.394723	+	0.918800i	$0.370841\pi$
$224$	−4.29708	−0.287111
$225$	−4.87410	−0.324940
$226$	−1.66877	−0.111005
$227$	−13.2654	−0.880458	−0.440229	−	0.897885i	$-0.645103\pi$
$227$	−13.2654	−0.880458	−0.440229	+	0.897885i	$0.645103\pi$
$228$	16.2760	1.07790
$229$	−24.1712	−1.59728	−0.798638	−	0.601811i	$-0.794446\pi$
$229$	−24.1712	−1.59728	−0.798638	+	0.601811i	$0.794446\pi$
$230$	−6.74172	−0.444536
$231$	−4.12849	−0.271635
$232$	25.1042	1.64817
$233$	−20.3485	−1.33307	−0.666536	−	0.745473i	$-0.732224\pi$
$233$	−20.3485	−1.33307	−0.666536	+	0.745473i	$0.732224\pi$
$234$	−15.7706	−1.03096
$235$	−1.08018	−0.0704631
$236$	−3.25624	−0.211963
$237$	6.41005	0.416378
$238$	11.1941	0.725607
$239$	6.35015	0.410757	0.205379	−	0.978683i	$-0.434157\pi$
$239$	6.35015	0.410757	0.205379	+	0.978683i	$0.434157\pi$
$240$	0.305451	0.0197168
$241$	−23.9689	−1.54397	−0.771987	−	0.635638i	$-0.780737\pi$
$241$	−23.9689	−1.54397	−0.771987	+	0.635638i	$0.780737\pi$
$242$	−20.1091	−1.29266
$243$	−1.00000	−0.0641500
$244$	−6.96528	−0.445906
$245$	2.17579	0.139006
$246$	−4.31927	−0.275387
$247$	−32.2268	−2.05054
$248$	4.01571	0.254998
$249$	−12.7318	−0.806846
$250$	−8.15731	−0.515914
$251$	7.14293	0.450858	0.225429	−	0.974260i	$-0.427622\pi$
$251$	7.14293	0.450858	0.225429	+	0.974260i	$0.427622\pi$
$252$	−3.18712	−0.200769
$253$	36.1624	2.27351
$254$	50.8587	3.19116
$255$	1.83110	0.114668
$256$	−21.1487	−1.32180
$257$	−2.01113	−0.125451	−0.0627255	−	0.998031i	$-0.519979\pi$
$257$	−2.01113	−0.125451	−0.0627255	+	0.998031i	$0.519979\pi$
$258$	−8.77676	−0.546417
$259$	4.54815	0.282608
$260$	−8.22184	−0.509897
$261$	−7.58823	−0.469700
$262$	−14.0784	−0.869767
$263$	27.6693	1.70616	0.853082	−	0.521776i	$-0.174730\pi$
$263$	27.6693	1.70616	0.853082	+	0.521776i	$0.174730\pi$
$264$	−14.6603	−0.902278
$265$	2.14444	0.131732
$266$	−10.3204	−0.632784
$267$	−14.4836	−0.886384
$268$	15.2004	0.928510
$269$	−27.3519	−1.66767	−0.833836	−	0.552012i	$-0.813860\pi$
$269$	−27.3519	−1.66767	−0.833836	+	0.552012i	$0.813860\pi$
$270$	−0.826132	−0.0502768
$271$	5.85728	0.355804	0.177902	−	0.984048i	$-0.443069\pi$
$271$	5.85728	0.355804	0.177902	+	0.984048i	$0.443069\pi$
$272$	4.44249	0.269366
$273$	6.31056	0.381932
$274$	−8.84285	−0.534216
$275$	21.5988	1.30246
$276$	27.9167	1.68039
$277$	31.2960	1.88039	0.940197	−	0.340632i	$-0.110641\pi$
$277$	31.2960	1.88039	0.940197	+	0.340632i	$0.110641\pi$
$278$	18.4402	1.10597
$279$	−1.21382	−0.0726698
$280$	−1.09364	−0.0653575
$281$	22.3589	1.33382	0.666911	−	0.745137i	$-0.267616\pi$
$281$	22.3589	1.33382	0.666911	+	0.745137i	$0.267616\pi$
$282$	7.08792	0.422080
$283$	15.1750	0.902060	0.451030	−	0.892509i	$-0.351057\pi$
$283$	15.1750	0.902060	0.451030	+	0.892509i	$0.351057\pi$
$284$	41.4445	2.45928
$285$	−1.68818	−0.0999990
$286$	69.8852	4.13240
$287$	1.72834	0.102021
$288$	4.61231	0.271783
$289$	9.63157	0.566563
$290$	−6.26888	−0.368121
$291$	5.18853	0.304157
$292$	−10.0959	−0.590820
$293$	−1.90181	−0.111105	−0.0555525	−	0.998456i	$-0.517692\pi$
$293$	−1.90181	−0.111105	−0.0555525	+	0.998456i	$0.517692\pi$
$294$	−14.2771	−0.832657
$295$	0.337743	0.0196642
$296$	16.1505	0.938728
$297$	4.43135	0.257133
$298$	42.5229	2.46329
$299$	−55.2756	−3.19667
$300$	16.6739	0.962668
$301$	3.51199	0.202427
$302$	−35.2220	−2.02680
$303$	18.1079	1.04027
$304$	−4.09575	−0.234907
$305$	0.722452	0.0413675
$306$	−12.0153	−0.686869
$307$	−33.7217	−1.92460	−0.962300	−	0.271989i	$-0.912318\pi$
$307$	−33.7217	−1.92460	−0.962300	+	0.271989i	$0.912318\pi$
$308$	14.1232	0.804746
$309$	1.00000	0.0568880
$310$	−1.00278	−0.0569541
$311$	27.9423	1.58446	0.792230	−	0.610223i	$-0.208920\pi$
$311$	27.9423	1.58446	0.792230	+	0.610223i	$0.208920\pi$
$312$	22.4088	1.26865
$313$	8.05949	0.455549	0.227775	−	0.973714i	$-0.426855\pi$
$313$	8.05949	0.455549	0.227775	+	0.973714i	$0.426855\pi$
$314$	−39.7657	−2.24411
$315$	0.330574	0.0186257
$316$	−21.9283	−1.23356
$317$	−17.1748	−0.964630	−0.482315	−	0.875998i	$-0.660204\pi$
$317$	−17.1748	−0.964630	−0.482315	+	0.875998i	$0.660204\pi$
$318$	−14.0714	−0.789083
$319$	33.6261	1.88270
$320$	4.42128	0.247157
$321$	9.02002	0.503448
$322$	−17.7016	−0.986471
$323$	−24.5529	−1.36616
$324$	3.42092	0.190051
$325$	−33.0147	−1.83133
$326$	−7.65339	−0.423882
$327$	−2.84184	−0.157154
$328$	6.13733	0.338878
$329$	−2.83621	−0.156365
$330$	3.66088	0.201525
$331$	31.3536	1.72335	0.861674	−	0.507462i	$-0.169416\pi$
$331$	31.3536	1.72335	0.861674	+	0.507462i	$0.169416\pi$
$332$	43.5545	2.39036
$333$	−4.88180	−0.267521
$334$	−22.7324	−1.24386
$335$	−1.57661	−0.0861394
$336$	0.802016	0.0437536
$337$	−18.4494	−1.00500	−0.502502	−	0.864576i	$-0.667587\pi$
$337$	−18.4494	−1.00500	−0.502502	+	0.864576i	$0.667587\pi$
$338$	−76.5546	−4.16402
$339$	−0.716737	−0.0389278
$340$	−6.26404	−0.339715
$341$	5.37888	0.291283
$342$	11.0775	0.599002
$343$	12.2345	0.660601
$344$	12.4711	0.672395
$345$	−2.89557	−0.155892
$346$	−6.85232	−0.368383
$347$	−27.1015	−1.45488	−0.727442	−	0.686169i	$-0.759291\pi$
$347$	−27.1015	−1.45488	−0.727442	+	0.686169i	$0.759291\pi$
$348$	25.9587	1.39153
$349$	−8.90829	−0.476850	−0.238425	−	0.971161i	$-0.576631\pi$
$349$	−8.90829	−0.476850	−0.238425	+	0.971161i	$0.576631\pi$
$350$	−10.5727	−0.565135
$351$	−6.77349	−0.361542
$352$	−20.4388	−1.08939
$353$	−9.82182	−0.522763	−0.261381	−	0.965236i	$-0.584178\pi$
$353$	−9.82182	−0.522763	−0.261381	+	0.965236i	$0.584178\pi$
$354$	−2.21621	−0.117790
$355$	−4.29870	−0.228152
$356$	49.5473	2.62600
$357$	4.80788	0.254460
$358$	34.1217	1.80339
$359$	−16.2184	−0.855974	−0.427987	−	0.903785i	$-0.640777\pi$
$359$	−16.2184	−0.855974	−0.427987	+	0.903785i	$0.640777\pi$
$360$	1.17387	0.0618683
$361$	3.63654	0.191397
$362$	−43.6665	−2.29506
$363$	−8.63687	−0.453318
$364$	−21.5879	−1.13151
$365$	1.04717	0.0548113
$366$	−4.74059	−0.247795
$367$	−13.6759	−0.713877	−0.356938	−	0.934128i	$-0.616179\pi$
$367$	−13.6759	−0.713877	−0.356938	+	0.934128i	$0.616179\pi$
$368$	−7.02505	−0.366206
$369$	−1.85513	−0.0965741
$370$	−4.03301	−0.209666
$371$	5.63060	0.292326
$372$	4.15240	0.215292
$373$	24.4162	1.26422	0.632110	−	0.774878i	$-0.282189\pi$
$373$	24.4162	1.26422	0.632110	+	0.774878i	$0.282189\pi$
$374$	53.2440	2.75318
$375$	−3.50357	−0.180924
$376$	−10.0714	−0.519391
$377$	−51.3988	−2.64717
$378$	−2.16916	−0.111570
$379$	4.91432	0.252432	0.126216	−	0.992003i	$-0.459717\pi$
$379$	4.91432	0.252432	0.126216	+	0.992003i	$0.459717\pi$
$380$	5.77512	0.296257
$381$	21.8438	1.11909
$382$	5.53731	0.283313
$383$	−1.24589	−0.0636623	−0.0318311	−	0.999493i	$-0.510134\pi$
$383$	−1.24589	−0.0636623	−0.0318311	+	0.999493i	$0.510134\pi$
$384$	−19.7870	−1.00975
$385$	−1.46489	−0.0746576
$386$	−7.34166	−0.373681
$387$	−3.76962	−0.191621
$388$	−17.7495	−0.901097
$389$	1.91517	0.0971029	0.0485515	−	0.998821i	$-0.484540\pi$
$389$	1.91517	0.0971029	0.0485515	+	0.998821i	$0.484540\pi$
$390$	−5.59580	−0.283354
$391$	−42.1133	−2.12976
$392$	20.2866	1.02463
$393$	−6.04668	−0.305015
$394$	10.8612	0.547178
$395$	2.27444	0.114440
$396$	−15.1593	−0.761783
$397$	28.7014	1.44048	0.720240	−	0.693725i	$-0.244032\pi$
$397$	28.7014	1.44048	0.720240	+	0.693725i	$0.244032\pi$
$398$	−23.5786	−1.18189
$399$	−4.43262	−0.221908
$400$	−4.19588	−0.209794
$401$	−2.38641	−0.119172	−0.0595858	−	0.998223i	$-0.518978\pi$
$401$	−2.38641	−0.119172	−0.0595858	+	0.998223i	$0.518978\pi$
$402$	10.3454	0.515982
$403$	−8.22184	−0.409559
$404$	−61.9458	−3.08192
$405$	−0.354824	−0.0176314
$406$	−16.4601	−0.816900
$407$	21.6330	1.07231
$408$	17.0728	0.845229
$409$	−7.84566	−0.387943	−0.193972	−	0.981007i	$-0.562137\pi$
$409$	−7.84566	−0.387943	−0.193972	+	0.981007i	$0.562137\pi$
$410$	−1.53258	−0.0756888
$411$	−3.79801	−0.187342
$412$	−3.42092	−0.168537
$413$	0.886806	0.0436369
$414$	19.0002	0.933807
$415$	−4.51756	−0.221758
$416$	31.2414	1.53174
$417$	7.92009	0.387848
$418$	−49.0883	−2.40099
$419$	8.18033	0.399635	0.199818	−	0.979833i	$-0.435965\pi$
$419$	8.18033	0.399635	0.199818	+	0.979833i	$0.435965\pi$
$420$	−1.13087	−0.0551806
$421$	−32.3646	−1.57735	−0.788676	−	0.614808i	$-0.789233\pi$
$421$	−32.3646	−1.57735	−0.788676	+	0.614808i	$0.789233\pi$
$422$	25.4064	1.23677
$423$	3.04427	0.148017
$424$	19.9943	0.971008
$425$	−25.1532	−1.22011
$426$	28.2073	1.36665
$427$	1.89693	0.0917988
$428$	−30.8567	−1.49152
$429$	30.0157	1.44917
$430$	−3.11421	−0.150180
$431$	17.2399	0.830417	0.415209	−	0.909726i	$-0.363709\pi$
$431$	17.2399	0.830417	0.415209	+	0.909726i	$0.363709\pi$
$432$	−0.860851	−0.0414177
$433$	19.2924	0.927132	0.463566	−	0.886063i	$-0.346570\pi$
$433$	19.2924	0.927132	0.463566	+	0.886063i	$0.346570\pi$
$434$	−2.63298	−0.126387
$435$	−2.69249	−0.129095
$436$	9.72170	0.465585
$437$	38.8263	1.85731
$438$	−6.87132	−0.328324
$439$	11.7950	0.562945	0.281472	−	0.959569i	$-0.409177\pi$
$439$	11.7950	0.562945	0.281472	+	0.959569i	$0.409177\pi$
$440$	−5.20182	−0.247987
$441$	−6.13202	−0.292001
$442$	−81.3856	−3.87112
$443$	−9.91294	−0.470978	−0.235489	−	0.971877i	$-0.575669\pi$
$443$	−9.91294	−0.470978	−0.235489	+	0.971877i	$0.575669\pi$
$444$	16.7002	0.792558
$445$	−5.13914	−0.243619
$446$	−27.4480	−1.29970
$447$	18.2636	0.863839
$448$	11.6089	0.548467
$449$	−0.300272	−0.0141707	−0.00708536	−	0.999975i	$-0.502255\pi$
$449$	−0.300272	−0.0141707	−0.00708536	+	0.999975i	$0.502255\pi$
$450$	11.3483	0.534964
$451$	8.22072	0.387099
$452$	2.45190	0.115328
$453$	−15.1279	−0.710770
$454$	30.8858	1.44954
$455$	2.23914	0.104972
$456$	−15.7402	−0.737104
$457$	22.4619	1.05072	0.525361	−	0.850879i	$-0.323930\pi$
$457$	22.4619	1.05072	0.525361	+	0.850879i	$0.323930\pi$
$458$	56.2774	2.62967
$459$	−5.16058	−0.240875
$460$	9.90551	0.461847
$461$	−19.1847	−0.893522	−0.446761	−	0.894653i	$-0.647423\pi$
$461$	−19.1847	−0.893522	−0.446761	+	0.894653i	$0.647423\pi$
$462$	9.61231	0.447205
$463$	28.6915	1.33341	0.666703	−	0.745324i	$-0.267705\pi$
$463$	28.6915	1.33341	0.666703	+	0.745324i	$0.267705\pi$
$464$	−6.53234	−0.303256
$465$	−0.430694	−0.0199730
$466$	47.3770	2.19470
$467$	17.0731	0.790050	0.395025	−	0.918670i	$-0.370736\pi$
$467$	17.0731	0.790050	0.395025	+	0.918670i	$0.370736\pi$
$468$	23.1716	1.07111
$469$	−4.13967	−0.191152
$470$	2.51497	0.116007
$471$	−17.0794	−0.786976
$472$	3.14905	0.144947
$473$	16.7045	0.768074
$474$	−14.9244	−0.685502
$475$	23.1899	1.06403
$476$	−16.4474	−0.753864
$477$	−6.04366	−0.276720
$478$	−14.7850	−0.676249
$479$	−3.55817	−0.162577	−0.0812885	−	0.996691i	$-0.525904\pi$
$479$	−3.55817	−0.162577	−0.0812885	+	0.996691i	$0.525904\pi$
$480$	1.63656	0.0746983
$481$	−33.0668	−1.50772
$482$	55.8065	2.54192
$483$	−7.60284	−0.345941
$484$	29.5460	1.34300
$485$	1.84102	0.0835962
$486$	2.32829	0.105613
$487$	−10.5087	−0.476195	−0.238097	−	0.971241i	$-0.576524\pi$
$487$	−10.5087	−0.476195	−0.238097	+	0.971241i	$0.576524\pi$
$488$	6.73599	0.304924
$489$	−3.28714	−0.148649
$490$	−5.06586	−0.228852
$491$	2.01321	0.0908548	0.0454274	−	0.998968i	$-0.485535\pi$
$491$	2.01321	0.0908548	0.0454274	+	0.998968i	$0.485535\pi$
$492$	6.34624	0.286111
$493$	−39.1597	−1.76366
$494$	75.0333	3.37591
$495$	1.57235	0.0706719
$496$	−1.04492	−0.0469184
$497$	−11.2870	−0.506292
$498$	29.6433	1.32835
$499$	−14.4376	−0.646318	−0.323159	−	0.946345i	$-0.604745\pi$
$499$	−14.4376	−0.646318	−0.323159	+	0.946345i	$0.604745\pi$
$500$	11.9854	0.536005
$501$	−9.76359	−0.436205
$502$	−16.6308	−0.742269
$503$	19.4378	0.866690	0.433345	−	0.901228i	$-0.357333\pi$
$503$	19.4378	0.866690	0.433345	+	0.901228i	$0.357333\pi$
$504$	3.08220	0.137292
$505$	6.42513	0.285915
$506$	−84.1964	−3.74299
$507$	−32.8802	−1.46026
$508$	−74.7260	−3.31543
$509$	−5.24263	−0.232375	−0.116188	−	0.993227i	$-0.537067\pi$
$509$	−5.24263	−0.232375	−0.116188	+	0.993227i	$0.537067\pi$
$510$	−4.26332	−0.188783
$511$	2.74953	0.121632
$512$	9.66643	0.427200
$513$	4.75779	0.210061
$514$	4.68249	0.206536
$515$	0.354824	0.0156354
$516$	12.8956	0.567696
$517$	−13.4902	−0.593299
$518$	−10.5894	−0.465271
$519$	−2.94307	−0.129187
$520$	7.95119	0.348683
$521$	−24.0785	−1.05490	−0.527448	−	0.849587i	$-0.676851\pi$
$521$	−24.0785	−1.05490	−0.527448	+	0.849587i	$0.676851\pi$
$522$	17.6676	0.773289
$523$	7.77156	0.339827	0.169913	−	0.985459i	$-0.445651\pi$
$523$	7.77156	0.339827	0.169913	+	0.985459i	$0.445651\pi$
$524$	20.6852	0.903638
$525$	−4.54098	−0.198185
$526$	−64.4222	−2.80894
$527$	−6.26404	−0.272866
$528$	3.81473	0.166015
$529$	43.5950	1.89544
$530$	−4.99286	−0.216876
$531$	−0.951861	−0.0413073
$532$	15.1636	0.657426
$533$	−12.5657	−0.544281
$534$	33.7220	1.45930
$535$	3.20052	0.138371
$536$	−14.7000	−0.634943
$537$	14.6553	0.632422
$538$	63.6830	2.74557
$539$	27.1731	1.17043
$540$	1.21382	0.0522347
$541$	13.9750	0.600831	0.300415	−	0.953808i	$-0.402875\pi$
$541$	13.9750	0.600831	0.300415	+	0.953808i	$0.402875\pi$
$542$	−13.6374	−0.585778
$543$	−18.7548	−0.804845
$544$	23.8022	1.02051
$545$	−1.00835	−0.0431931
$546$	−14.6928	−0.628793
$547$	24.5002	1.04755	0.523777	−	0.851855i	$-0.324523\pi$
$547$	24.5002	1.04755	0.523777	+	0.851855i	$0.324523\pi$
$548$	12.9927	0.555020
$549$	−2.03608	−0.0868980
$550$	−50.2883	−2.14430
$551$	36.1032	1.53805
$552$	−26.9977	−1.14910
$553$	5.97196	0.253953
$554$	−72.8660	−3.09578
$555$	−1.73218	−0.0735269
$556$	−27.0940	−1.14904
$557$	20.1243	0.852694	0.426347	−	0.904560i	$-0.359800\pi$
$557$	20.1243	0.852694	0.426347	+	0.904560i	$0.359800\pi$
$558$	2.82613	0.119640
$559$	−25.5335	−1.07995
$560$	0.284575	0.0120255
$561$	22.8683	0.965502
$562$	−52.0580	−2.19594
$563$	−15.9285	−0.671308	−0.335654	−	0.941985i	$-0.608957\pi$
$563$	−15.9285	−0.671308	−0.335654	+	0.941985i	$0.608957\pi$
$564$	−10.4142	−0.438516
$565$	−0.254316	−0.0106991
$566$	−35.3318	−1.48510
$567$	−0.931655	−0.0391258
$568$	−40.0803	−1.68173
$569$	−38.9207	−1.63164	−0.815821	−	0.578305i	$-0.803714\pi$
$569$	−38.9207	−1.63164	−0.815821	+	0.578305i	$0.803714\pi$
$570$	3.93056	0.164633
$571$	7.61725	0.318772	0.159386	−	0.987216i	$-0.449049\pi$
$571$	7.61725	0.318772	0.159386	+	0.987216i	$0.449049\pi$
$572$	−102.681	−4.29332
$573$	2.37828	0.0993539
$574$	−4.02407	−0.167961
$575$	39.7755	1.65875
$576$	−12.4605	−0.519187
$577$	31.5966	1.31538	0.657692	−	0.753287i	$-0.271533\pi$
$577$	31.5966	1.31538	0.657692	+	0.753287i	$0.271533\pi$
$578$	−22.4251	−0.932760
$579$	−3.15324	−0.131044
$580$	9.21078	0.382457
$581$	−11.8617	−0.492105
$582$	−12.0804	−0.500748
$583$	26.7816	1.10918
$584$	9.76359	0.404020
$585$	−2.40340	−0.0993683
$586$	4.42796	0.182917
$587$	6.51923	0.269077	0.134539	−	0.990908i	$-0.457045\pi$
$587$	6.51923	0.269077	0.134539	+	0.990908i	$0.457045\pi$
$588$	20.9771	0.865083
$589$	5.77512	0.237960
$590$	−0.786363	−0.0323741
$591$	4.66488	0.191887
$592$	−4.20250	−0.172722
$593$	21.4854	0.882298	0.441149	−	0.897434i	$-0.354571\pi$
$593$	21.4854	0.882298	0.441149	+	0.897434i	$0.354571\pi$
$594$	−10.3175	−0.423330
$595$	1.70595	0.0699372
$596$	−62.4783	−2.55921
$597$	−10.1270	−0.414472
$598$	128.698	5.26283
$599$	−12.2839	−0.501908	−0.250954	−	0.967999i	$-0.580744\pi$
$599$	−12.2839	−0.501908	−0.250954	+	0.967999i	$0.580744\pi$
$600$	−16.1250	−0.658301
$601$	1.58774	0.0647654	0.0323827	−	0.999476i	$-0.489690\pi$
$601$	1.58774	0.0647654	0.0323827	+	0.999476i	$0.489690\pi$
$602$	−8.17691	−0.333266
$603$	4.44336	0.180947
$604$	51.7513	2.10573
$605$	−3.06457	−0.124593
$606$	−42.1605	−1.71265
$607$	−9.49599	−0.385431	−0.192715	−	0.981255i	$-0.561729\pi$
$607$	−9.49599	−0.385431	−0.192715	+	0.981255i	$0.561729\pi$
$608$	−21.9444	−0.889962
$609$	−7.06961	−0.286475
$610$	−1.68208	−0.0681052
$611$	20.6203	0.834209
$612$	17.6539	0.713618
$613$	0.0808033	0.00326362	0.00163181	−	0.999999i	$-0.499481\pi$
$613$	0.0808033	0.00326362	0.00163181	+	0.999999i	$0.499481\pi$
$614$	78.5138	3.16856
$615$	−0.658244	−0.0265430
$616$	−13.6583	−0.550309
$617$	33.3263	1.34167	0.670833	−	0.741609i	$-0.265937\pi$
$617$	33.3263	1.34167	0.670833	+	0.741609i	$0.265937\pi$
$618$	−2.32829	−0.0936574
$619$	−46.6937	−1.87678	−0.938388	−	0.345583i	$-0.887681\pi$
$619$	−46.6937	−1.87678	−0.938388	+	0.345583i	$0.887681\pi$
$620$	1.47337	0.0591720
$621$	8.16058	0.327473
$622$	−65.0576	−2.60857
$623$	−13.4937	−0.540615
$624$	−5.83097	−0.233426
$625$	23.1273	0.925094
$626$	−18.7648	−0.749992
$627$	−21.0834	−0.841991
$628$	58.4272	2.33150
$629$	−25.1929	−1.00451
$630$	−0.769670	−0.0306644
$631$	−38.0045	−1.51293	−0.756467	−	0.654032i	$-0.773076\pi$
$631$	−38.0045	−1.51293	−0.756467	+	0.654032i	$0.773076\pi$
$632$	21.2064	0.843546
$633$	10.9121	0.433716
$634$	39.9878	1.58812
$635$	7.75071	0.307578
$636$	20.6749	0.819812
$637$	−41.5352	−1.64568
$638$	−78.2912	−3.09958
$639$	12.1150	0.479263
$640$	−7.02089	−0.277525
$641$	11.4133	0.450798	0.225399	−	0.974267i	$-0.427631\pi$
$641$	11.4133	0.450798	0.225399	+	0.974267i	$0.427631\pi$
$642$	−21.0012	−0.828851
$643$	−47.9554	−1.89118	−0.945589	−	0.325363i	$-0.894513\pi$
$643$	−47.9554	−1.89118	−0.945589	+	0.325363i	$0.894513\pi$
$644$	26.0087	1.02489
$645$	−1.33755	−0.0526661
$646$	57.1663	2.24918
$647$	28.6804	1.12754	0.563771	−	0.825931i	$-0.309350\pi$
$647$	28.6804	1.12754	0.563771	+	0.825931i	$0.309350\pi$
$648$	−3.30831	−0.129963
$649$	4.21803	0.165572
$650$	76.8677	3.01500
$651$	−1.13087	−0.0443221
$652$	11.2450	0.440389
$653$	5.67828	0.222208	0.111104	−	0.993809i	$-0.464561\pi$
$653$	5.67828	0.222208	0.111104	+	0.993809i	$0.464561\pi$
$654$	6.61662	0.258730
$655$	−2.14551	−0.0838320
$656$	−1.59699	−0.0623520
$657$	−2.95123	−0.115139
$658$	6.60350	0.257431
$659$	−27.3186	−1.06418	−0.532090	−	0.846687i	$-0.678593\pi$
$659$	−27.3186	−1.06418	−0.532090	+	0.846687i	$0.678593\pi$
$660$	−5.37888	−0.209373
$661$	17.6184	0.685275	0.342637	−	0.939468i	$-0.388680\pi$
$661$	17.6184	0.685275	0.342637	+	0.939468i	$0.388680\pi$
$662$	−73.0001	−2.83723
$663$	−34.9551	−1.35755
$664$	−42.1208	−1.63460
$665$	−1.57280	−0.0609905
$666$	11.3662	0.440432
$667$	61.9243	2.39772
$668$	33.4005	1.29230
$669$	−11.7889	−0.455787
$670$	3.67080	0.141815
$671$	9.02260	0.348314
$672$	4.29708	0.165763
$673$	−4.78128	−0.184305	−0.0921524	−	0.995745i	$-0.529375\pi$
$673$	−4.78128	−0.184305	−0.0921524	+	0.995745i	$0.529375\pi$
$674$	42.9556	1.65459
$675$	4.87410	0.187604
$676$	112.481	4.32618
$677$	−2.52958	−0.0972197	−0.0486098	−	0.998818i	$-0.515479\pi$
$677$	−2.52958	−0.0972197	−0.0486098	+	0.998818i	$0.515479\pi$
$678$	1.66877	0.0640887
$679$	4.83392	0.185509
$680$	6.05784	0.232307
$681$	13.2654	0.508333
$682$	−12.5236	−0.479553
$683$	−32.3512	−1.23789	−0.618943	−	0.785436i	$-0.712439\pi$
$683$	−32.3512	−1.23789	−0.618943	+	0.785436i	$0.712439\pi$
$684$	−16.2760	−0.622329
$685$	−1.34763	−0.0514901
$686$	−28.4854	−1.08758
$687$	24.1712	0.922188
$688$	−3.24508	−0.123718
$689$	−40.9367	−1.55956
$690$	6.74172	0.256653
$691$	−42.4357	−1.61433	−0.807166	−	0.590325i	$-0.799000\pi$
$691$	−42.4357	−1.61433	−0.807166	+	0.590325i	$0.799000\pi$
$692$	10.0680	0.382728
$693$	4.12849	0.156828
$694$	63.1001	2.39525
$695$	2.81024	0.106598
$696$	−25.1042	−0.951572
$697$	−9.57353	−0.362623
$698$	20.7411	0.785061
$699$	20.3485	0.769649
$700$	15.5343	0.587142
$701$	29.2058	1.10309	0.551544	−	0.834146i	$-0.314039\pi$
$701$	29.2058	1.10309	0.551544	+	0.834146i	$0.314039\pi$
$702$	15.7706	0.595224
$703$	23.2265	0.876006
$704$	55.2168	2.08106
$705$	1.08018	0.0406819
$706$	22.8680	0.860649
$707$	16.8703	0.634475
$708$	3.25624	0.122377
$709$	−29.1910	−1.09629	−0.548145	−	0.836383i	$-0.684666\pi$
$709$	−29.1910	−1.09629	−0.548145	+	0.836383i	$0.684666\pi$
$710$	10.0086	0.375617
$711$	−6.41005	−0.240396
$712$	−47.9163	−1.79574
$713$	9.90551	0.370964
$714$	−11.1941	−0.418929
$715$	10.6503	0.398299
$716$	−50.1346	−1.87362
$717$	−6.35015	−0.237151
$718$	37.7611	1.40923
$719$	37.8740	1.41246	0.706230	−	0.707982i	$-0.250394\pi$
$719$	37.8740	1.41246	0.706230	+	0.707982i	$0.250394\pi$
$720$	−0.305451	−0.0113835
$721$	0.931655	0.0346966
$722$	−8.46691	−0.315106
$723$	23.9689	0.891414
$724$	64.1586	2.38444
$725$	36.9858	1.37362
$726$	20.1091	0.746319
$727$	5.61338	0.208189	0.104094	−	0.994567i	$-0.466806\pi$
$727$	5.61338	0.208189	0.104094	+	0.994567i	$0.466806\pi$
$728$	20.8773	0.773763
$729$	1.00000	0.0370370
$730$	−2.43811	−0.0902385
$731$	−19.4534	−0.719511
$732$	6.96528	0.257444
$733$	−13.1704	−0.486460	−0.243230	−	0.969969i	$-0.578207\pi$
$733$	−13.1704	−0.486460	−0.243230	+	0.969969i	$0.578207\pi$
$734$	31.8414	1.17529
$735$	−2.17579	−0.0802552
$736$	−37.6391	−1.38740
$737$	−19.6901	−0.725293
$738$	4.31927	0.158995
$739$	−21.3892	−0.786813	−0.393406	−	0.919365i	$-0.628703\pi$
$739$	−21.3892	−0.786813	−0.393406	+	0.919365i	$0.628703\pi$
$740$	5.92565	0.217831
$741$	32.2268	1.18388
$742$	−13.1097	−0.481271
$743$	−29.8537	−1.09523	−0.547613	−	0.836732i	$-0.684463\pi$
$743$	−29.8537	−1.09523	−0.547613	+	0.836732i	$0.684463\pi$
$744$	−4.01571	−0.147223
$745$	6.48037	0.237422
$746$	−56.8478	−2.08135
$747$	12.7318	0.465833
$748$	−78.2307	−2.86040
$749$	8.40354	0.307059
$750$	8.15731	0.297863
$751$	−37.8028	−1.37944	−0.689721	−	0.724075i	$-0.742267\pi$
$751$	−37.8028	−1.37944	−0.689721	+	0.724075i	$0.742267\pi$
$752$	2.62066	0.0955657
$753$	−7.14293	−0.260303
$754$	119.671	4.35817
$755$	−5.36774	−0.195352
$756$	3.18712	0.115914
$757$	47.8169	1.73793	0.868967	−	0.494870i	$-0.164784\pi$
$757$	47.8169	1.73793	0.868967	+	0.494870i	$0.164784\pi$
$758$	−11.4420	−0.415590
$759$	−36.1624	−1.31261
$760$	−5.58501	−0.202590
$761$	−26.8855	−0.974599	−0.487300	−	0.873235i	$-0.662018\pi$
$761$	−26.8855	−0.974599	−0.487300	+	0.873235i	$0.662018\pi$
$762$	−50.8587	−1.84242
$763$	−2.64761	−0.0958500
$764$	−8.13589	−0.294346
$765$	−1.83110	−0.0662035
$766$	2.90080	0.104810
$767$	−6.44743	−0.232803
$768$	21.1487	0.763139
$769$	−2.13386	−0.0769490	−0.0384745	−	0.999260i	$-0.512250\pi$
$769$	−2.13386	−0.0769490	−0.0384745	+	0.999260i	$0.512250\pi$
$770$	3.41068	0.122912
$771$	2.01113	0.0724292
$772$	10.7870	0.388232
$773$	15.0928	0.542849	0.271424	−	0.962460i	$-0.412505\pi$
$773$	15.0928	0.542849	0.271424	+	0.962460i	$0.412505\pi$
$774$	8.77676	0.315474
$775$	5.91630	0.212520
$776$	17.1653	0.616197
$777$	−4.54815	−0.163164
$778$	−4.45906	−0.159865
$779$	8.82630	0.316235
$780$	8.22184	0.294389
$781$	−53.6859	−1.92103
$782$	98.0519	3.50633
$783$	7.58823	0.271181
$784$	−5.27876	−0.188527
$785$	−6.06018	−0.216297
$786$	14.0784	0.502160
$787$	−4.88464	−0.174119	−0.0870594	−	0.996203i	$-0.527747\pi$
$787$	−4.88464	−0.174119	−0.0870594	+	0.996203i	$0.527747\pi$
$788$	−15.9582	−0.568486
$789$	−27.6693	−0.985055
$790$	−5.29555	−0.188407
$791$	−0.667752	−0.0237425
$792$	14.6603	0.520930
$793$	−13.7914	−0.489747
$794$	−66.8250	−2.37153
$795$	−2.14444	−0.0760553
$796$	34.6438	1.22792
$797$	−26.1320	−0.925644	−0.462822	−	0.886451i	$-0.653163\pi$
$797$	−26.1320	−0.925644	−0.462822	+	0.886451i	$0.653163\pi$
$798$	10.3204	0.365338
$799$	15.7102	0.555786
$800$	−22.4808	−0.794818
$801$	14.4836	0.511754
$802$	5.55624	0.196198
$803$	13.0780	0.461511
$804$	−15.2004	−0.536076
$805$	−2.69767	−0.0950804
$806$	19.1428	0.674276
$807$	27.3519	0.962831
$808$	59.9066	2.10751
$809$	−10.4234	−0.366467	−0.183233	−	0.983069i	$-0.558656\pi$
$809$	−10.4234	−0.366467	−0.183233	+	0.983069i	$0.558656\pi$
$810$	0.826132	0.0290273
$811$	34.1557	1.19937	0.599685	−	0.800236i	$-0.295293\pi$
$811$	34.1557	1.19937	0.599685	+	0.800236i	$0.295293\pi$
$812$	24.1846	0.848712
$813$	−5.85728	−0.205424
$814$	−50.3677	−1.76539
$815$	−1.16636	−0.0408556
$816$	−4.44249	−0.155518
$817$	17.9351	0.627468
$818$	18.2670	0.638689
$819$	−6.31056	−0.220509
$820$	2.25180	0.0786363
$821$	8.76077	0.305753	0.152877	−	0.988245i	$-0.451146\pi$
$821$	8.76077	0.305753	0.152877	+	0.988245i	$0.451146\pi$
$822$	8.84285	0.308430
$823$	−19.8115	−0.690586	−0.345293	−	0.938495i	$-0.612220\pi$
$823$	−19.8115	−0.690586	−0.345293	+	0.938495i	$0.612220\pi$
$824$	3.30831	0.115250
$825$	−21.5988	−0.751975
$826$	−2.06474	−0.0718414
$827$	−0.406444	−0.0141334	−0.00706672	−	0.999975i	$-0.502249\pi$
$827$	−0.406444	−0.0141334	−0.00706672	+	0.999975i	$0.502249\pi$
$828$	−27.9167	−0.970172
$829$	−1.70631	−0.0592626	−0.0296313	−	0.999561i	$-0.509433\pi$
$829$	−1.70631	−0.0592626	−0.0296313	+	0.999561i	$0.509433\pi$
$830$	10.5182	0.365091
$831$	−31.2960	−1.08565
$832$	−84.4010	−2.92608
$833$	−31.6448	−1.09643
$834$	−18.4402	−0.638533
$835$	−3.46436	−0.119889
$836$	72.1247	2.49448
$837$	1.21382	0.0419559
$838$	−19.0462	−0.657938
$839$	4.21249	0.145431	0.0727157	−	0.997353i	$-0.476833\pi$
$839$	4.21249	0.145431	0.0727157	+	0.997353i	$0.476833\pi$
$840$	1.09364	0.0377341
$841$	28.5812	0.985559
$842$	75.3540	2.59687
$843$	−22.3589	−0.770083
$844$	−37.3293	−1.28493
$845$	−11.6667	−0.401347
$846$	−7.08792	−0.243688
$847$	−8.04658	−0.276484
$848$	−5.20269	−0.178661
$849$	−15.1750	−0.520805
$850$	58.5638	2.00872
$851$	39.8383	1.36564
$852$	−41.4445	−1.41987
$853$	−39.7474	−1.36093	−0.680463	−	0.732783i	$-0.738221\pi$
$853$	−39.7474	−1.36093	−0.680463	+	0.732783i	$0.738221\pi$
$854$	−4.41659	−0.151133
$855$	1.68818	0.0577345
$856$	29.8410	1.01994
$857$	−30.6505	−1.04700	−0.523501	−	0.852025i	$-0.675374\pi$
$857$	−30.6505	−1.04700	−0.523501	+	0.852025i	$0.675374\pi$
$858$	−69.8852	−2.38584
$859$	−40.2091	−1.37192	−0.685959	−	0.727640i	$-0.740617\pi$
$859$	−40.2091	−1.37192	−0.685959	+	0.727640i	$0.740617\pi$
$860$	4.57566	0.156029
$861$	−1.72834	−0.0589016
$862$	−40.1395	−1.36716
$863$	8.45830	0.287924	0.143962	−	0.989583i	$-0.454016\pi$
$863$	8.45830	0.287924	0.143962	+	0.989583i	$0.454016\pi$
$864$	−4.61231	−0.156914
$865$	−1.04427	−0.0355063
$866$	−44.9181	−1.52638
$867$	−9.63157	−0.327105
$868$	3.86860	0.131309
$869$	28.4052	0.963580
$870$	6.26888	0.212535
$871$	30.0970	1.01980
$872$	−9.40168	−0.318381
$873$	−5.18853	−0.175605
$874$	−90.3988	−3.05778
$875$	−3.26412	−0.110347
$876$	10.0959	0.341110
$877$	−32.9806	−1.11367	−0.556837	−	0.830622i	$-0.687985\pi$
$877$	−32.9806	−1.11367	−0.556837	+	0.830622i	$0.687985\pi$
$878$	−27.4622	−0.926803
$879$	1.90181	0.0641465
$880$	1.35356	0.0456285
$881$	56.4373	1.90142	0.950710	−	0.310082i	$-0.100356\pi$
$881$	56.4373	1.90142	0.950710	+	0.310082i	$0.100356\pi$
$882$	14.2771	0.480735
$883$	23.1585	0.779346	0.389673	−	0.920953i	$-0.372588\pi$
$883$	23.1585	0.779346	0.389673	+	0.920953i	$0.372588\pi$
$884$	119.579	4.02187
$885$	−0.337743	−0.0113531
$886$	23.0802	0.775394
$887$	54.5885	1.83290	0.916452	−	0.400145i	$-0.131040\pi$
$887$	54.5885	1.83290	0.916452	+	0.400145i	$0.131040\pi$
$888$	−16.1505	−0.541975
$889$	20.3509	0.682547
$890$	11.9654	0.401081
$891$	−4.43135	−0.148456
$892$	40.3290	1.35031
$893$	−14.4840	−0.484688
$894$	−42.5229	−1.42218
$895$	5.20005	0.173819
$896$	−18.4346	−0.615857
$897$	55.2756	1.84560
$898$	0.699120	0.0233299
$899$	9.21078	0.307197
$900$	−16.6739	−0.555797
$901$	−31.1888	−1.03905
$902$	−19.1402	−0.637299
$903$	−3.51199	−0.116872
$904$	−2.37119	−0.0788645
$905$	−6.65465	−0.221208
$906$	35.2220	1.17017
$907$	−44.9341	−1.49201	−0.746007	−	0.665939i	$-0.768031\pi$
$907$	−44.9341	−1.49201	−0.746007	+	0.665939i	$0.768031\pi$
$908$	−45.3800	−1.50599
$909$	−18.1079	−0.600602
$910$	−5.21336	−0.172821
$911$	−34.3859	−1.13926	−0.569628	−	0.821903i	$-0.692913\pi$
$911$	−34.3859	−1.13926	−0.569628	+	0.821903i	$0.692913\pi$
$912$	4.09575	0.135624
$913$	−56.4192	−1.86720
$914$	−52.2977	−1.72986
$915$	−0.722452	−0.0238835
$916$	−82.6877	−2.73208
$917$	−5.63342	−0.186032
$918$	12.0153	0.396564
$919$	−12.5655	−0.414497	−0.207248	−	0.978288i	$-0.566451\pi$
$919$	−12.5655	−0.414497	−0.207248	+	0.978288i	$0.566451\pi$
$920$	−9.57944	−0.315825
$921$	33.7217	1.11117
$922$	44.6676	1.47105
$923$	82.0611	2.70107
$924$	−14.1232	−0.464620
$925$	23.7944	0.782354
$926$	−66.8020	−2.19525
$927$	−1.00000	−0.0328443
$928$	−34.9992	−1.14891
$929$	3.57840	0.117403	0.0587017	−	0.998276i	$-0.481304\pi$
$929$	3.57840	0.117403	0.0587017	+	0.998276i	$0.481304\pi$
$930$	1.00278	0.0328825
$931$	29.1748	0.956167
$932$	−69.6104	−2.28017
$933$	−27.9423	−0.914788
$934$	−39.7511	−1.30070
$935$	8.11424	0.265364
$936$	−22.4088	−0.732455
$937$	−6.93063	−0.226414	−0.113207	−	0.993571i	$-0.536112\pi$
$937$	−6.93063	−0.226414	−0.113207	+	0.993571i	$0.536112\pi$
$938$	9.63835	0.314703
$939$	−8.05949	−0.263011
$940$	−3.69521	−0.120524
$941$	42.5766	1.38796	0.693978	−	0.719996i	$-0.255856\pi$
$941$	42.5766	1.38796	0.693978	+	0.719996i	$0.255856\pi$
$942$	39.7657	1.29564
$943$	15.1389	0.492991
$944$	−0.819411	−0.0266696
$945$	−0.330574	−0.0107536
$946$	−38.8929	−1.26452
$947$	−44.1688	−1.43529	−0.717646	−	0.696408i	$-0.754781\pi$
$947$	−44.1688	−1.43529	−0.717646	+	0.696408i	$0.754781\pi$
$948$	21.9283	0.712197
$949$	−19.9902	−0.648908
$950$	−53.9928	−1.75176
$951$	17.1748	0.556930
$952$	15.9059	0.515515
$953$	−47.9473	−1.55317	−0.776583	−	0.630015i	$-0.783049\pi$
$953$	−47.9473	−1.55317	−0.776583	+	0.630015i	$0.783049\pi$
$954$	14.0714	0.455577
$955$	0.843870	0.0273070
$956$	21.7234	0.702584
$957$	−33.6261	−1.08698
$958$	8.28445	0.267658
$959$	−3.53843	−0.114262
$960$	−4.42128	−0.142696
$961$	−29.5266	−0.952472
$962$	76.9890	2.48223
$963$	−9.02002	−0.290666
$964$	−81.9958	−2.64091
$965$	−1.11885	−0.0360170
$966$	17.7016	0.569540
$967$	14.4169	0.463615	0.231807	−	0.972762i	$-0.425536\pi$
$967$	14.4169	0.463615	0.231807	+	0.972762i	$0.425536\pi$
$968$	−28.5734	−0.918385
$969$	24.5529	0.788754
$970$	−4.28641	−0.137628
$971$	−42.4989	−1.36386	−0.681928	−	0.731419i	$-0.738858\pi$
$971$	−42.4989	−1.36386	−0.681928	+	0.731419i	$0.738858\pi$
$972$	−3.42092	−0.109726
$973$	7.37879	0.236553
$974$	24.4673	0.783982
$975$	33.0147	1.05732
$976$	−1.75277	−0.0561047
$977$	−26.4519	−0.846270	−0.423135	−	0.906067i	$-0.639070\pi$
$977$	−26.4519	−0.846270	−0.423135	+	0.906067i	$0.639070\pi$
$978$	7.65339	0.244729
$979$	−64.1820	−2.05127
$980$	7.44320	0.237764
$981$	2.84184	0.0907329
$982$	−4.68733	−0.149579
$983$	−16.3761	−0.522316	−0.261158	−	0.965296i	$-0.584104\pi$
$983$	−16.3761	−0.522316	−0.261158	+	0.965296i	$0.584104\pi$
$984$	−6.13733	−0.195651
$985$	1.65521	0.0527394
$986$	91.1749	2.90360
$987$	2.83621	0.0902774
$988$	−110.245	−3.50737
$989$	30.7623	0.978184
$990$	−3.66088	−0.116350
$991$	37.5708	1.19347	0.596737	−	0.802437i	$-0.296464\pi$
$991$	37.5708	1.19347	0.596737	+	0.802437i	$0.296464\pi$
$992$	−5.59853	−0.177754
$993$	−31.3536	−0.994976
$994$	26.2794	0.833533
$995$	−3.59332	−0.113916
$996$	−43.5545	−1.38008
$997$	−49.4836	−1.56716	−0.783581	−	0.621290i	$-0.786609\pi$
$997$	−49.4836	−1.56716	−0.783581	+	0.621290i	$0.786609\pi$
$998$	33.6150	1.06406
$999$	4.88180	0.154453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.2.a.c.1.1	✓	5
3.2	odd	2		927.2.a.e.1.5		5
4.3	odd	2		4944.2.a.bb.1.4		5
5.4	even	2		7725.2.a.t.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.a.c.1.1	✓	5	1.1	even	1	trivial
927.2.a.e.1.5		5	3.2	odd	2
4944.2.a.bb.1.4		5	4.3	odd	2
7725.2.a.t.1.5		5	5.4	even	2

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32829 q^{2} -1.00000 q^{3} +3.42092 q^{4} -0.354824 q^{5} +2.32829 q^{6} -0.931655 q^{7} -3.30831 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.32829 q^{2} -1.00000 q^{3} +3.42092 q^{4} -0.354824 q^{5} +2.32829 q^{6} -0.931655 q^{7} -3.30831 q^{8} +1.00000 q^{9} +0.826132 q^{10} -4.43135 q^{11} -3.42092 q^{12} +6.77349 q^{13} +2.16916 q^{14} +0.354824 q^{15} +0.860851 q^{16} +5.16058 q^{17} -2.32829 q^{18} -4.75779 q^{19} -1.21382 q^{20} +0.931655 q^{21} +10.3175 q^{22} -8.16058 q^{23} +3.30831 q^{24} -4.87410 q^{25} -15.7706 q^{26} -1.00000 q^{27} -3.18712 q^{28} -7.58823 q^{29} -0.826132 q^{30} -1.21382 q^{31} +4.61231 q^{32} +4.43135 q^{33} -12.0153 q^{34} +0.330574 q^{35} +3.42092 q^{36} -4.88180 q^{37} +11.0775 q^{38} -6.77349 q^{39} +1.17387 q^{40} -1.85513 q^{41} -2.16916 q^{42} -3.76962 q^{43} -15.1593 q^{44} -0.354824 q^{45} +19.0002 q^{46} +3.04427 q^{47} -0.860851 q^{48} -6.13202 q^{49} +11.3483 q^{50} -5.16058 q^{51} +23.1716 q^{52} -6.04366 q^{53} +2.32829 q^{54} +1.57235 q^{55} +3.08220 q^{56} +4.75779 q^{57} +17.6676 q^{58} -0.951861 q^{59} +1.21382 q^{60} -2.03608 q^{61} +2.82613 q^{62} -0.931655 q^{63} -12.4605 q^{64} -2.40340 q^{65} -10.3175 q^{66} +4.44336 q^{67} +17.6539 q^{68} +8.16058 q^{69} -0.769670 q^{70} +12.1150 q^{71} -3.30831 q^{72} -2.95123 q^{73} +11.3662 q^{74} +4.87410 q^{75} -16.2760 q^{76} +4.12849 q^{77} +15.7706 q^{78} -6.41005 q^{79} -0.305451 q^{80} +1.00000 q^{81} +4.31927 q^{82} +12.7318 q^{83} +3.18712 q^{84} -1.83110 q^{85} +8.77676 q^{86} +7.58823 q^{87} +14.6603 q^{88} +14.4836 q^{89} +0.826132 q^{90} -6.31056 q^{91} -27.9167 q^{92} +1.21382 q^{93} -7.08792 q^{94} +1.68818 q^{95} -4.61231 q^{96} -5.18853 q^{97} +14.2771 q^{98} -4.43135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 5 q^{3} + 2 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 5 * q^3 + 2 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 2 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 5 q^{9} - q^{10} - 12 q^{11} - 2 q^{12} + q^{13} - 8 q^{14} + 5 q^{15} - 4 q^{16} - 10 q^{17} - 2 q^{18} - 16 q^{19} - 13 q^{20} + 2 q^{21} + 4 q^{22} - 5 q^{23} + 6 q^{24} + 12 q^{25} - 10 q^{26} - 5 q^{27} + 7 q^{28} - 16 q^{29} + q^{30} - 13 q^{31} + 11 q^{32} + 12 q^{33} - 2 q^{34} - 22 q^{35} + 2 q^{36} + 4 q^{37} + 21 q^{38} - q^{39} + 11 q^{40} - 20 q^{41} + 8 q^{42} + 7 q^{43} + 2 q^{44} - 5 q^{45} + 8 q^{46} + 8 q^{47} + 4 q^{48} + 23 q^{49} + 13 q^{50} + 10 q^{51} + 31 q^{52} - 8 q^{53} + 2 q^{54} - 6 q^{55} + 5 q^{56} + 16 q^{57} + 20 q^{58} - 19 q^{59} + 13 q^{60} - 19 q^{61} + 9 q^{62} - 2 q^{63} - 16 q^{64} + q^{65} - 4 q^{66} + 11 q^{67} + 15 q^{68} + 5 q^{69} + 44 q^{70} - 10 q^{71} - 6 q^{72} + 20 q^{73} + 44 q^{74} - 12 q^{75} - 8 q^{76} + 8 q^{77} + 10 q^{78} - 14 q^{79} + 45 q^{80} + 5 q^{81} - 3 q^{82} - 11 q^{83} - 7 q^{84} + 12 q^{85} - 11 q^{86} + 16 q^{87} + 30 q^{88} + 22 q^{89} - q^{90} - 42 q^{91} - 21 q^{92} + 13 q^{93} - 6 q^{94} - 10 q^{95} - 11 q^{96} + 7 q^{97} - 11 q^{98} - 12 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 2 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 5 * q^9 - q^10 - 12 * q^11 - 2 * q^12 + q^13 - 8 * q^14 + 5 * q^15 - 4 * q^16 - 10 * q^17 - 2 * q^18 - 16 * q^19 - 13 * q^20 + 2 * q^21 + 4 * q^22 - 5 * q^23 + 6 * q^24 + 12 * q^25 - 10 * q^26 - 5 * q^27 + 7 * q^28 - 16 * q^29 + q^30 - 13 * q^31 + 11 * q^32 + 12 * q^33 - 2 * q^34 - 22 * q^35 + 2 * q^36 + 4 * q^37 + 21 * q^38 - q^39 + 11 * q^40 - 20 * q^41 + 8 * q^42 + 7 * q^43 + 2 * q^44 - 5 * q^45 + 8 * q^46 + 8 * q^47 + 4 * q^48 + 23 * q^49 + 13 * q^50 + 10 * q^51 + 31 * q^52 - 8 * q^53 + 2 * q^54 - 6 * q^55 + 5 * q^56 + 16 * q^57 + 20 * q^58 - 19 * q^59 + 13 * q^60 - 19 * q^61 + 9 * q^62 - 2 * q^63 - 16 * q^64 + q^65 - 4 * q^66 + 11 * q^67 + 15 * q^68 + 5 * q^69 + 44 * q^70 - 10 * q^71 - 6 * q^72 + 20 * q^73 + 44 * q^74 - 12 * q^75 - 8 * q^76 + 8 * q^77 + 10 * q^78 - 14 * q^79 + 45 * q^80 + 5 * q^81 - 3 * q^82 - 11 * q^83 - 7 * q^84 + 12 * q^85 - 11 * q^86 + 16 * q^87 + 30 * q^88 + 22 * q^89 - q^90 - 42 * q^91 - 21 * q^92 + 13 * q^93 - 6 * q^94 - 10 * q^95 - 11 * q^96 + 7 * q^97 - 11 * q^98 - 12 * q^99

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