LMFDB - Embedded newform 1205.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
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			$-2.07008$ of defining polynomial
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58701 q^{2} -2.62253 q^{3} +4.69261 q^{4} +1.00000 q^{5} +6.78451 q^{6} -4.29833 q^{7} -6.96581 q^{8} +3.87767 q^{9} +O(q^{10})$	\(q-2.58701 q^{2} -2.62253 q^{3} +4.69261 q^{4} +1.00000 q^{5} +6.78451 q^{6} -4.29833 q^{7} -6.96581 q^{8} +3.87767 q^{9} -2.58701 q^{10} +0.392733 q^{11} -12.3065 q^{12} +3.86215 q^{13} +11.1198 q^{14} -2.62253 q^{15} +8.63539 q^{16} +2.28113 q^{17} -10.0316 q^{18} -6.51433 q^{19} +4.69261 q^{20} +11.2725 q^{21} -1.01600 q^{22} -3.95733 q^{23} +18.2681 q^{24} +1.00000 q^{25} -9.99141 q^{26} -2.30173 q^{27} -20.1704 q^{28} -2.20828 q^{29} +6.78451 q^{30} +0.970075 q^{31} -8.40821 q^{32} -1.02995 q^{33} -5.90130 q^{34} -4.29833 q^{35} +18.1964 q^{36} +3.07546 q^{37} +16.8526 q^{38} -10.1286 q^{39} -6.96581 q^{40} +8.48761 q^{41} -29.1621 q^{42} +4.56989 q^{43} +1.84294 q^{44} +3.87767 q^{45} +10.2376 q^{46} +10.9885 q^{47} -22.6466 q^{48} +11.4757 q^{49} -2.58701 q^{50} -5.98233 q^{51} +18.1236 q^{52} +0.970867 q^{53} +5.95460 q^{54} +0.392733 q^{55} +29.9414 q^{56} +17.0840 q^{57} +5.71284 q^{58} +2.47906 q^{59} -12.3065 q^{60} -8.72003 q^{61} -2.50959 q^{62} -16.6675 q^{63} +4.48133 q^{64} +3.86215 q^{65} +2.66450 q^{66} -14.8157 q^{67} +10.7045 q^{68} +10.3782 q^{69} +11.1198 q^{70} +7.87706 q^{71} -27.0112 q^{72} +5.53782 q^{73} -7.95625 q^{74} -2.62253 q^{75} -30.5692 q^{76} -1.68810 q^{77} +26.2028 q^{78} +1.20590 q^{79} +8.63539 q^{80} -5.59666 q^{81} -21.9575 q^{82} +10.3757 q^{83} +52.8976 q^{84} +2.28113 q^{85} -11.8223 q^{86} +5.79128 q^{87} -2.73570 q^{88} -15.3272 q^{89} -10.0316 q^{90} -16.6008 q^{91} -18.5702 q^{92} -2.54405 q^{93} -28.4273 q^{94} -6.51433 q^{95} +22.0508 q^{96} -6.20641 q^{97} -29.6877 q^{98} +1.52289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9	\( 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 28 q^{12} - 9 q^{13} + 2 q^{14} - 8 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} - 33 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{22} - 31 q^{23} + 32 q^{24} + 11 q^{25} - 20 q^{26} - 32 q^{27} - q^{28} + q^{29} + 7 q^{30} + 6 q^{31} + 7 q^{32} - 35 q^{33} + 9 q^{34} - 9 q^{35} + 33 q^{36} - 23 q^{37} + 20 q^{38} + 14 q^{39} - 12 q^{40} + 8 q^{41} - 26 q^{42} - 19 q^{43} + 9 q^{45} + 6 q^{46} - 35 q^{47} + 16 q^{48} + 4 q^{49} - 4 q^{50} - 3 q^{51} - 3 q^{52} + 14 q^{53} + 9 q^{54} - 3 q^{55} + 33 q^{56} + q^{57} - 11 q^{58} - 6 q^{59} - 28 q^{60} + 9 q^{61} - 23 q^{62} - 31 q^{63} + 18 q^{64} - 9 q^{65} - 36 q^{66} - 54 q^{67} + q^{68} + 17 q^{69} + 2 q^{70} - 5 q^{71} - 64 q^{72} + 17 q^{73} + 8 q^{74} - 8 q^{75} - 31 q^{76} - 18 q^{77} + 15 q^{78} - 16 q^{79} - 16 q^{80} + 43 q^{81} - 61 q^{82} - 29 q^{83} + 69 q^{84} - 4 q^{85} + 5 q^{86} + 5 q^{87} - 14 q^{88} - 5 q^{89} - 6 q^{90} - 54 q^{91} - 6 q^{92} - 25 q^{93} - 19 q^{94} - 33 q^{95} + 9 q^{96} + 6 q^{97} - 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 28 * q^12 - 9 * q^13 + 2 * q^14 - 8 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 - 33 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^22 - 31 * q^23 + 32 * q^24 + 11 * q^25 - 20 * q^26 - 32 * q^27 - q^28 + q^29 + 7 * q^30 + 6 * q^31 + 7 * q^32 - 35 * q^33 + 9 * q^34 - 9 * q^35 + 33 * q^36 - 23 * q^37 + 20 * q^38 + 14 * q^39 - 12 * q^40 + 8 * q^41 - 26 * q^42 - 19 * q^43 + 9 * q^45 + 6 * q^46 - 35 * q^47 + 16 * q^48 + 4 * q^49 - 4 * q^50 - 3 * q^51 - 3 * q^52 + 14 * q^53 + 9 * q^54 - 3 * q^55 + 33 * q^56 + q^57 - 11 * q^58 - 6 * q^59 - 28 * q^60 + 9 * q^61 - 23 * q^62 - 31 * q^63 + 18 * q^64 - 9 * q^65 - 36 * q^66 - 54 * q^67 + q^68 + 17 * q^69 + 2 * q^70 - 5 * q^71 - 64 * q^72 + 17 * q^73 + 8 * q^74 - 8 * q^75 - 31 * q^76 - 18 * q^77 + 15 * q^78 - 16 * q^79 - 16 * q^80 + 43 * q^81 - 61 * q^82 - 29 * q^83 + 69 * q^84 - 4 * q^85 + 5 * q^86 + 5 * q^87 - 14 * q^88 - 5 * q^89 - 6 * q^90 - 54 * q^91 - 6 * q^92 - 25 * q^93 - 19 * q^94 - 33 * q^95 + 9 * q^96 + 6 * q^97 - 29 * q^98 + 60 * 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 $

$2$	−2.58701	−1.82929	−0.914646	−	0.404256i	$-0.867530\pi$
$2$	−2.58701	−1.82929	−0.914646	+	0.404256i	$0.867530\pi$
$3$	−2.62253	−1.51412	−0.757060	−	0.653346i	$-0.773365\pi$
$3$	−2.62253	−1.51412	−0.757060	+	0.653346i	$0.773365\pi$
$4$	4.69261	2.34631
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	6.78451	2.76977
$7$	−4.29833	−1.62462	−0.812309	−	0.583228i	$-0.801790\pi$
$7$	−4.29833	−1.62462	−0.812309	+	0.583228i	$0.801790\pi$
$8$	−6.96581	−2.46279
$9$	3.87767	1.29256
$10$	−2.58701	−0.818084
$11$	0.392733	0.118413	0.0592067	−	0.998246i	$-0.481143\pi$
$11$	0.392733	0.118413	0.0592067	+	0.998246i	$0.481143\pi$
$12$	−12.3065	−3.55259
$13$	3.86215	1.07117	0.535584	−	0.844482i	$-0.320092\pi$
$13$	3.86215	1.07117	0.535584	+	0.844482i	$0.320092\pi$
$14$	11.1198	2.97190
$15$	−2.62253	−0.677135
$16$	8.63539	2.15885
$17$	2.28113	0.553255	0.276627	−	0.960977i	$-0.410783\pi$
$17$	2.28113	0.553255	0.276627	+	0.960977i	$0.410783\pi$
$18$	−10.0316	−2.36447
$19$	−6.51433	−1.49449	−0.747245	−	0.664549i	$-0.768624\pi$
$19$	−6.51433	−1.49449	−0.747245	+	0.664549i	$0.768624\pi$
$20$	4.69261	1.04930
$21$	11.2725	2.45987
$22$	−1.01600	−0.216613
$23$	−3.95733	−0.825159	−0.412580	−	0.910921i	$-0.635372\pi$
$23$	−3.95733	−0.825159	−0.412580	+	0.910921i	$0.635372\pi$
$24$	18.2681	3.72895
$25$	1.00000	0.200000
$26$	−9.99141	−1.95948
$27$	−2.30173	−0.442968
$28$	−20.1704	−3.81185
$29$	−2.20828	−0.410067	−0.205034	−	0.978755i	$-0.565730\pi$
$29$	−2.20828	−0.410067	−0.205034	+	0.978755i	$0.565730\pi$
$30$	6.78451	1.23868
$31$	0.970075	0.174231	0.0871153	−	0.996198i	$-0.472235\pi$
$31$	0.970075	0.174231	0.0871153	+	0.996198i	$0.472235\pi$
$32$	−8.40821	−1.48638
$33$	−1.02995	−0.179292
$34$	−5.90130	−1.01206
$35$	−4.29833	−0.726551
$36$	18.1964	3.03274
$37$	3.07546	0.505603	0.252802	−	0.967518i	$-0.418648\pi$
$37$	3.07546	0.505603	0.252802	+	0.967518i	$0.418648\pi$
$38$	16.8526	2.73386
$39$	−10.1286	−1.62188
$40$	−6.96581	−1.10139
$41$	8.48761	1.32554	0.662771	−	0.748822i	$-0.269380\pi$
$41$	8.48761	1.32554	0.662771	+	0.748822i	$0.269380\pi$
$42$	−29.1621	−4.49981
$43$	4.56989	0.696901	0.348450	−	0.937327i	$-0.386708\pi$
$43$	4.56989	0.696901	0.348450	+	0.937327i	$0.386708\pi$
$44$	1.84294	0.277834
$45$	3.87767	0.578050
$46$	10.2376	1.50946
$47$	10.9885	1.60284	0.801419	−	0.598104i	$-0.204079\pi$
$47$	10.9885	1.60284	0.801419	+	0.598104i	$0.204079\pi$
$48$	−22.6466	−3.26876
$49$	11.4757	1.63938
$50$	−2.58701	−0.365858
$51$	−5.98233	−0.837694
$52$	18.1236	2.51329
$53$	0.970867	0.133359	0.0666794	−	0.997774i	$-0.478760\pi$
$53$	0.970867	0.133359	0.0666794	+	0.997774i	$0.478760\pi$
$54$	5.95460	0.810318
$55$	0.392733	0.0529561
$56$	29.9414	4.00109
$57$	17.0840	2.26284
$58$	5.71284	0.750132
$59$	2.47906	0.322746	0.161373	−	0.986893i	$-0.448408\pi$
$59$	2.47906	0.322746	0.161373	+	0.986893i	$0.448408\pi$
$60$	−12.3065	−1.58877
$61$	−8.72003	−1.11649	−0.558243	−	0.829678i	$-0.688524\pi$
$61$	−8.72003	−1.11649	−0.558243	+	0.829678i	$0.688524\pi$
$62$	−2.50959	−0.318718
$63$	−16.6675	−2.09991
$64$	4.48133	0.560166
$65$	3.86215	0.479041
$66$	2.66450	0.327977
$67$	−14.8157	−1.81003	−0.905014	−	0.425381i	$-0.860140\pi$
$67$	−14.8157	−1.81003	−0.905014	+	0.425381i	$0.860140\pi$
$68$	10.7045	1.29811
$69$	10.3782	1.24939
$70$	11.1198	1.32907
$71$	7.87706	0.934834	0.467417	−	0.884037i	$-0.345185\pi$
$71$	7.87706	0.934834	0.467417	+	0.884037i	$0.345185\pi$
$72$	−27.0112	−3.18330
$73$	5.53782	0.648153	0.324076	−	0.946031i	$-0.394947\pi$
$73$	5.53782	0.648153	0.324076	+	0.946031i	$0.394947\pi$
$74$	−7.95625	−0.924896
$75$	−2.62253	−0.302824
$76$	−30.5692	−3.50653
$77$	−1.68810	−0.192377
$78$	26.2028	2.96688
$79$	1.20590	0.135675	0.0678373	−	0.997696i	$-0.478390\pi$
$79$	1.20590	0.135675	0.0678373	+	0.997696i	$0.478390\pi$
$80$	8.63539	0.965466
$81$	−5.59666	−0.621851
$82$	−21.9575	−2.42480
$83$	10.3757	1.13888	0.569442	−	0.822031i	$-0.307159\pi$
$83$	10.3757	1.13888	0.569442	+	0.822031i	$0.307159\pi$
$84$	52.8976	5.77160
$85$	2.28113	0.247423
$86$	−11.8223	−1.27483
$87$	5.79128	0.620891
$88$	−2.73570	−0.291627
$89$	−15.3272	−1.62468	−0.812339	−	0.583186i	$-0.801806\pi$
$89$	−15.3272	−1.62468	−0.812339	+	0.583186i	$0.801806\pi$
$90$	−10.0316	−1.05742
$91$	−16.6008	−1.74024
$92$	−18.5702	−1.93608
$93$	−2.54405	−0.263806
$94$	−28.4273	−2.93206
$95$	−6.51433	−0.668356
$96$	22.0508	2.25055
$97$	−6.20641	−0.630165	−0.315083	−	0.949064i	$-0.602032\pi$
$97$	−6.20641	−0.630165	−0.315083	+	0.949064i	$0.602032\pi$
$98$	−29.6877	−2.99891
$99$	1.52289	0.153056
$100$	4.69261	0.469261
$101$	6.33910	0.630764	0.315382	−	0.948965i	$-0.397867\pi$
$101$	6.33910	0.630764	0.315382	+	0.948965i	$0.397867\pi$
$102$	15.4763	1.53239
$103$	−17.2615	−1.70082	−0.850412	−	0.526118i	$-0.823647\pi$
$103$	−17.2615	−1.70082	−0.850412	+	0.526118i	$0.823647\pi$
$104$	−26.9030	−2.63806
$105$	11.2725	1.10009
$106$	−2.51164	−0.243952
$107$	20.1199	1.94507	0.972533	−	0.232764i	$-0.0747769\pi$
$107$	20.1199	1.94507	0.972533	+	0.232764i	$0.0747769\pi$
$108$	−10.8011	−1.03934
$109$	2.66248	0.255019	0.127510	−	0.991837i	$-0.459302\pi$
$109$	2.66248	0.255019	0.127510	+	0.991837i	$0.459302\pi$
$110$	−1.01600	−0.0968721
$111$	−8.06550	−0.765544
$112$	−37.1178	−3.50730
$113$	−18.1521	−1.70761	−0.853803	−	0.520596i	$-0.825710\pi$
$113$	−18.1521	−1.70761	−0.853803	+	0.520596i	$0.825710\pi$
$114$	−44.1966	−4.13939
$115$	−3.95733	−0.369023
$116$	−10.3626	−0.962143
$117$	14.9762	1.38455
$118$	−6.41335	−0.590397
$119$	−9.80505	−0.898828
$120$	18.2681	1.66764
$121$	−10.8458	−0.985978
$122$	22.5588	2.04238
$123$	−22.2590	−2.00703
$124$	4.55218	0.408798
$125$	1.00000	0.0894427
$126$	43.1191	3.84135
$127$	−10.1820	−0.903506	−0.451753	−	0.892143i	$-0.649201\pi$
$127$	−10.1820	−0.903506	−0.451753	+	0.892143i	$0.649201\pi$
$128$	5.22319	0.461669
$129$	−11.9847	−1.05519
$130$	−9.99141	−0.876305
$131$	12.2069	1.06652	0.533261	−	0.845951i	$-0.320966\pi$
$131$	12.2069	1.06652	0.533261	+	0.845951i	$0.320966\pi$
$132$	−4.83318	−0.420674
$133$	28.0008	2.42797
$134$	38.3284	3.31107
$135$	−2.30173	−0.198101
$136$	−15.8899	−1.36255
$137$	−13.4160	−1.14621	−0.573105	−	0.819482i	$-0.694261\pi$
$137$	−13.4160	−1.14621	−0.573105	+	0.819482i	$0.694261\pi$
$138$	−26.8485	−2.28550
$139$	−11.6854	−0.991147	−0.495573	−	0.868566i	$-0.665042\pi$
$139$	−11.6854	−0.991147	−0.495573	+	0.868566i	$0.665042\pi$
$140$	−20.1704	−1.70471
$141$	−28.8177	−2.42689
$142$	−20.3780	−1.71008
$143$	1.51679	0.126841
$144$	33.4853	2.79044
$145$	−2.20828	−0.183388
$146$	−14.3264	−1.18566
$147$	−30.0953	−2.48222
$148$	14.4320	1.18630
$149$	−11.5450	−0.945805	−0.472902	−	0.881115i	$-0.656794\pi$
$149$	−11.5450	−0.945805	−0.472902	+	0.881115i	$0.656794\pi$
$150$	6.78451	0.553953
$151$	7.09477	0.577364	0.288682	−	0.957425i	$-0.406783\pi$
$151$	7.09477	0.577364	0.288682	+	0.957425i	$0.406783\pi$
$152$	45.3776	3.68061
$153$	8.84547	0.715114
$154$	4.36712	0.351913
$155$	0.970075	0.0779183
$156$	−47.5296	−3.80542
$157$	−22.5748	−1.80166	−0.900831	−	0.434170i	$-0.857042\pi$
$157$	−22.5748	−1.80166	−0.900831	+	0.434170i	$0.857042\pi$
$158$	−3.11968	−0.248188
$159$	−2.54613	−0.201921
$160$	−8.40821	−0.664727
$161$	17.0099	1.34057
$162$	14.4786	1.13755
$163$	−17.8281	−1.39640	−0.698201	−	0.715902i	$-0.746016\pi$
$163$	−17.8281	−1.39640	−0.698201	+	0.715902i	$0.746016\pi$
$164$	39.8291	3.11013
$165$	−1.02995	−0.0801819
$166$	−26.8421	−2.08335
$167$	−10.3380	−0.799981	−0.399990	−	0.916519i	$-0.630987\pi$
$167$	−10.3380	−0.799981	−0.399990	+	0.916519i	$0.630987\pi$
$168$	−78.5223	−6.05813
$169$	1.91619	0.147399
$170$	−5.90130	−0.452609
$171$	−25.2605	−1.93171
$172$	21.4447	1.63514
$173$	4.53402	0.344715	0.172358	−	0.985034i	$-0.444862\pi$
$173$	4.53402	0.344715	0.172358	+	0.985034i	$0.444862\pi$
$174$	−14.9821	−1.13579
$175$	−4.29833	−0.324924
$176$	3.39140	0.255637
$177$	−6.50142	−0.488676
$178$	39.6515	2.97201
$179$	9.96262	0.744641	0.372321	−	0.928104i	$-0.378562\pi$
$179$	9.96262	0.744641	0.372321	+	0.928104i	$0.378562\pi$
$180$	18.1964	1.35628
$181$	−12.5806	−0.935111	−0.467555	−	0.883964i	$-0.654865\pi$
$181$	−12.5806	−0.935111	−0.467555	+	0.883964i	$0.654865\pi$
$182$	42.9464	3.18340
$183$	22.8686	1.69049
$184$	27.5660	2.03219
$185$	3.07546	0.226113
$186$	6.58148	0.482578
$187$	0.895874	0.0655128
$188$	51.5648	3.76075
$189$	9.89361	0.719654
$190$	16.8526	1.22262
$191$	−13.6635	−0.988658	−0.494329	−	0.869275i	$-0.664586\pi$
$191$	−13.6635	−0.988658	−0.494329	+	0.869275i	$0.664586\pi$
$192$	−11.7524	−0.848158
$193$	22.7940	1.64075	0.820375	−	0.571826i	$-0.193765\pi$
$193$	22.7940	1.64075	0.820375	+	0.571826i	$0.193765\pi$
$194$	16.0560	1.15276
$195$	−10.1286	−0.725325
$196$	53.8509	3.84649
$197$	3.68078	0.262245	0.131123	−	0.991366i	$-0.458142\pi$
$197$	3.68078	0.262245	0.131123	+	0.991366i	$0.458142\pi$
$198$	−3.93973	−0.279984
$199$	10.9051	0.773044	0.386522	−	0.922280i	$-0.373676\pi$
$199$	10.9051	0.773044	0.386522	+	0.922280i	$0.373676\pi$
$200$	−6.96581	−0.492557
$201$	38.8547	2.74060
$202$	−16.3993	−1.15385
$203$	9.49192	0.666202
$204$	−28.0728	−1.96549
$205$	8.48761	0.592800
$206$	44.6556	3.11130
$207$	−15.3452	−1.06657
$208$	33.3512	2.31249
$209$	−2.55839	−0.176968
$210$	−29.1621	−2.01238
$211$	14.0951	0.970349	0.485174	−	0.874417i	$-0.338756\pi$
$211$	14.0951	0.970349	0.485174	+	0.874417i	$0.338756\pi$
$212$	4.55590	0.312901
$213$	−20.6578	−1.41545
$214$	−52.0504	−3.55809
$215$	4.56989	0.311664
$216$	16.0334	1.09094
$217$	−4.16970	−0.283058
$218$	−6.88785	−0.466504
$219$	−14.5231	−0.981380
$220$	1.84294	0.124251
$221$	8.81006	0.592628
$222$	20.8655	1.40040
$223$	16.6721	1.11645	0.558224	−	0.829691i	$-0.311483\pi$
$223$	16.6721	1.11645	0.558224	+	0.829691i	$0.311483\pi$
$224$	36.1413	2.41479
$225$	3.87767	0.258512
$226$	46.9596	3.12371
$227$	−19.0910	−1.26711	−0.633556	−	0.773697i	$-0.718405\pi$
$227$	−19.0910	−1.26711	−0.633556	+	0.773697i	$0.718405\pi$
$228$	80.1688	5.30931
$229$	−17.4855	−1.15547	−0.577736	−	0.816224i	$-0.696064\pi$
$229$	−17.4855	−1.15547	−0.577736	+	0.816224i	$0.696064\pi$
$230$	10.2376	0.675050
$231$	4.42709	0.291281
$232$	15.3825	1.00991
$233$	−25.9768	−1.70180	−0.850898	−	0.525332i	$-0.823941\pi$
$233$	−25.9768	−1.70180	−0.850898	+	0.525332i	$0.823941\pi$
$234$	−38.7434	−2.53274
$235$	10.9885	0.716811
$236$	11.6333	0.757262
$237$	−3.16252	−0.205428
$238$	25.3658	1.64422
$239$	−21.9518	−1.41995	−0.709973	−	0.704229i	$-0.751293\pi$
$239$	−21.9518	−1.41995	−0.709973	+	0.704229i	$0.751293\pi$
$240$	−22.6466	−1.46183
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	28.0581	1.80364
$243$	21.5826	1.38453
$244$	−40.9197	−2.61962
$245$	11.4757	0.733154
$246$	57.5843	3.67144
$247$	−25.1593	−1.60085
$248$	−6.75736	−0.429093
$249$	−27.2107	−1.72441
$250$	−2.58701	−0.163617
$251$	−21.8198	−1.37725	−0.688626	−	0.725116i	$-0.741786\pi$
$251$	−21.8198	−1.37725	−0.688626	+	0.725116i	$0.741786\pi$
$252$	−78.2143	−4.92704
$253$	−1.55417	−0.0977100
$254$	26.3409	1.65278
$255$	−5.98233	−0.374628
$256$	−22.4751	−1.40469
$257$	−14.1109	−0.880212	−0.440106	−	0.897946i	$-0.645059\pi$
$257$	−14.1109	−0.880212	−0.440106	+	0.897946i	$0.645059\pi$
$258$	31.0044	1.93025
$259$	−13.2194	−0.821412
$260$	18.1236	1.12398
$261$	−8.56299	−0.530036
$262$	−31.5793	−1.95098
$263$	22.9481	1.41504	0.707521	−	0.706692i	$-0.249813\pi$
$263$	22.9481	1.41504	0.707521	+	0.706692i	$0.249813\pi$
$264$	7.17447	0.441558
$265$	0.970867	0.0596399
$266$	−72.4382	−4.44147
$267$	40.1960	2.45996
$268$	−69.5245	−4.24688
$269$	−23.8837	−1.45621	−0.728106	−	0.685465i	$-0.759599\pi$
$269$	−23.8837	−1.45621	−0.728106	+	0.685465i	$0.759599\pi$
$270$	5.95460	0.362385
$271$	9.08280	0.551741	0.275870	−	0.961195i	$-0.411034\pi$
$271$	9.08280	0.551741	0.275870	+	0.961195i	$0.411034\pi$
$272$	19.6984	1.19439
$273$	43.5361	2.63493
$274$	34.7074	2.09675
$275$	0.392733	0.0236827
$276$	48.7009	2.93145
$277$	−3.96886	−0.238466	−0.119233	−	0.992866i	$-0.538043\pi$
$277$	−3.96886	−0.238466	−0.119233	+	0.992866i	$0.538043\pi$
$278$	30.2304	1.81310
$279$	3.76163	0.225203
$280$	29.9414	1.78934
$281$	18.1150	1.08065	0.540324	−	0.841457i	$-0.318302\pi$
$281$	18.1150	1.08065	0.540324	+	0.841457i	$0.318302\pi$
$282$	74.5516	4.43948
$283$	−6.95776	−0.413596	−0.206798	−	0.978384i	$-0.566304\pi$
$283$	−6.95776	−0.413596	−0.206798	+	0.978384i	$0.566304\pi$
$284$	36.9640	2.19341
$285$	17.0840	1.01197
$286$	−3.92396	−0.232028
$287$	−36.4826	−2.15350
$288$	−32.6043	−1.92123
$289$	−11.7965	−0.693909
$290$	5.71284	0.335469
$291$	16.2765	0.954146
$292$	25.9868	1.52076
$293$	22.1972	1.29678	0.648388	−	0.761310i	$-0.275444\pi$
$293$	22.1972	1.29678	0.648388	+	0.761310i	$0.275444\pi$
$294$	77.8569	4.54071
$295$	2.47906	0.144336
$296$	−21.4231	−1.24519
$297$	−0.903965	−0.0524534
$298$	29.8671	1.73015
$299$	−15.2838	−0.883884
$300$	−12.3065	−0.710518
$301$	−19.6429	−1.13220
$302$	−18.3542	−1.05617
$303$	−16.6245	−0.955052
$304$	−56.2538	−3.22638
$305$	−8.72003	−0.499308
$306$	−22.8833	−1.30815
$307$	−0.442232	−0.0252395	−0.0126197	−	0.999920i	$-0.504017\pi$
$307$	−0.442232	−0.0252395	−0.0126197	+	0.999920i	$0.504017\pi$
$308$	−7.92159	−0.451374
$309$	45.2688	2.57525
$310$	−2.50959	−0.142535
$311$	18.1575	1.02962	0.514810	−	0.857304i	$-0.327863\pi$
$311$	18.1575	1.02962	0.514810	+	0.857304i	$0.327863\pi$
$312$	70.5540	3.99433
$313$	18.3438	1.03685	0.518427	−	0.855122i	$-0.326518\pi$
$313$	18.3438	1.03685	0.518427	+	0.855122i	$0.326518\pi$
$314$	58.4011	3.29576
$315$	−16.6675	−0.939110
$316$	5.65883	0.318334
$317$	−21.2335	−1.19259	−0.596296	−	0.802765i	$-0.703362\pi$
$317$	−21.2335	−1.19259	−0.596296	+	0.802765i	$0.703362\pi$
$318$	6.58686	0.369373
$319$	−0.867264	−0.0485575
$320$	4.48133	0.250514
$321$	−52.7652	−2.94506
$322$	−44.0048	−2.45229
$323$	−14.8600	−0.826834
$324$	−26.2630	−1.45905
$325$	3.86215	0.214233
$326$	46.1214	2.55443
$327$	−6.98243	−0.386129
$328$	−59.1231	−3.26453
$329$	−47.2322	−2.60400
$330$	2.66450	0.146676
$331$	26.3096	1.44610	0.723052	−	0.690794i	$-0.242739\pi$
$331$	26.3096	1.44610	0.723052	+	0.690794i	$0.242739\pi$
$332$	48.6893	2.67217
$333$	11.9256	0.653522
$334$	26.7446	1.46340
$335$	−14.8157	−0.809469
$336$	97.3427	5.31048
$337$	−24.4944	−1.33429	−0.667147	−	0.744926i	$-0.732485\pi$
$337$	−24.4944	−1.33429	−0.667147	+	0.744926i	$0.732485\pi$
$338$	−4.95721	−0.269636
$339$	47.6045	2.58552
$340$	10.7045	0.580530
$341$	0.380980	0.0206312
$342$	65.3490	3.53367
$343$	−19.2380	−1.03875
$344$	−31.8330	−1.71632
$345$	10.3782	0.558744
$346$	−11.7295	−0.630584
$347$	−10.6167	−0.569936	−0.284968	−	0.958537i	$-0.591983\pi$
$347$	−10.6167	−0.569936	−0.284968	+	0.958537i	$0.591983\pi$
$348$	27.1763	1.45680
$349$	3.73173	0.199755	0.0998774	−	0.995000i	$-0.468155\pi$
$349$	3.73173	0.199755	0.0998774	+	0.995000i	$0.468155\pi$
$350$	11.1198	0.594380
$351$	−8.88962	−0.474493
$352$	−3.30218	−0.176007
$353$	−21.5973	−1.14951	−0.574754	−	0.818326i	$-0.694902\pi$
$353$	−21.5973	−1.14951	−0.574754	+	0.818326i	$0.694902\pi$
$354$	16.8192	0.893931
$355$	7.87706	0.418071
$356$	−71.9245	−3.81199
$357$	25.7141	1.36093
$358$	−25.7734	−1.36217
$359$	0.342423	0.0180724	0.00903619	−	0.999959i	$-0.497124\pi$
$359$	0.342423	0.0180724	0.00903619	+	0.999959i	$0.497124\pi$
$360$	−27.0112	−1.42361
$361$	23.4365	1.23350
$362$	32.5462	1.71059
$363$	28.4434	1.49289
$364$	−77.9012	−4.08313
$365$	5.53782	0.289863
$366$	−59.1612	−3.09240
$367$	−6.74979	−0.352336	−0.176168	−	0.984360i	$-0.556370\pi$
$367$	−6.74979	−0.352336	−0.176168	+	0.984360i	$0.556370\pi$
$368$	−34.1731	−1.78139
$369$	32.9122	1.71334
$370$	−7.95625	−0.413626
$371$	−4.17311	−0.216657
$372$	−11.9383	−0.618969
$373$	−20.0767	−1.03953	−0.519765	−	0.854309i	$-0.673981\pi$
$373$	−20.0767	−1.03953	−0.519765	+	0.854309i	$0.673981\pi$
$374$	−2.31763	−0.119842
$375$	−2.62253	−0.135427
$376$	−76.5438	−3.94745
$377$	−8.52870	−0.439251
$378$	−25.5948	−1.31646
$379$	15.5218	0.797302	0.398651	−	0.917103i	$-0.369479\pi$
$379$	15.5218	0.797302	0.398651	+	0.917103i	$0.369479\pi$
$380$	−30.5692	−1.56817
$381$	26.7026	1.36802
$382$	35.3476	1.80854
$383$	6.88079	0.351592	0.175796	−	0.984427i	$-0.443750\pi$
$383$	6.88079	0.351592	0.175796	+	0.984427i	$0.443750\pi$
$384$	−13.6980	−0.699023
$385$	−1.68810	−0.0860334
$386$	−58.9683	−3.00141
$387$	17.7205	0.900785
$388$	−29.1243	−1.47856
$389$	24.2174	1.22787	0.613935	−	0.789356i	$-0.289586\pi$
$389$	24.2174	1.22787	0.613935	+	0.789356i	$0.289586\pi$
$390$	26.2028	1.32683
$391$	−9.02717	−0.456523
$392$	−79.9374	−4.03745
$393$	−32.0130	−1.61484
$394$	−9.52222	−0.479723
$395$	1.20590	0.0606755
$396$	7.14634	0.359117
$397$	−15.0023	−0.752945	−0.376473	−	0.926428i	$-0.622863\pi$
$397$	−15.0023	−0.752945	−0.376473	+	0.926428i	$0.622863\pi$
$398$	−28.2117	−1.41412
$399$	−73.4329	−3.67624
$400$	8.63539	0.431770
$401$	21.2639	1.06187	0.530935	−	0.847412i	$-0.321841\pi$
$401$	21.2639	1.06187	0.530935	+	0.847412i	$0.321841\pi$
$402$	−100.517	−5.01336
$403$	3.74657	0.186630
$404$	29.7469	1.47997
$405$	−5.59666	−0.278100
$406$	−24.5557	−1.21868
$407$	1.20784	0.0598702
$408$	41.6718	2.06306
$409$	4.22088	0.208709	0.104355	−	0.994540i	$-0.466722\pi$
$409$	4.22088	0.208709	0.104355	+	0.994540i	$0.466722\pi$
$410$	−21.9575	−1.08440
$411$	35.1840	1.73550
$412$	−81.0014	−3.99065
$413$	−10.6558	−0.524339
$414$	39.6982	1.95106
$415$	10.3757	0.509324
$416$	−32.4738	−1.59216
$417$	30.6455	1.50071
$418$	6.61858	0.323725
$419$	−27.1247	−1.32513	−0.662563	−	0.749006i	$-0.730531\pi$
$419$	−27.1247	−1.32513	−0.662563	+	0.749006i	$0.730531\pi$
$420$	52.8976	2.58114
$421$	15.8371	0.771855	0.385927	−	0.922529i	$-0.373882\pi$
$421$	15.8371	0.771855	0.385927	+	0.922529i	$0.373882\pi$
$422$	−36.4642	−1.77505
$423$	42.6098	2.07176
$424$	−6.76288	−0.328435
$425$	2.28113	0.110651
$426$	53.4420	2.58927
$427$	37.4816	1.81386
$428$	94.4150	4.56372
$429$	−3.97784	−0.192052
$430$	−11.8223	−0.570123
$431$	−24.6898	−1.18926	−0.594632	−	0.803998i	$-0.702702\pi$
$431$	−24.6898	−1.18926	−0.594632	+	0.803998i	$0.702702\pi$
$432$	−19.8763	−0.956301
$433$	−7.59142	−0.364820	−0.182410	−	0.983223i	$-0.558390\pi$
$433$	−7.59142	−0.364820	−0.182410	+	0.983223i	$0.558390\pi$
$434$	10.7871	0.517796
$435$	5.79128	0.277671
$436$	12.4940	0.598353
$437$	25.7793	1.23319
$438$	37.5714	1.79523
$439$	1.75383	0.0837055	0.0418528	−	0.999124i	$-0.486674\pi$
$439$	1.75383	0.0837055	0.0418528	+	0.999124i	$0.486674\pi$
$440$	−2.73570	−0.130420
$441$	44.4989	2.11900
$442$	−22.7917	−1.08409
$443$	20.9752	0.996562	0.498281	−	0.867016i	$-0.333965\pi$
$443$	20.9752	0.996562	0.498281	+	0.867016i	$0.333965\pi$
$444$	−37.8483	−1.79620
$445$	−15.3272	−0.726578
$446$	−43.1309	−2.04231
$447$	30.2772	1.43206
$448$	−19.2622	−0.910055
$449$	26.3840	1.24514	0.622570	−	0.782564i	$-0.286089\pi$
$449$	26.3840	1.24514	0.622570	+	0.782564i	$0.286089\pi$
$450$	−10.0316	−0.472893
$451$	3.33336	0.156962
$452$	−85.1808	−4.00657
$453$	−18.6063	−0.874198
$454$	49.3885	2.31792
$455$	−16.6008	−0.778258
$456$	−119.004	−5.57288
$457$	26.3144	1.23094	0.615469	−	0.788161i	$-0.288967\pi$
$457$	26.3144	1.23094	0.615469	+	0.788161i	$0.288967\pi$
$458$	45.2350	2.11369
$459$	−5.25054	−0.245074
$460$	−18.5702	−0.865840
$461$	−24.5160	−1.14182	−0.570912	−	0.821012i	$-0.693410\pi$
$461$	−24.5160	−1.14182	−0.570912	+	0.821012i	$0.693410\pi$
$462$	−11.4529	−0.532838
$463$	−10.4600	−0.486119	−0.243060	−	0.970011i	$-0.578151\pi$
$463$	−10.4600	−0.486119	−0.243060	+	0.970011i	$0.578151\pi$
$464$	−19.0694	−0.885273
$465$	−2.54405	−0.117978
$466$	67.2021	3.11308
$467$	−13.1235	−0.607284	−0.303642	−	0.952786i	$-0.598203\pi$
$467$	−13.1235	−0.607284	−0.303642	+	0.952786i	$0.598203\pi$
$468$	70.2773	3.24857
$469$	63.6829	2.94060
$470$	−28.4273	−1.31126
$471$	59.2030	2.72793
$472$	−17.2687	−0.794855
$473$	1.79474	0.0825224
$474$	8.18146	0.375787
$475$	−6.51433	−0.298898
$476$	−46.0113	−2.10893
$477$	3.76471	0.172374
$478$	56.7896	2.59750
$479$	−0.348871	−0.0159403	−0.00797016	−	0.999968i	$-0.502537\pi$
$479$	−0.348871	−0.0159403	−0.00797016	+	0.999968i	$0.502537\pi$
$480$	22.0508	1.00648
$481$	11.8779	0.541586
$482$	−2.58701	−0.117835
$483$	−44.6090	−2.02978
$484$	−50.8950	−2.31341
$485$	−6.20641	−0.281819
$486$	−55.8344	−2.53270
$487$	−15.7693	−0.714576	−0.357288	−	0.933994i	$-0.616299\pi$
$487$	−15.7693	−0.714576	−0.357288	+	0.933994i	$0.616299\pi$
$488$	60.7421	2.74967
$489$	46.7547	2.11432
$490$	−29.6877	−1.34115
$491$	−41.8057	−1.88667	−0.943333	−	0.331848i	$-0.892328\pi$
$491$	−41.8057	−1.88667	−0.943333	+	0.331848i	$0.892328\pi$
$492$	−104.453	−4.70911
$493$	−5.03737	−0.226872
$494$	65.0873	2.92842
$495$	1.52289	0.0684488
$496$	8.37698	0.376137
$497$	−33.8582	−1.51875
$498$	70.3943	3.15444
$499$	−9.90463	−0.443392	−0.221696	−	0.975116i	$-0.571159\pi$
$499$	−9.90463	−0.443392	−0.221696	+	0.975116i	$0.571159\pi$
$500$	4.69261	0.209860
$501$	27.1118	1.21127
$502$	56.4480	2.51940
$503$	4.86635	0.216980	0.108490	−	0.994098i	$-0.465398\pi$
$503$	4.86635	0.216980	0.108490	+	0.994098i	$0.465398\pi$
$504$	116.103	5.17164
$505$	6.33910	0.282086
$506$	4.02066	0.178740
$507$	−5.02528	−0.223180
$508$	−47.7802	−2.11990
$509$	37.0006	1.64002	0.820011	−	0.572348i	$-0.193967\pi$
$509$	37.0006	1.64002	0.820011	+	0.572348i	$0.193967\pi$
$510$	15.4763	0.685304
$511$	−23.8034	−1.05300
$512$	47.6969	2.10792
$513$	14.9942	0.662011
$514$	36.5049	1.61016
$515$	−17.2615	−0.760632
$516$	−56.2394	−2.47580
$517$	4.31554	0.189797
$518$	34.1986	1.50260
$519$	−11.8906	−0.521940
$520$	−26.9030	−1.17978
$521$	1.70970	0.0749035	0.0374517	−	0.999298i	$-0.488076\pi$
$521$	1.70970	0.0749035	0.0374517	+	0.999298i	$0.488076\pi$
$522$	22.1525	0.969590
$523$	−27.8507	−1.21782	−0.608912	−	0.793238i	$-0.708394\pi$
$523$	−27.8507	−1.21782	−0.608912	+	0.793238i	$0.708394\pi$
$524$	57.2822	2.50239
$525$	11.2725	0.491973
$526$	−59.3670	−2.58852
$527$	2.21286	0.0963939
$528$	−8.89407	−0.387065
$529$	−7.33957	−0.319112
$530$	−2.51164	−0.109099
$531$	9.61299	0.417168
$532$	131.397	5.69677
$533$	32.7804	1.41988
$534$	−103.987	−4.49998
$535$	20.1199	0.869860
$536$	103.204	4.45772
$537$	−26.1273	−1.12748
$538$	61.7872	2.66384
$539$	4.50688	0.194125
$540$	−10.8011	−0.464807
$541$	22.5917	0.971294	0.485647	−	0.874155i	$-0.338584\pi$
$541$	22.5917	0.971294	0.485647	+	0.874155i	$0.338584\pi$
$542$	−23.4973	−1.00929
$543$	32.9931	1.41587
$544$	−19.1802	−0.822345
$545$	2.66248	0.114048
$546$	−112.628	−4.82005
$547$	8.99990	0.384808	0.192404	−	0.981316i	$-0.438372\pi$
$547$	8.99990	0.384808	0.192404	+	0.981316i	$0.438372\pi$
$548$	−62.9563	−2.68936
$549$	−33.8134	−1.44312
$550$	−1.01600	−0.0433225
$551$	14.3855	0.612841
$552$	−72.2927	−3.07698
$553$	−5.18337	−0.220419
$554$	10.2675	0.436223
$555$	−8.06550	−0.342362
$556$	−54.8353	−2.32553
$557$	20.8858	0.884959	0.442480	−	0.896779i	$-0.354099\pi$
$557$	20.8858	0.884959	0.442480	+	0.896779i	$0.354099\pi$
$558$	−9.73138	−0.411962
$559$	17.6496	0.746498
$560$	−37.1178	−1.56851
$561$	−2.34946	−0.0991942
$562$	−46.8636	−1.97682
$563$	−11.7929	−0.497012	−0.248506	−	0.968630i	$-0.579940\pi$
$563$	−11.7929	−0.497012	−0.248506	+	0.968630i	$0.579940\pi$
$564$	−135.230	−5.69422
$565$	−18.1521	−0.763664
$566$	17.9998	0.756587
$567$	24.0563	1.01027
$568$	−54.8701	−2.30230
$569$	−22.5814	−0.946661	−0.473330	−	0.880885i	$-0.656948\pi$
$569$	−22.5814	−0.946661	−0.473330	+	0.880885i	$0.656948\pi$
$570$	−44.1966	−1.85119
$571$	−29.3013	−1.22622	−0.613110	−	0.789997i	$-0.710082\pi$
$571$	−29.3013	−1.22622	−0.613110	+	0.789997i	$0.710082\pi$
$572$	7.11772	0.297607
$573$	35.8330	1.49695
$574$	94.3808	3.93938
$575$	−3.95733	−0.165032
$576$	17.3771	0.724047
$577$	19.6490	0.817997	0.408999	−	0.912535i	$-0.365878\pi$
$577$	19.6490	0.817997	0.408999	+	0.912535i	$0.365878\pi$
$578$	30.5175	1.26936
$579$	−59.7781	−2.48429
$580$	−10.3626	−0.430284
$581$	−44.5984	−1.85025
$582$	−42.1075	−1.74541
$583$	0.381292	0.0157915
$584$	−38.5754	−1.59626
$585$	14.9762	0.619188
$586$	−57.4244	−2.37218
$587$	−3.27853	−0.135319	−0.0676596	−	0.997708i	$-0.521553\pi$
$587$	−3.27853	−0.135319	−0.0676596	+	0.997708i	$0.521553\pi$
$588$	−141.226	−5.82405
$589$	−6.31939	−0.260386
$590$	−6.41335	−0.264033
$591$	−9.65298	−0.397070
$592$	26.5578	1.09152
$593$	−27.0287	−1.10994	−0.554968	−	0.831872i	$-0.687269\pi$
$593$	−27.0287	−1.10994	−0.554968	+	0.831872i	$0.687269\pi$
$594$	2.33857	0.0959525
$595$	−9.80505	−0.401968
$596$	−54.1763	−2.21915
$597$	−28.5991	−1.17048
$598$	39.5393	1.61688
$599$	35.1311	1.43542	0.717710	−	0.696342i	$-0.245190\pi$
$599$	35.1311	1.43542	0.717710	+	0.696342i	$0.245190\pi$
$600$	18.2681	0.745791
$601$	−21.6912	−0.884803	−0.442401	−	0.896817i	$-0.645873\pi$
$601$	−21.6912	−0.884803	−0.442401	+	0.896817i	$0.645873\pi$
$602$	50.8163	2.07112
$603$	−57.4506	−2.33957
$604$	33.2930	1.35467
$605$	−10.8458	−0.440943
$606$	43.0077	1.74707
$607$	−15.6513	−0.635266	−0.317633	−	0.948214i	$-0.602888\pi$
$607$	−15.6513	−0.635266	−0.317633	+	0.948214i	$0.602888\pi$
$608$	54.7739	2.22137
$609$	−24.8929	−1.00871
$610$	22.5588	0.913379
$611$	42.4392	1.71691
$612$	41.5084	1.67788
$613$	−31.7379	−1.28188	−0.640941	−	0.767590i	$-0.721456\pi$
$613$	−31.7379	−1.28188	−0.640941	+	0.767590i	$0.721456\pi$
$614$	1.14406	0.0461704
$615$	−22.2590	−0.897571
$616$	11.7590	0.473783
$617$	6.37933	0.256822	0.128411	−	0.991721i	$-0.459012\pi$
$617$	6.37933	0.256822	0.128411	+	0.991721i	$0.459012\pi$
$618$	−117.111	−4.71088
$619$	−20.4880	−0.823483	−0.411742	−	0.911301i	$-0.635079\pi$
$619$	−20.4880	−0.823483	−0.411742	+	0.911301i	$0.635079\pi$
$620$	4.55218	0.182820
$621$	9.10870	0.365519
$622$	−46.9737	−1.88347
$623$	65.8813	2.63948
$624$	−87.4645	−3.50138
$625$	1.00000	0.0400000
$626$	−47.4556	−1.89671
$627$	6.70946	0.267950
$628$	−105.935	−4.22725
$629$	7.01553	0.279727
$630$	43.1191	1.71791
$631$	34.1846	1.36087	0.680434	−	0.732809i	$-0.261791\pi$
$631$	34.1846	1.36087	0.680434	+	0.732809i	$0.261791\pi$
$632$	−8.40009	−0.334138
$633$	−36.9649	−1.46922
$634$	54.9312	2.18160
$635$	−10.1820	−0.404060
$636$	−11.9480	−0.473769
$637$	44.3208	1.75605
$638$	2.24362	0.0888257
$639$	30.5447	1.20833
$640$	5.22319	0.206465
$641$	40.8997	1.61544	0.807721	−	0.589565i	$-0.200701\pi$
$641$	40.8997	1.61544	0.807721	+	0.589565i	$0.200701\pi$
$642$	136.504	5.38738
$643$	8.39595	0.331104	0.165552	−	0.986201i	$-0.447059\pi$
$643$	8.39595	0.331104	0.165552	+	0.986201i	$0.447059\pi$
$644$	79.8209	3.14539
$645$	−11.9847	−0.471896
$646$	38.4430	1.51252
$647$	−8.33727	−0.327772	−0.163886	−	0.986479i	$-0.552403\pi$
$647$	−8.33727	−0.327772	−0.163886	+	0.986479i	$0.552403\pi$
$648$	38.9853	1.53149
$649$	0.973609	0.0382175
$650$	−9.99141	−0.391895
$651$	10.9352	0.428584
$652$	−83.6603	−3.27639
$653$	−22.0468	−0.862759	−0.431379	−	0.902171i	$-0.641973\pi$
$653$	−22.0468	−0.862759	−0.431379	+	0.902171i	$0.641973\pi$
$654$	18.0636	0.706343
$655$	12.2069	0.476963
$656$	73.2939	2.86164
$657$	21.4739	0.837775
$658$	122.190	4.76347
$659$	7.05259	0.274730	0.137365	−	0.990521i	$-0.456137\pi$
$659$	7.05259	0.274730	0.137365	+	0.990521i	$0.456137\pi$
$660$	−4.83318	−0.188131
$661$	−0.213425	−0.00830127	−0.00415063	−	0.999991i	$-0.501321\pi$
$661$	−0.213425	−0.00830127	−0.00415063	+	0.999991i	$0.501321\pi$
$662$	−68.0630	−2.64535
$663$	−23.1047	−0.897310
$664$	−72.2754	−2.80483
$665$	28.0008	1.08582
$666$	−30.8518	−1.19548
$667$	8.73888	0.338371
$668$	−48.5124	−1.87700
$669$	−43.7231	−1.69043
$670$	38.3284	1.48076
$671$	−3.42464	−0.132207
$672$	−94.7817	−3.65628
$673$	27.4723	1.05898	0.529489	−	0.848317i	$-0.322384\pi$
$673$	27.4723	1.05898	0.529489	+	0.848317i	$0.322384\pi$
$674$	63.3672	2.44081
$675$	−2.30173	−0.0885936
$676$	8.99195	0.345844
$677$	−44.4995	−1.71026	−0.855128	−	0.518417i	$-0.826521\pi$
$677$	−44.4995	−1.71026	−0.855128	+	0.518417i	$0.826521\pi$
$678$	−123.153	−4.72967
$679$	26.6772	1.02378
$680$	−15.8899	−0.609350
$681$	50.0667	1.91856
$682$	−0.985599	−0.0377405
$683$	−36.8604	−1.41042	−0.705211	−	0.708997i	$-0.749148\pi$
$683$	−36.8604	−1.41042	−0.705211	+	0.708997i	$0.749148\pi$
$684$	−118.538	−4.53240
$685$	−13.4160	−0.512600
$686$	49.7688	1.90018
$687$	45.8562	1.74952
$688$	39.4628	1.50450
$689$	3.74963	0.142850
$690$	−26.8485	−1.02211
$691$	−34.6351	−1.31758	−0.658791	−	0.752326i	$-0.728932\pi$
$691$	−34.6351	−1.31758	−0.658791	+	0.752326i	$0.728932\pi$
$692$	21.2764	0.808807
$693$	−6.54589	−0.248658
$694$	27.4656	1.04258
$695$	−11.6854	−0.443254
$696$	−40.3410	−1.52912
$697$	19.3613	0.733362
$698$	−9.65401	−0.365410
$699$	68.1249	2.57672
$700$	−20.1704	−0.762370
$701$	−1.17164	−0.0442521	−0.0221260	−	0.999755i	$-0.507044\pi$
$701$	−1.17164	−0.0442521	−0.0221260	+	0.999755i	$0.507044\pi$
$702$	22.9975	0.867986
$703$	−20.0346	−0.755619
$704$	1.75996	0.0663312
$705$	−28.8177	−1.08534
$706$	55.8724	2.10279
$707$	−27.2476	−1.02475
$708$	−30.5086	−1.14658
$709$	−42.7315	−1.60481	−0.802407	−	0.596777i	$-0.796448\pi$
$709$	−42.7315	−1.60481	−0.802407	+	0.596777i	$0.796448\pi$
$710$	−20.3780	−0.764773
$711$	4.67610	0.175367
$712$	106.766	4.00123
$713$	−3.83890	−0.143768
$714$	−66.5225	−2.48954
$715$	1.51679	0.0567248
$716$	46.7507	1.74716
$717$	57.5694	2.14997
$718$	−0.885850	−0.0330596
$719$	−41.9975	−1.56624	−0.783122	−	0.621868i	$-0.786374\pi$
$719$	−41.9975	−1.56624	−0.783122	+	0.621868i	$0.786374\pi$
$720$	33.4853	1.24792
$721$	74.1956	2.76319
$722$	−60.6304	−2.25643
$723$	−2.62253	−0.0975330
$724$	−59.0360	−2.19406
$725$	−2.20828	−0.0820134
$726$	−73.5832	−2.73093
$727$	12.9516	0.480350	0.240175	−	0.970730i	$-0.422795\pi$
$727$	12.9516	0.480350	0.240175	+	0.970730i	$0.422795\pi$
$728$	115.638	4.28583
$729$	−39.8111	−1.47449
$730$	−14.3264	−0.530243
$731$	10.4245	0.385564
$732$	107.313	3.96641
$733$	10.9185	0.403283	0.201641	−	0.979459i	$-0.435372\pi$
$733$	10.9185	0.403283	0.201641	+	0.979459i	$0.435372\pi$
$734$	17.4618	0.644525
$735$	−30.0953	−1.11008
$736$	33.2740	1.22650
$737$	−5.81862	−0.214332
$738$	−85.1441	−3.13420
$739$	−41.7541	−1.53595	−0.767975	−	0.640480i	$-0.778735\pi$
$739$	−41.7541	−1.53595	−0.767975	+	0.640480i	$0.778735\pi$
$740$	14.4320	0.530530
$741$	65.9811	2.42388
$742$	10.7959	0.396329
$743$	26.5560	0.974246	0.487123	−	0.873333i	$-0.338046\pi$
$743$	26.5560	0.974246	0.487123	+	0.873333i	$0.338046\pi$
$744$	17.7214	0.649698
$745$	−11.5450	−0.422977
$746$	51.9385	1.90160
$747$	40.2337	1.47207
$748$	4.20399	0.153713
$749$	−86.4822	−3.15999
$750$	6.78451	0.247735
$751$	−39.8014	−1.45237	−0.726187	−	0.687497i	$-0.758710\pi$
$751$	−39.8014	−1.45237	−0.726187	+	0.687497i	$0.758710\pi$
$752$	94.8900	3.46028
$753$	57.2231	2.08533
$754$	22.0638	0.803517
$755$	7.09477	0.258205
$756$	46.4269	1.68853
$757$	2.82083	0.102525	0.0512623	−	0.998685i	$-0.483676\pi$
$757$	2.82083	0.102525	0.0512623	+	0.998685i	$0.483676\pi$
$758$	−40.1551	−1.45850
$759$	4.07587	0.147945
$760$	45.3776	1.64602
$761$	−32.9918	−1.19595	−0.597975	−	0.801515i	$-0.704028\pi$
$761$	−32.9918	−1.19595	−0.597975	+	0.801515i	$0.704028\pi$
$762$	−69.0799	−2.50250
$763$	−11.4442	−0.414309
$764$	−64.1176	−2.31969
$765$	8.84547	0.319809
$766$	−17.8007	−0.643164
$767$	9.57450	0.345715
$768$	58.9417	2.12687
$769$	0.243111	0.00876681	0.00438341	−	0.999990i	$-0.498605\pi$
$769$	0.243111	0.00876681	0.00438341	+	0.999990i	$0.498605\pi$
$770$	4.36712	0.157380
$771$	37.0062	1.33275
$772$	106.964	3.84970
$773$	−5.21480	−0.187563	−0.0937817	−	0.995593i	$-0.529896\pi$
$773$	−5.21480	−0.187563	−0.0937817	+	0.995593i	$0.529896\pi$
$774$	−45.8432	−1.64780
$775$	0.970075	0.0348461
$776$	43.2327	1.55196
$777$	34.6682	1.24372
$778$	−62.6506	−2.24613
$779$	−55.2911	−1.98101
$780$	−47.5296	−1.70183
$781$	3.09358	0.110697
$782$	23.3534	0.835114
$783$	5.08286	0.181647
$784$	99.0970	3.53918
$785$	−22.5748	−0.805728
$786$	82.8178	2.95401
$787$	22.2230	0.792163	0.396082	−	0.918215i	$-0.370370\pi$
$787$	22.2230	0.792163	0.396082	+	0.918215i	$0.370370\pi$
$788$	17.2725	0.615307
$789$	−60.1822	−2.14254
$790$	−3.11968	−0.110993
$791$	78.0238	2.77421
$792$	−10.6082	−0.376945
$793$	−33.6781	−1.19594
$794$	38.8111	1.37736
$795$	−2.54613	−0.0903019
$796$	51.1736	1.81380
$797$	−0.864482	−0.0306215	−0.0153108	−	0.999883i	$-0.504874\pi$
$797$	−0.864482	−0.0306215	−0.0153108	+	0.999883i	$0.504874\pi$
$798$	189.972	6.72492
$799$	25.0662	0.886777
$800$	−8.40821	−0.297275
$801$	−59.4338	−2.09999
$802$	−55.0100	−1.94247
$803$	2.17488	0.0767500
$804$	182.330	6.43029
$805$	17.0099	0.599520
$806$	−9.69241	−0.341401
$807$	62.6356	2.20488
$808$	−44.1570	−1.55344
$809$	45.0997	1.58562	0.792810	−	0.609468i	$-0.208617\pi$
$809$	45.0997	1.58562	0.792810	+	0.609468i	$0.208617\pi$
$810$	14.4786	0.508727
$811$	−28.1179	−0.987354	−0.493677	−	0.869645i	$-0.664347\pi$
$811$	−28.1179	−0.987354	−0.493677	+	0.869645i	$0.664347\pi$
$812$	44.5419	1.56312
$813$	−23.8199	−0.835401
$814$	−3.12468	−0.109520
$815$	−17.8281	−0.624490
$816$	−51.6598	−1.80845
$817$	−29.7697	−1.04151
$818$	−10.9195	−0.381790
$819$	−64.3725	−2.24936
$820$	39.8291	1.39089
$821$	−30.3753	−1.06011	−0.530053	−	0.847964i	$-0.677828\pi$
$821$	−30.3753	−1.06011	−0.530053	+	0.847964i	$0.677828\pi$
$822$	−91.0213	−3.17473
$823$	55.5506	1.93637	0.968185	−	0.250234i	$-0.0805075\pi$
$823$	55.5506	1.93637	0.968185	+	0.250234i	$0.0805075\pi$
$824$	120.240	4.18877
$825$	−1.02995	−0.0358584
$826$	27.5667	0.959169
$827$	−1.95094	−0.0678408	−0.0339204	−	0.999425i	$-0.510799\pi$
$827$	−1.95094	−0.0678408	−0.0339204	+	0.999425i	$0.510799\pi$
$828$	−72.0092	−2.50249
$829$	20.8527	0.724244	0.362122	−	0.932131i	$-0.382052\pi$
$829$	20.8527	0.724244	0.362122	+	0.932131i	$0.382052\pi$
$830$	−26.8421	−0.931703
$831$	10.4085	0.361066
$832$	17.3075	0.600031
$833$	26.1775	0.906996
$834$	−79.2801	−2.74524
$835$	−10.3380	−0.357762
$836$	−12.0055	−0.415220
$837$	−2.23285	−0.0771786
$838$	70.1717	2.42404
$839$	−28.1542	−0.971992	−0.485996	−	0.873961i	$-0.661543\pi$
$839$	−28.1542	−0.971992	−0.485996	+	0.873961i	$0.661543\pi$
$840$	−78.5223	−2.70928
$841$	−24.1235	−0.831845
$842$	−40.9708	−1.41195
$843$	−47.5071	−1.63623
$844$	66.1430	2.27674
$845$	1.91619	0.0659190
$846$	−110.232	−3.78985
$847$	46.6187	1.60184
$848$	8.38382	0.287902
$849$	18.2469	0.626233
$850$	−5.90130	−0.202413
$851$	−12.1706	−0.417203
$852$	−96.9392	−3.32108
$853$	37.0256	1.26773	0.633866	−	0.773443i	$-0.281467\pi$
$853$	37.0256	1.26773	0.633866	+	0.773443i	$0.281467\pi$
$854$	−96.9652	−3.31808
$855$	−25.2605	−0.863889
$856$	−140.152	−4.79029
$857$	13.2564	0.452831	0.226415	−	0.974031i	$-0.427299\pi$
$857$	13.2564	0.452831	0.226415	+	0.974031i	$0.427299\pi$
$858$	10.2907	0.351319
$859$	−56.4702	−1.92674	−0.963370	−	0.268176i	$-0.913579\pi$
$859$	−56.4702	−1.92674	−0.963370	+	0.268176i	$0.913579\pi$
$860$	21.4447	0.731258
$861$	95.6767	3.26065
$862$	63.8727	2.17551
$863$	−0.366270	−0.0124680	−0.00623398	−	0.999981i	$-0.501984\pi$
$863$	−0.366270	−0.0124680	−0.00623398	+	0.999981i	$0.501984\pi$
$864$	19.3534	0.658417
$865$	4.53402	0.154161
$866$	19.6391	0.667363
$867$	30.9366	1.05066
$868$	−19.5668	−0.664141
$869$	0.473597	0.0160657
$870$	−14.9821	−0.507941
$871$	−57.2205	−1.93884
$872$	−18.5463	−0.628058
$873$	−24.0664	−0.814526
$874$	−66.6913	−2.25587
$875$	−4.29833	−0.145310
$876$	−68.1513	−2.30262
$877$	15.2141	0.513745	0.256872	−	0.966445i	$-0.417308\pi$
$877$	15.2141	0.513745	0.256872	+	0.966445i	$0.417308\pi$
$878$	−4.53716	−0.153122
$879$	−58.2129	−1.96347
$880$	3.39140	0.114324
$881$	−30.1389	−1.01541	−0.507703	−	0.861532i	$-0.669505\pi$
$881$	−30.1389	−1.01541	−0.507703	+	0.861532i	$0.669505\pi$
$882$	−115.119	−3.87626
$883$	−7.14871	−0.240573	−0.120287	−	0.992739i	$-0.538381\pi$
$883$	−7.14871	−0.240573	−0.120287	+	0.992739i	$0.538381\pi$
$884$	41.3422	1.39049
$885$	−6.50142	−0.218543
$886$	−54.2630	−1.82300
$887$	40.8402	1.37128	0.685639	−	0.727942i	$-0.259523\pi$
$887$	40.8402	1.37128	0.685639	+	0.727942i	$0.259523\pi$
$888$	56.1828	1.88537
$889$	43.7656	1.46785
$890$	39.6515	1.32912
$891$	−2.19799	−0.0736356
$892$	78.2358	2.61953
$893$	−71.5827	−2.39542
$894$	−78.3273	−2.61966
$895$	9.96262	0.333014
$896$	−22.4510	−0.750036
$897$	40.0822	1.33831
$898$	−68.2558	−2.27772
$899$	−2.14220	−0.0714462
$900$	18.1964	0.606548
$901$	2.21467	0.0737814
$902$	−8.62344	−0.287129
$903$	51.5141	1.71428
$904$	126.444	4.20547
$905$	−12.5806	−0.418194
$906$	48.1345	1.59916
$907$	31.0528	1.03109	0.515545	−	0.856862i	$-0.327589\pi$
$907$	31.0528	1.03109	0.515545	+	0.856862i	$0.327589\pi$
$908$	−89.5865	−2.97303
$909$	24.5810	0.815299
$910$	42.9464	1.42366
$911$	41.1039	1.36183	0.680916	−	0.732362i	$-0.261582\pi$
$911$	41.1039	1.36183	0.680916	+	0.732362i	$0.261582\pi$
$912$	147.527	4.88512
$913$	4.07489	0.134859
$914$	−68.0757	−2.25174
$915$	22.8686	0.756011
$916$	−82.0525	−2.71109
$917$	−52.4693	−1.73269
$918$	13.5832	0.448312
$919$	−42.8124	−1.41225	−0.706125	−	0.708087i	$-0.749558\pi$
$919$	−42.8124	−1.41225	−0.706125	+	0.708087i	$0.749558\pi$
$920$	27.5660	0.908824
$921$	1.15977	0.0382156
$922$	63.4231	2.08873
$923$	30.4224	1.00136
$924$	20.7746	0.683435
$925$	3.07546	0.101121
$926$	27.0602	0.889254
$927$	−66.9344	−2.19841
$928$	18.5677	0.609514
$929$	9.39377	0.308200	0.154100	−	0.988055i	$-0.450752\pi$
$929$	9.39377	0.308200	0.154100	+	0.988055i	$0.450752\pi$
$930$	6.58148	0.215815
$931$	−74.7563	−2.45004
$932$	−121.899	−3.99293
$933$	−47.6187	−1.55897
$934$	33.9507	1.11090
$935$	0.895874	0.0292982
$936$	−104.321	−3.40984
$937$	−11.8593	−0.387425	−0.193713	−	0.981058i	$-0.562053\pi$
$937$	−11.8593	−0.387425	−0.193713	+	0.981058i	$0.562053\pi$
$938$	−164.748	−5.37922
$939$	−48.1073	−1.56992
$940$	51.5648	1.68186
$941$	9.22870	0.300847	0.150424	−	0.988622i	$-0.451936\pi$
$941$	9.22870	0.300847	0.150424	+	0.988622i	$0.451936\pi$
$942$	−153.159	−4.99018
$943$	−33.5882	−1.09378
$944$	21.4077	0.696760
$945$	9.89361	0.321839
$946$	−4.64302	−0.150958
$947$	−9.63658	−0.313147	−0.156573	−	0.987666i	$-0.550045\pi$
$947$	−9.63658	−0.313147	−0.156573	+	0.987666i	$0.550045\pi$
$948$	−14.8405	−0.481996
$949$	21.3879	0.694280
$950$	16.8526	0.546771
$951$	55.6855	1.80573
$952$	68.3002	2.21362
$953$	−1.81806	−0.0588929	−0.0294464	−	0.999566i	$-0.509374\pi$
$953$	−1.81806	−0.0588929	−0.0294464	+	0.999566i	$0.509374\pi$
$954$	−9.73933	−0.315322
$955$	−13.6635	−0.442141
$956$	−103.012	−3.33163
$957$	2.27443	0.0735218
$958$	0.902532	0.0291595
$959$	57.6666	1.86215
$960$	−11.7524	−0.379308
$961$	−30.0590	−0.969644
$962$	−30.7282	−0.990718
$963$	78.0185	2.51411
$964$	4.69261	0.151139
$965$	22.7940	0.733765
$966$	115.404	3.71306
$967$	3.53944	0.113821	0.0569104	−	0.998379i	$-0.481875\pi$
$967$	3.53944	0.113821	0.0569104	+	0.998379i	$0.481875\pi$
$968$	75.5496	2.42825
$969$	38.9709	1.25193
$970$	16.0560	0.515528
$971$	23.3662	0.749858	0.374929	−	0.927054i	$-0.377667\pi$
$971$	23.3662	0.749858	0.374929	+	0.927054i	$0.377667\pi$
$972$	101.279	3.24852
$973$	50.2280	1.61023
$974$	40.7954	1.30717
$975$	−10.1286	−0.324375
$976$	−75.3009	−2.41032
$977$	4.90755	0.157006	0.0785031	−	0.996914i	$-0.474986\pi$
$977$	4.90755	0.157006	0.0785031	+	0.996914i	$0.474986\pi$
$978$	−120.955	−3.86771
$979$	−6.01949	−0.192384
$980$	53.8509	1.72020
$981$	10.3242	0.329627
$982$	108.152	3.45126
$983$	3.60795	0.115076	0.0575379	−	0.998343i	$-0.481675\pi$
$983$	3.60795	0.115076	0.0575379	+	0.998343i	$0.481675\pi$
$984$	155.052	4.94289
$985$	3.68078	0.117280
$986$	13.0317	0.415014
$987$	123.868	3.94276
$988$	−118.063	−3.75608
$989$	−18.0845	−0.575054
$990$	−3.93973	−0.125213
$991$	52.9546	1.68216	0.841080	−	0.540911i	$-0.181920\pi$
$991$	52.9546	1.68216	0.841080	+	0.540911i	$0.181920\pi$
$992$	−8.15659	−0.258972
$993$	−68.9976	−2.18957
$994$	87.5915	2.77823
$995$	10.9051	0.345716
$996$	−127.689	−4.04599
$997$	33.1318	1.04929	0.524647	−	0.851320i	$-0.324197\pi$
$997$	33.1318	1.04929	0.524647	+	0.851320i	$0.324197\pi$
$998$	25.6234	0.811094
$999$	−7.07889	−0.223966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.b.1.1	✓	11
5.4	even	2		6025.2.a.g.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.1	✓	11	1.1	even	1	trivial
6025.2.a.g.1.11		11	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58701 q^{2} -2.62253 q^{3} +4.69261 q^{4} +1.00000 q^{5} +6.78451 q^{6} -4.29833 q^{7} -6.96581 q^{8} +3.87767 q^{9} +O(q^{10})\)	\(q-2.58701 q^{2} -2.62253 q^{3} +4.69261 q^{4} +1.00000 q^{5} +6.78451 q^{6} -4.29833 q^{7} -6.96581 q^{8} +3.87767 q^{9} -2.58701 q^{10} +0.392733 q^{11} -12.3065 q^{12} +3.86215 q^{13} +11.1198 q^{14} -2.62253 q^{15} +8.63539 q^{16} +2.28113 q^{17} -10.0316 q^{18} -6.51433 q^{19} +4.69261 q^{20} +11.2725 q^{21} -1.01600 q^{22} -3.95733 q^{23} +18.2681 q^{24} +1.00000 q^{25} -9.99141 q^{26} -2.30173 q^{27} -20.1704 q^{28} -2.20828 q^{29} +6.78451 q^{30} +0.970075 q^{31} -8.40821 q^{32} -1.02995 q^{33} -5.90130 q^{34} -4.29833 q^{35} +18.1964 q^{36} +3.07546 q^{37} +16.8526 q^{38} -10.1286 q^{39} -6.96581 q^{40} +8.48761 q^{41} -29.1621 q^{42} +4.56989 q^{43} +1.84294 q^{44} +3.87767 q^{45} +10.2376 q^{46} +10.9885 q^{47} -22.6466 q^{48} +11.4757 q^{49} -2.58701 q^{50} -5.98233 q^{51} +18.1236 q^{52} +0.970867 q^{53} +5.95460 q^{54} +0.392733 q^{55} +29.9414 q^{56} +17.0840 q^{57} +5.71284 q^{58} +2.47906 q^{59} -12.3065 q^{60} -8.72003 q^{61} -2.50959 q^{62} -16.6675 q^{63} +4.48133 q^{64} +3.86215 q^{65} +2.66450 q^{66} -14.8157 q^{67} +10.7045 q^{68} +10.3782 q^{69} +11.1198 q^{70} +7.87706 q^{71} -27.0112 q^{72} +5.53782 q^{73} -7.95625 q^{74} -2.62253 q^{75} -30.5692 q^{76} -1.68810 q^{77} +26.2028 q^{78} +1.20590 q^{79} +8.63539 q^{80} -5.59666 q^{81} -21.9575 q^{82} +10.3757 q^{83} +52.8976 q^{84} +2.28113 q^{85} -11.8223 q^{86} +5.79128 q^{87} -2.73570 q^{88} -15.3272 q^{89} -10.0316 q^{90} -16.6008 q^{91} -18.5702 q^{92} -2.54405 q^{93} -28.4273 q^{94} -6.51433 q^{95} +22.0508 q^{96} -6.20641 q^{97} -29.6877 q^{98} +1.52289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9	\( 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 28 q^{12} - 9 q^{13} + 2 q^{14} - 8 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} - 33 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{22} - 31 q^{23} + 32 q^{24} + 11 q^{25} - 20 q^{26} - 32 q^{27} - q^{28} + q^{29} + 7 q^{30} + 6 q^{31} + 7 q^{32} - 35 q^{33} + 9 q^{34} - 9 q^{35} + 33 q^{36} - 23 q^{37} + 20 q^{38} + 14 q^{39} - 12 q^{40} + 8 q^{41} - 26 q^{42} - 19 q^{43} + 9 q^{45} + 6 q^{46} - 35 q^{47} + 16 q^{48} + 4 q^{49} - 4 q^{50} - 3 q^{51} - 3 q^{52} + 14 q^{53} + 9 q^{54} - 3 q^{55} + 33 q^{56} + q^{57} - 11 q^{58} - 6 q^{59} - 28 q^{60} + 9 q^{61} - 23 q^{62} - 31 q^{63} + 18 q^{64} - 9 q^{65} - 36 q^{66} - 54 q^{67} + q^{68} + 17 q^{69} + 2 q^{70} - 5 q^{71} - 64 q^{72} + 17 q^{73} + 8 q^{74} - 8 q^{75} - 31 q^{76} - 18 q^{77} + 15 q^{78} - 16 q^{79} - 16 q^{80} + 43 q^{81} - 61 q^{82} - 29 q^{83} + 69 q^{84} - 4 q^{85} + 5 q^{86} + 5 q^{87} - 14 q^{88} - 5 q^{89} - 6 q^{90} - 54 q^{91} - 6 q^{92} - 25 q^{93} - 19 q^{94} - 33 q^{95} + 9 q^{96} + 6 q^{97} - 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 28 * q^12 - 9 * q^13 + 2 * q^14 - 8 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 - 33 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^22 - 31 * q^23 + 32 * q^24 + 11 * q^25 - 20 * q^26 - 32 * q^27 - q^28 + q^29 + 7 * q^30 + 6 * q^31 + 7 * q^32 - 35 * q^33 + 9 * q^34 - 9 * q^35 + 33 * q^36 - 23 * q^37 + 20 * q^38 + 14 * q^39 - 12 * q^40 + 8 * q^41 - 26 * q^42 - 19 * q^43 + 9 * q^45 + 6 * q^46 - 35 * q^47 + 16 * q^48 + 4 * q^49 - 4 * q^50 - 3 * q^51 - 3 * q^52 + 14 * q^53 + 9 * q^54 - 3 * q^55 + 33 * q^56 + q^57 - 11 * q^58 - 6 * q^59 - 28 * q^60 + 9 * q^61 - 23 * q^62 - 31 * q^63 + 18 * q^64 - 9 * q^65 - 36 * q^66 - 54 * q^67 + q^68 + 17 * q^69 + 2 * q^70 - 5 * q^71 - 64 * q^72 + 17 * q^73 + 8 * q^74 - 8 * q^75 - 31 * q^76 - 18 * q^77 + 15 * q^78 - 16 * q^79 - 16 * q^80 + 43 * q^81 - 61 * q^82 - 29 * q^83 + 69 * q^84 - 4 * q^85 + 5 * q^86 + 5 * q^87 - 14 * q^88 - 5 * q^89 - 6 * q^90 - 54 * q^91 - 6 * q^92 - 25 * q^93 - 19 * q^94 - 33 * q^95 + 9 * q^96 + 6 * q^97 - 29 * q^98 + 60 * q^99

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