LMFDB - Embedded newform 6031.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08654 q^{2} -0.221531 q^{3} +2.35365 q^{4} +3.05486 q^{5} +0.462234 q^{6} -0.0600719 q^{7} -0.737910 q^{8} -2.95092 q^{9} +O(q^{10})$	\(q-2.08654 q^{2} -0.221531 q^{3} +2.35365 q^{4} +3.05486 q^{5} +0.462234 q^{6} -0.0600719 q^{7} -0.737910 q^{8} -2.95092 q^{9} -6.37409 q^{10} +1.44952 q^{11} -0.521407 q^{12} +1.68466 q^{13} +0.125342 q^{14} -0.676747 q^{15} -3.16762 q^{16} -0.611238 q^{17} +6.15722 q^{18} +4.11973 q^{19} +7.19008 q^{20} +0.0133078 q^{21} -3.02448 q^{22} -7.65824 q^{23} +0.163470 q^{24} +4.33217 q^{25} -3.51511 q^{26} +1.31832 q^{27} -0.141388 q^{28} -1.22968 q^{29} +1.41206 q^{30} -6.43268 q^{31} +8.08520 q^{32} -0.321114 q^{33} +1.27537 q^{34} -0.183511 q^{35} -6.94545 q^{36} +1.00000 q^{37} -8.59599 q^{38} -0.373205 q^{39} -2.25421 q^{40} +4.90455 q^{41} -0.0277673 q^{42} +0.815704 q^{43} +3.41167 q^{44} -9.01466 q^{45} +15.9792 q^{46} -1.31943 q^{47} +0.701728 q^{48} -6.99639 q^{49} -9.03926 q^{50} +0.135408 q^{51} +3.96511 q^{52} -7.23555 q^{53} -2.75072 q^{54} +4.42808 q^{55} +0.0443277 q^{56} -0.912649 q^{57} +2.56577 q^{58} +6.54773 q^{59} -1.59283 q^{60} +3.08978 q^{61} +13.4220 q^{62} +0.177268 q^{63} -10.5348 q^{64} +5.14640 q^{65} +0.670018 q^{66} +2.35255 q^{67} -1.43864 q^{68} +1.69654 q^{69} +0.382904 q^{70} -13.0175 q^{71} +2.17752 q^{72} -1.65899 q^{73} -2.08654 q^{74} -0.959711 q^{75} +9.69641 q^{76} -0.0870755 q^{77} +0.778707 q^{78} -8.49161 q^{79} -9.67665 q^{80} +8.56072 q^{81} -10.2335 q^{82} +0.450114 q^{83} +0.0313219 q^{84} -1.86725 q^{85} -1.70200 q^{86} +0.272412 q^{87} -1.06962 q^{88} -6.88425 q^{89} +18.8095 q^{90} -0.101201 q^{91} -18.0248 q^{92} +1.42504 q^{93} +2.75304 q^{94} +12.5852 q^{95} -1.79112 q^{96} +2.94365 q^{97} +14.5983 q^{98} -4.27743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.08654	−1.47541	−0.737704	−	0.675125i	$-0.764090\pi$
$2$	−2.08654	−1.47541	−0.737704	+	0.675125i	$0.764090\pi$
$3$	−0.221531	−0.127901	−0.0639505	−	0.997953i	$-0.520370\pi$
$3$	−0.221531	−0.127901	−0.0639505	+	0.997953i	$0.520370\pi$
$4$	2.35365	1.17683
$5$	3.05486	1.36618	0.683088	−	0.730336i	$-0.260637\pi$
$5$	3.05486	1.36618	0.683088	+	0.730336i	$0.260637\pi$
$6$	0.462234	0.188706
$7$	−0.0600719	−0.0227050	−0.0113525	−	0.999936i	$-0.503614\pi$
$7$	−0.0600719	−0.0227050	−0.0113525	+	0.999936i	$0.503614\pi$
$8$	−0.737910	−0.260891
$9$	−2.95092	−0.983641
$10$	−6.37409	−2.01566
$11$	1.44952	0.437047	0.218524	−	0.975832i	$-0.429876\pi$
$11$	1.44952	0.437047	0.218524	+	0.975832i	$0.429876\pi$
$12$	−0.521407	−0.150517
$13$	1.68466	0.467241	0.233620	−	0.972328i	$-0.424943\pi$
$13$	1.68466	0.467241	0.233620	+	0.972328i	$0.424943\pi$
$14$	0.125342	0.0334992
$15$	−0.676747	−0.174735
$16$	−3.16762	−0.791906
$17$	−0.611238	−0.148247	−0.0741235	−	0.997249i	$-0.523616\pi$
$17$	−0.611238	−0.148247	−0.0741235	+	0.997249i	$0.523616\pi$
$18$	6.15722	1.45127
$19$	4.11973	0.945131	0.472565	−	0.881296i	$-0.343328\pi$
$19$	4.11973	0.945131	0.472565	+	0.881296i	$0.343328\pi$
$20$	7.19008	1.60775
$21$	0.0133078	0.00290400
$22$	−3.02448	−0.644822
$23$	−7.65824	−1.59685	−0.798427	−	0.602092i	$-0.794334\pi$
$23$	−7.65824	−1.59685	−0.798427	+	0.602092i	$0.794334\pi$
$24$	0.163470	0.0333682
$25$	4.33217	0.866435
$26$	−3.51511	−0.689371
$27$	1.31832	0.253710
$28$	−0.141388	−0.0267199
$29$	−1.22968	−0.228345	−0.114173	−	0.993461i	$-0.536422\pi$
$29$	−1.22968	−0.228345	−0.114173	+	0.993461i	$0.536422\pi$
$30$	1.41206	0.257806
$31$	−6.43268	−1.15534	−0.577671	−	0.816269i	$-0.696039\pi$
$31$	−6.43268	−1.15534	−0.577671	+	0.816269i	$0.696039\pi$
$32$	8.08520	1.42927
$33$	−0.321114	−0.0558988
$34$	1.27537	0.218725
$35$	−0.183511	−0.0310191
$36$	−6.94545	−1.15757
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−8.59599	−1.39445
$39$	−0.373205	−0.0597606
$40$	−2.25421	−0.356422
$41$	4.90455	0.765961	0.382981	−	0.923756i	$-0.374898\pi$
$41$	4.90455	0.765961	0.382981	+	0.923756i	$0.374898\pi$
$42$	−0.0277673	−0.00428458
$43$	0.815704	0.124394	0.0621969	−	0.998064i	$-0.480189\pi$
$43$	0.815704	0.124394	0.0621969	+	0.998064i	$0.480189\pi$
$44$	3.41167	0.514328
$45$	−9.01466	−1.34383
$46$	15.9792	2.35601
$47$	−1.31943	−0.192458	−0.0962291	−	0.995359i	$-0.530678\pi$
$47$	−1.31943	−0.192458	−0.0962291	+	0.995359i	$0.530678\pi$
$48$	0.701728	0.101286
$49$	−6.99639	−0.999484
$50$	−9.03926	−1.27834
$51$	0.135408	0.0189610
$52$	3.96511	0.549861
$53$	−7.23555	−0.993879	−0.496940	−	0.867785i	$-0.665543\pi$
$53$	−7.23555	−0.993879	−0.496940	+	0.867785i	$0.665543\pi$
$54$	−2.75072	−0.374325
$55$	4.42808	0.597083
$56$	0.0443277	0.00592353
$57$	−0.912649	−0.120883
$58$	2.56577	0.336903
$59$	6.54773	0.852442	0.426221	−	0.904619i	$-0.359845\pi$
$59$	6.54773	0.852442	0.426221	+	0.904619i	$0.359845\pi$
$60$	−1.59283	−0.205633
$61$	3.08978	0.395606	0.197803	−	0.980242i	$-0.436619\pi$
$61$	3.08978	0.395606	0.197803	+	0.980242i	$0.436619\pi$
$62$	13.4220	1.70460
$63$	0.177268	0.0223336
$64$	−10.5348	−1.31686
$65$	5.14640	0.638333
$66$	0.670018	0.0824735
$67$	2.35255	0.287410	0.143705	−	0.989621i	$-0.454098\pi$
$67$	2.35255	0.287410	0.143705	+	0.989621i	$0.454098\pi$
$68$	−1.43864	−0.174461
$69$	1.69654	0.204239
$70$	0.382904	0.0457657
$71$	−13.0175	−1.54489	−0.772446	−	0.635080i	$-0.780967\pi$
$71$	−13.0175	−1.54489	−0.772446	+	0.635080i	$0.780967\pi$
$72$	2.17752	0.256623
$73$	−1.65899	−0.194170	−0.0970852	−	0.995276i	$-0.530952\pi$
$73$	−1.65899	−0.194170	−0.0970852	+	0.995276i	$0.530952\pi$
$74$	−2.08654	−0.242555
$75$	−0.959711	−0.110818
$76$	9.69641	1.11225
$77$	−0.0870755	−0.00992317
$78$	0.778707	0.0881712
$79$	−8.49161	−0.955381	−0.477690	−	0.878528i	$-0.658526\pi$
$79$	−8.49161	−0.955381	−0.477690	+	0.878528i	$0.658526\pi$
$80$	−9.67665	−1.08188
$81$	8.56072	0.951192
$82$	−10.2335	−1.13010
$83$	0.450114	0.0494065	0.0247032	−	0.999695i	$-0.492136\pi$
$83$	0.450114	0.0494065	0.0247032	+	0.999695i	$0.492136\pi$
$84$	0.0313219	0.00341750
$85$	−1.86725	−0.202531
$86$	−1.70200	−0.183531
$87$	0.272412	0.0292056
$88$	−1.06962	−0.114022
$89$	−6.88425	−0.729729	−0.364864	−	0.931061i	$-0.618885\pi$
$89$	−6.88425	−0.729729	−0.364864	+	0.931061i	$0.618885\pi$
$90$	18.8095	1.98269
$91$	−0.101201	−0.0106087
$92$	−18.0248	−1.87922
$93$	1.42504	0.147770
$94$	2.75304	0.283954
$95$	12.5852	1.29121
$96$	−1.79112	−0.182806
$97$	2.94365	0.298882	0.149441	−	0.988771i	$-0.452253\pi$
$97$	2.94365	0.298882	0.149441	+	0.988771i	$0.452253\pi$
$98$	14.5983	1.47465
$99$	−4.27743	−0.429898
$100$	10.1964	1.01964
$101$	−7.39275	−0.735606	−0.367803	−	0.929904i	$-0.619890\pi$
$101$	−7.39275	−0.735606	−0.367803	+	0.929904i	$0.619890\pi$
$102$	−0.282535	−0.0279751
$103$	−8.86238	−0.873236	−0.436618	−	0.899647i	$-0.643824\pi$
$103$	−8.86238	−0.873236	−0.436618	+	0.899647i	$0.643824\pi$
$104$	−1.24313	−0.121899
$105$	0.0406535	0.00396737
$106$	15.0973	1.46638
$107$	16.8883	1.63266	0.816328	−	0.577588i	$-0.196006\pi$
$107$	16.8883	1.63266	0.816328	+	0.577588i	$0.196006\pi$
$108$	3.10286	0.298572
$109$	−3.34407	−0.320304	−0.160152	−	0.987092i	$-0.551198\pi$
$109$	−3.34407	−0.320304	−0.160152	+	0.987092i	$0.551198\pi$
$110$	−9.23938	−0.880940
$111$	−0.221531	−0.0210268
$112$	0.190285	0.0179803
$113$	−9.22081	−0.867421	−0.433710	−	0.901052i	$-0.642796\pi$
$113$	−9.22081	−0.867421	−0.433710	+	0.901052i	$0.642796\pi$
$114$	1.90428	0.178352
$115$	−23.3949	−2.18158
$116$	−2.89423	−0.268723
$117$	−4.97131	−0.459597
$118$	−13.6621	−1.25770
$119$	0.0367182	0.00336595
$120$	0.499379	0.0455868
$121$	−8.89889	−0.808990
$122$	−6.44696	−0.583680
$123$	−1.08651	−0.0979673
$124$	−15.1403	−1.35964
$125$	−2.04012	−0.182474
$126$	−0.369876	−0.0329512
$127$	−3.74450	−0.332271	−0.166136	−	0.986103i	$-0.553129\pi$
$127$	−3.74450	−0.332271	−0.166136	+	0.986103i	$0.553129\pi$
$128$	5.81099	0.513624
$129$	−0.180704	−0.0159101
$130$	−10.7382	−0.941801
$131$	18.2122	1.59121	0.795605	−	0.605816i	$-0.207153\pi$
$131$	18.2122	1.59121	0.795605	+	0.605816i	$0.207153\pi$
$132$	−0.755791	−0.0657832
$133$	−0.247480	−0.0214592
$134$	−4.90869	−0.424046
$135$	4.02727	0.346612
$136$	0.451039	0.0386763
$137$	−17.7070	−1.51281	−0.756406	−	0.654102i	$-0.773047\pi$
$137$	−17.7070	−1.51281	−0.756406	+	0.654102i	$0.773047\pi$
$138$	−3.53990	−0.301336
$139$	−13.3064	−1.12864	−0.564318	−	0.825557i	$-0.690861\pi$
$139$	−13.3064	−1.12864	−0.564318	+	0.825557i	$0.690861\pi$
$140$	−0.431922	−0.0365040
$141$	0.292294	0.0246156
$142$	27.1615	2.27935
$143$	2.44195	0.204206
$144$	9.34742	0.778952
$145$	−3.75649	−0.311960
$146$	3.46156	0.286481
$147$	1.54992	0.127835
$148$	2.35365	0.193469
$149$	4.97197	0.407319	0.203660	−	0.979042i	$-0.434716\pi$
$149$	4.97197	0.407319	0.203660	+	0.979042i	$0.434716\pi$
$150$	2.00248	0.163502
$151$	19.4057	1.57922	0.789608	−	0.613611i	$-0.210284\pi$
$151$	19.4057	1.57922	0.789608	+	0.613611i	$0.210284\pi$
$152$	−3.03999	−0.246576
$153$	1.80372	0.145822
$154$	0.181687	0.0146407
$155$	−19.6509	−1.57840
$156$	−0.878395	−0.0703279
$157$	−18.1218	−1.44628	−0.723140	−	0.690701i	$-0.757302\pi$
$157$	−18.1218	−1.44628	−0.723140	+	0.690701i	$0.757302\pi$
$158$	17.7181	1.40958
$159$	1.60290	0.127118
$160$	24.6992	1.95264
$161$	0.460045	0.0362566
$162$	−17.8623	−1.40339
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	11.5436	0.901403
$165$	−0.980959	−0.0763675
$166$	−0.939182	−0.0728946
$167$	−6.56635	−0.508119	−0.254060	−	0.967189i	$-0.581766\pi$
$167$	−6.56635	−0.508119	−0.254060	+	0.967189i	$0.581766\pi$
$168$	−0.00981996	−0.000757627 0
$169$	−10.1619	−0.781686
$170$	3.89609	0.298816
$171$	−12.1570	−0.929670
$172$	1.91988	0.146390
$173$	−22.4529	−1.70706	−0.853531	−	0.521042i	$-0.825544\pi$
$173$	−22.4529	−1.70706	−0.853531	+	0.521042i	$0.825544\pi$
$174$	−0.568399	−0.0430902
$175$	−0.260242	−0.0196724
$176$	−4.59154	−0.346100
$177$	−1.45053	−0.109028
$178$	14.3643	1.07665
$179$	5.18925	0.387863	0.193931	−	0.981015i	$-0.437876\pi$
$179$	5.18925	0.387863	0.193931	+	0.981015i	$0.437876\pi$
$180$	−21.2174	−1.58145
$181$	−9.70023	−0.721013	−0.360506	−	0.932757i	$-0.617396\pi$
$181$	−9.70023	−0.721013	−0.360506	+	0.932757i	$0.617396\pi$
$182$	0.211160	0.0156522
$183$	−0.684483	−0.0505985
$184$	5.65109	0.416604
$185$	3.05486	0.224598
$186$	−2.97340	−0.218020
$187$	−0.886003	−0.0647909
$188$	−3.10547	−0.226490
$189$	−0.0791937	−0.00576049
$190$	−26.2595	−1.90507
$191$	−7.48181	−0.541365	−0.270682	−	0.962669i	$-0.587249\pi$
$191$	−7.48181	−0.541365	−0.270682	+	0.962669i	$0.587249\pi$
$192$	2.33380	0.168427
$193$	−2.90971	−0.209445	−0.104723	−	0.994501i	$-0.533396\pi$
$193$	−2.90971	−0.209445	−0.104723	+	0.994501i	$0.533396\pi$
$194$	−6.14204	−0.440972
$195$	−1.14009	−0.0816435
$196$	−16.4671	−1.17622
$197$	18.5562	1.32207	0.661036	−	0.750354i	$-0.270117\pi$
$197$	18.5562	1.32207	0.661036	+	0.750354i	$0.270117\pi$
$198$	8.92502	0.634274
$199$	−9.16281	−0.649534	−0.324767	−	0.945794i	$-0.605286\pi$
$199$	−9.16281	−0.649534	−0.324767	+	0.945794i	$0.605286\pi$
$200$	−3.19676	−0.226045
$201$	−0.521163	−0.0367600
$202$	15.4253	1.08532
$203$	0.0738691	0.00518459
$204$	0.318704	0.0223138
$205$	14.9827	1.04644
$206$	18.4917	1.28838
$207$	22.5989	1.57073
$208$	−5.33637	−0.370011
$209$	5.97164	0.413067
$210$	−0.0848251	−0.00585349
$211$	−16.2152	−1.11630	−0.558151	−	0.829739i	$-0.688489\pi$
$211$	−16.2152	−1.11630	−0.558151	+	0.829739i	$0.688489\pi$
$212$	−17.0300	−1.16962
$213$	2.88378	0.197593
$214$	−35.2382	−2.40883
$215$	2.49186	0.169944
$216$	−0.972799	−0.0661906
$217$	0.386423	0.0262321
$218$	6.97755	0.472579
$219$	0.367519	0.0248346
$220$	10.4222	0.702663
$221$	−1.02973	−0.0692671
$222$	0.462234	0.0310231
$223$	19.4923	1.30530	0.652652	−	0.757658i	$-0.273657\pi$
$223$	19.4923	1.30530	0.652652	+	0.757658i	$0.273657\pi$
$224$	−0.485693	−0.0324517
$225$	−12.7839	−0.852261
$226$	19.2396	1.27980
$227$	−17.3224	−1.14973	−0.574863	−	0.818249i	$-0.694945\pi$
$227$	−17.3224	−1.14973	−0.574863	+	0.818249i	$0.694945\pi$
$228$	−2.14806	−0.142259
$229$	20.5617	1.35875	0.679376	−	0.733790i	$-0.262250\pi$
$229$	20.5617	1.35875	0.679376	+	0.733790i	$0.262250\pi$
$230$	48.8143	3.21872
$231$	0.0192899	0.00126918
$232$	0.907392	0.0595732
$233$	17.6548	1.15660	0.578302	−	0.815823i	$-0.303716\pi$
$233$	17.6548	1.15660	0.578302	+	0.815823i	$0.303716\pi$
$234$	10.3728	0.678093
$235$	−4.03067	−0.262932
$236$	15.4111	1.00318
$237$	1.88116	0.122194
$238$	−0.0766141	−0.00496615
$239$	10.1958	0.659512	0.329756	−	0.944066i	$-0.393034\pi$
$239$	10.1958	0.659512	0.329756	+	0.944066i	$0.393034\pi$
$240$	2.14368	0.138374
$241$	20.5233	1.32202	0.661012	−	0.750376i	$-0.270127\pi$
$241$	20.5233	1.32202	0.661012	+	0.750376i	$0.270127\pi$
$242$	18.5679	1.19359
$243$	−5.85141	−0.375368
$244$	7.27228	0.465560
$245$	−21.3730	−1.36547
$246$	2.26705	0.144542
$247$	6.94035	0.441604
$248$	4.74674	0.301418
$249$	−0.0997143	−0.00631914
$250$	4.25679	0.269223
$251$	−14.1491	−0.893081	−0.446540	−	0.894763i	$-0.647344\pi$
$251$	−14.1491	−0.893081	−0.446540	+	0.894763i	$0.647344\pi$
$252$	0.417226	0.0262828
$253$	−11.1008	−0.697900
$254$	7.81306	0.490235
$255$	0.413654	0.0259040
$256$	8.94482	0.559051
$257$	−12.4838	−0.778719	−0.389360	−	0.921086i	$-0.627304\pi$
$257$	−12.4838	−0.778719	−0.389360	+	0.921086i	$0.627304\pi$
$258$	0.377046	0.0234739
$259$	−0.0600719	−0.00373269
$260$	12.1128	0.751207
$261$	3.62869	0.224610
$262$	−38.0006	−2.34768
$263$	26.7051	1.64671	0.823353	−	0.567529i	$-0.192101\pi$
$263$	26.7051	1.64671	0.823353	+	0.567529i	$0.192101\pi$
$264$	0.236953	0.0145835
$265$	−22.1036	−1.35781
$266$	0.516377	0.0316611
$267$	1.52508	0.0933331
$268$	5.53709	0.338231
$269$	17.4841	1.06602	0.533012	−	0.846108i	$-0.321060\pi$
$269$	17.4841	1.06602	0.533012	+	0.846108i	$0.321060\pi$
$270$	−8.40306	−0.511394
$271$	16.6560	1.01178	0.505891	−	0.862598i	$-0.331164\pi$
$271$	16.6560	1.01178	0.505891	+	0.862598i	$0.331164\pi$
$272$	1.93617	0.117398
$273$	0.0224191	0.00135687
$274$	36.9464	2.23201
$275$	6.27958	0.378673
$276$	3.99306	0.240354
$277$	19.3925	1.16518	0.582592	−	0.812765i	$-0.302039\pi$
$277$	19.3925	1.16518	0.582592	+	0.812765i	$0.302039\pi$
$278$	27.7644	1.66520
$279$	18.9823	1.13644
$280$	0.135415	0.00809259
$281$	−32.7713	−1.95497	−0.977487	−	0.210996i	$-0.932329\pi$
$281$	−32.7713	−1.95497	−0.977487	+	0.210996i	$0.932329\pi$
$282$	−0.609884	−0.0363181
$283$	9.49758	0.564572	0.282286	−	0.959330i	$-0.408907\pi$
$283$	9.49758	0.564572	0.282286	+	0.959330i	$0.408907\pi$
$284$	−30.6387	−1.81807
$285$	−2.78801	−0.165148
$286$	−5.09523	−0.301287
$287$	−0.294625	−0.0173912
$288$	−23.8588	−1.40589
$289$	−16.6264	−0.978023
$290$	7.83808	0.460268
$291$	−0.652109	−0.0382273
$292$	−3.90469	−0.228505
$293$	−13.0273	−0.761062	−0.380531	−	0.924768i	$-0.624259\pi$
$293$	−13.0273	−0.761062	−0.380531	+	0.924768i	$0.624259\pi$
$294$	−3.23397	−0.188609
$295$	20.0024	1.16458
$296$	−0.737910	−0.0428902
$297$	1.91093	0.110883
$298$	−10.3742	−0.600962
$299$	−12.9015	−0.746115
$300$	−2.25883	−0.130413
$301$	−0.0490009	−0.00282436
$302$	−40.4909	−2.32999
$303$	1.63772	0.0940848
$304$	−13.0498	−0.748455
$305$	9.43886	0.540467
$306$	−3.76353	−0.215147
$307$	−13.2164	−0.754300	−0.377150	−	0.926152i	$-0.623096\pi$
$307$	−13.2164	−0.754300	−0.377150	+	0.926152i	$0.623096\pi$
$308$	−0.204945	−0.0116778
$309$	1.96329	0.111688
$310$	41.0025	2.32878
$311$	5.14121	0.291532	0.145766	−	0.989319i	$-0.453435\pi$
$311$	5.14121	0.291532	0.145766	+	0.989319i	$0.453435\pi$
$312$	0.275392	0.0155910
$313$	7.95381	0.449576	0.224788	−	0.974408i	$-0.427831\pi$
$313$	7.95381	0.449576	0.224788	+	0.974408i	$0.427831\pi$
$314$	37.8120	2.13385
$315$	0.541528	0.0305116
$316$	−19.9863	−1.12432
$317$	11.6079	0.651967	0.325983	−	0.945376i	$-0.394305\pi$
$317$	11.6079	0.651967	0.325983	+	0.945376i	$0.394305\pi$
$318$	−3.34452	−0.187551
$319$	−1.78244	−0.0997977
$320$	−32.1825	−1.79906
$321$	−3.74129	−0.208819
$322$	−0.959902	−0.0534933
$323$	−2.51814	−0.140113
$324$	20.1490	1.11939
$325$	7.29824	0.404834
$326$	−2.08654	−0.115563
$327$	0.740817	0.0409673
$328$	−3.61912	−0.199832
$329$	0.0792605	0.00436977
$330$	2.04681	0.112673
$331$	−11.5015	−0.632177	−0.316089	−	0.948730i	$-0.602370\pi$
$331$	−11.5015	−0.632177	−0.316089	+	0.948730i	$0.602370\pi$
$332$	1.05941	0.0581428
$333$	−2.95092	−0.161710
$334$	13.7010	0.749683
$335$	7.18671	0.392652
$336$	−0.0421541	−0.00229970
$337$	−8.23750	−0.448725	−0.224363	−	0.974506i	$-0.572030\pi$
$337$	−8.23750	−0.448725	−0.224363	+	0.974506i	$0.572030\pi$
$338$	21.2033	1.15331
$339$	2.04270	0.110944
$340$	−4.39485	−0.238344
$341$	−9.32430	−0.504939
$342$	25.3661	1.37164
$343$	0.840790	0.0453984
$344$	−0.601917	−0.0324532
$345$	5.18269	0.279027
$346$	46.8489	2.51861
$347$	6.28615	0.337458	0.168729	−	0.985662i	$-0.446034\pi$
$347$	6.28615	0.337458	0.168729	+	0.985662i	$0.446034\pi$
$348$	0.641163	0.0343700
$349$	30.8187	1.64969	0.824843	−	0.565362i	$-0.191264\pi$
$349$	30.8187	1.64969	0.824843	+	0.565362i	$0.191264\pi$
$350$	0.543005	0.0290248
$351$	2.22091	0.118544
$352$	11.7197	0.624660
$353$	25.8016	1.37328	0.686640	−	0.726997i	$-0.259085\pi$
$353$	25.8016	1.37328	0.686640	+	0.726997i	$0.259085\pi$
$354$	3.02658	0.160861
$355$	−39.7666	−2.11059
$356$	−16.2031	−0.858764
$357$	−0.00813423	−0.000430509 0
$358$	−10.8276	−0.572256
$359$	9.89303	0.522134	0.261067	−	0.965321i	$-0.415926\pi$
$359$	9.89303	0.522134	0.261067	+	0.965321i	$0.415926\pi$
$360$	6.65201	0.350592
$361$	−2.02782	−0.106727
$362$	20.2399	1.06379
$363$	1.97138	0.103471
$364$	−0.238191	−0.0124846
$365$	−5.06799	−0.265271
$366$	1.42820	0.0746533
$367$	−16.7539	−0.874547	−0.437274	−	0.899328i	$-0.644056\pi$
$367$	−16.7539	−0.874547	−0.437274	+	0.899328i	$0.644056\pi$
$368$	24.2584	1.26456
$369$	−14.4729	−0.753431
$370$	−6.37409	−0.331373
$371$	0.434653	0.0225661
$372$	3.35405	0.173899
$373$	19.9759	1.03431	0.517157	−	0.855891i	$-0.326990\pi$
$373$	19.9759	1.03431	0.517157	+	0.855891i	$0.326990\pi$
$374$	1.84868	0.0955930
$375$	0.451950	0.0233386
$376$	0.973619	0.0502106
$377$	−2.07159	−0.106692
$378$	0.165241	0.00849907
$379$	29.3983	1.51009	0.755044	−	0.655674i	$-0.227616\pi$
$379$	29.3983	1.51009	0.755044	+	0.655674i	$0.227616\pi$
$380$	29.6212	1.51954
$381$	0.829524	0.0424978
$382$	15.6111	0.798733
$383$	6.91468	0.353324	0.176662	−	0.984272i	$-0.443470\pi$
$383$	6.91468	0.353324	0.176662	+	0.984272i	$0.443470\pi$
$384$	−1.28732	−0.0656931
$385$	−0.266003	−0.0135568
$386$	6.07123	0.309017
$387$	−2.40708	−0.122359
$388$	6.92832	0.351732
$389$	−32.3746	−1.64146	−0.820728	−	0.571319i	$-0.806432\pi$
$389$	−32.3746	−1.64146	−0.820728	+	0.571319i	$0.806432\pi$
$390$	2.37884	0.120457
$391$	4.68101	0.236729
$392$	5.16271	0.260756
$393$	−4.03458	−0.203517
$394$	−38.7182	−1.95059
$395$	−25.9407	−1.30522
$396$	−10.0676	−0.505915
$397$	22.6042	1.13447	0.567236	−	0.823555i	$-0.308013\pi$
$397$	22.6042	1.13447	0.567236	+	0.823555i	$0.308013\pi$
$398$	19.1186	0.958328
$399$	0.0548245	0.00274466
$400$	−13.7227	−0.686135
$401$	−26.3907	−1.31789	−0.658943	−	0.752193i	$-0.728996\pi$
$401$	−26.3907	−1.31789	−0.658943	+	0.752193i	$0.728996\pi$
$402$	1.08743	0.0542360
$403$	−10.8369	−0.539823
$404$	−17.4000	−0.865681
$405$	26.1518	1.29949
$406$	−0.154131	−0.00764939
$407$	1.44952	0.0718501
$408$	−0.0999192	−0.00494674
$409$	14.5246	0.718197	0.359098	−	0.933300i	$-0.383084\pi$
$409$	14.5246	0.718197	0.359098	+	0.933300i	$0.383084\pi$
$410$	−31.2620	−1.54392
$411$	3.92266	0.193490
$412$	−20.8590	−1.02765
$413$	−0.393334	−0.0193547
$414$	−47.1535	−2.31747
$415$	1.37504	0.0674979
$416$	13.6208	0.667816
$417$	2.94779	0.144354
$418$	−12.4601	−0.609442
$419$	−7.62250	−0.372383	−0.186192	−	0.982513i	$-0.559615\pi$
$419$	−7.62250	−0.372383	−0.186192	+	0.982513i	$0.559615\pi$
$420$	0.0956841	0.00466891
$421$	−15.8195	−0.770993	−0.385497	−	0.922709i	$-0.625970\pi$
$421$	−15.8195	−0.770993	−0.385497	+	0.922709i	$0.625970\pi$
$422$	33.8338	1.64700
$423$	3.89353	0.189310
$424$	5.33919	0.259294
$425$	−2.64799	−0.128446
$426$	−6.01713	−0.291531
$427$	−0.185609	−0.00898226
$428$	39.7493	1.92135
$429$	−0.540968	−0.0261182
$430$	−5.19937	−0.250736
$431$	−24.0817	−1.15998	−0.579988	−	0.814625i	$-0.696943\pi$
$431$	−24.0817	−1.15998	−0.579988	+	0.814625i	$0.696943\pi$
$432$	−4.17593	−0.200914
$433$	−3.28261	−0.157752	−0.0788761	−	0.996884i	$-0.525133\pi$
$433$	−3.28261	−0.157752	−0.0788761	+	0.996884i	$0.525133\pi$
$434$	−0.806288	−0.0387030
$435$	0.832181	0.0399000
$436$	−7.87079	−0.376942
$437$	−31.5499	−1.50924
$438$	−0.766843	−0.0366412
$439$	15.4989	0.739720	0.369860	−	0.929088i	$-0.379406\pi$
$439$	15.4989	0.739720	0.369860	+	0.929088i	$0.379406\pi$
$440$	−3.26753	−0.155773
$441$	20.6458	0.983134
$442$	2.14857	0.102197
$443$	7.17340	0.340819	0.170409	−	0.985373i	$-0.445491\pi$
$443$	7.17340	0.340819	0.170409	+	0.985373i	$0.445491\pi$
$444$	−0.521407	−0.0247449
$445$	−21.0304	−0.996937
$446$	−40.6715	−1.92585
$447$	−1.10145	−0.0520966
$448$	0.632848	0.0298993
$449$	−29.6344	−1.39853	−0.699267	−	0.714861i	$-0.746490\pi$
$449$	−29.6344	−1.39853	−0.699267	+	0.714861i	$0.746490\pi$
$450$	26.6742	1.25743
$451$	7.10924	0.334761
$452$	−21.7026	−1.02080
$453$	−4.29898	−0.201984
$454$	36.1439	1.69632
$455$	−0.309154	−0.0144934
$456$	0.673453	0.0315373
$457$	−22.2534	−1.04097	−0.520486	−	0.853870i	$-0.674249\pi$
$457$	−22.2534	−1.04097	−0.520486	+	0.853870i	$0.674249\pi$
$458$	−42.9027	−2.00471
$459$	−0.805805	−0.0376117
$460$	−55.0633	−2.56734
$461$	−36.3339	−1.69224	−0.846119	−	0.532994i	$-0.821067\pi$
$461$	−36.3339	−1.69224	−0.846119	+	0.532994i	$0.821067\pi$
$462$	−0.0402492	−0.00187256
$463$	−6.90574	−0.320937	−0.160468	−	0.987041i	$-0.551300\pi$
$463$	−6.90574	−0.320937	−0.160468	+	0.987041i	$0.551300\pi$
$464$	3.89516	0.180828
$465$	4.35329	0.201879
$466$	−36.8374	−1.70646
$467$	−25.2645	−1.16910	−0.584552	−	0.811357i	$-0.698730\pi$
$467$	−25.2645	−1.16910	−0.584552	+	0.811357i	$0.698730\pi$
$468$	−11.7007	−0.540866
$469$	−0.141322	−0.00652565
$470$	8.41015	0.387931
$471$	4.01455	0.184981
$472$	−4.83164	−0.222394
$473$	1.18238	0.0543659
$474$	−3.92511	−0.180286
$475$	17.8474	0.818894
$476$	0.0864220	0.00396114
$477$	21.3516	0.977620
$478$	−21.2740	−0.973049
$479$	18.8664	0.862027	0.431014	−	0.902345i	$-0.358156\pi$
$479$	18.8664	0.862027	0.431014	+	0.902345i	$0.358156\pi$
$480$	−5.47163	−0.249745
$481$	1.68466	0.0768139
$482$	−42.8227	−1.95052
$483$	−0.101914	−0.00463726
$484$	−20.9449	−0.952041
$485$	8.99243	0.408325
$486$	12.2092	0.553821
$487$	15.9125	0.721064	0.360532	−	0.932747i	$-0.382595\pi$
$487$	15.9125	0.721064	0.360532	+	0.932747i	$0.382595\pi$
$488$	−2.27998	−0.103210
$489$	−0.221531	−0.0100180
$490$	44.5956	2.01463
$491$	−15.2056	−0.686221	−0.343111	−	0.939295i	$-0.611481\pi$
$491$	−15.2056	−0.686221	−0.343111	+	0.939295i	$0.611481\pi$
$492$	−2.55727	−0.115290
$493$	0.751626	0.0338515
$494$	−14.4813	−0.651545
$495$	−13.0669	−0.587315
$496$	20.3763	0.914923
$497$	0.781985	0.0350768
$498$	0.208058	0.00932330
$499$	−43.4668	−1.94584	−0.972920	−	0.231143i	$-0.925754\pi$
$499$	−43.4668	−1.94584	−0.972920	+	0.231143i	$0.925754\pi$
$500$	−4.80173	−0.214740
$501$	1.45465	0.0649890
$502$	29.5226	1.31766
$503$	−31.9085	−1.42273	−0.711364	−	0.702824i	$-0.751922\pi$
$503$	−31.9085	−1.42273	−0.711364	+	0.702824i	$0.751922\pi$
$504$	−0.130808	−0.00582663
$505$	−22.5838	−1.00497
$506$	23.1622	1.02969
$507$	2.25118	0.0999785
$508$	−8.81326	−0.391025
$509$	−7.23238	−0.320570	−0.160285	−	0.987071i	$-0.551241\pi$
$509$	−7.23238	−0.320570	−0.160285	+	0.987071i	$0.551241\pi$
$510$	−0.863105	−0.0382189
$511$	0.0996589	0.00440865
$512$	−30.2857	−1.33845
$513$	5.43110	0.239789
$514$	26.0480	1.14893
$515$	−27.0733	−1.19299
$516$	−0.425314	−0.0187234
$517$	−1.91254	−0.0841133
$518$	0.125342	0.00550723
$519$	4.97402	0.218335
$520$	−3.79759	−0.166535
$521$	−1.84954	−0.0810298	−0.0405149	−	0.999179i	$-0.512900\pi$
$521$	−1.84954	−0.0810298	−0.0405149	+	0.999179i	$0.512900\pi$
$522$	−7.57140	−0.331391
$523$	9.87616	0.431854	0.215927	−	0.976409i	$-0.430723\pi$
$523$	9.87616	0.431854	0.215927	+	0.976409i	$0.430723\pi$
$524$	42.8653	1.87258
$525$	0.0576517	0.00251613
$526$	−55.7213	−2.42956
$527$	3.93190	0.171276
$528$	1.01717	0.0442666
$529$	35.6486	1.54994
$530$	46.1200	2.00333
$531$	−19.3219	−0.838497
$532$	−0.582482	−0.0252538
$533$	8.26250	0.357888
$534$	−3.18213	−0.137704
$535$	51.5915	2.23049
$536$	−1.73597	−0.0749826
$537$	−1.14958	−0.0496081
$538$	−36.4813	−1.57282
$539$	−10.1414	−0.436822
$540$	9.47879	0.407902
$541$	−2.59252	−0.111461	−0.0557306	−	0.998446i	$-0.517749\pi$
$541$	−2.59252	−0.111461	−0.0557306	+	0.998446i	$0.517749\pi$
$542$	−34.7535	−1.49279
$543$	2.14890	0.0922183
$544$	−4.94198	−0.211886
$545$	−10.2157	−0.437592
$546$	−0.0467784	−0.00200193
$547$	−13.3677	−0.571562	−0.285781	−	0.958295i	$-0.592253\pi$
$547$	−13.3677	−0.571562	−0.285781	+	0.958295i	$0.592253\pi$
$548$	−41.6762	−1.78032
$549$	−9.11772	−0.389135
$550$	−13.1026	−0.558696
$551$	−5.06594	−0.215816
$552$	−1.25189	−0.0532841
$553$	0.510107	0.0216920
$554$	−40.4633	−1.71912
$555$	−0.676747	−0.0287263
$556$	−31.3187	−1.32821
$557$	−16.4831	−0.698412	−0.349206	−	0.937046i	$-0.613549\pi$
$557$	−16.4831	−0.698412	−0.349206	+	0.937046i	$0.613549\pi$
$558$	−39.6074	−1.67672
$559$	1.37419	0.0581218
$560$	0.581295	0.0245642
$561$	0.196277	0.00828683
$562$	68.3787	2.88438
$563$	−9.73615	−0.410330	−0.205165	−	0.978727i	$-0.565773\pi$
$563$	−9.73615	−0.410330	−0.205165	+	0.978727i	$0.565773\pi$
$564$	0.687959	0.0289683
$565$	−28.1683	−1.18505
$566$	−19.8171	−0.832974
$567$	−0.514259	−0.0215968
$568$	9.60574	0.403048
$569$	13.0858	0.548585	0.274293	−	0.961646i	$-0.411556\pi$
$569$	13.0858	0.548585	0.274293	+	0.961646i	$0.411556\pi$
$570$	5.81731	0.243660
$571$	3.89840	0.163143	0.0815715	−	0.996667i	$-0.474006\pi$
$571$	3.89840	0.163143	0.0815715	+	0.996667i	$0.474006\pi$
$572$	5.74751	0.240315
$573$	1.65745	0.0692411
$574$	0.614748	0.0256591
$575$	−33.1768	−1.38357
$576$	31.0875	1.29531
$577$	23.1930	0.965539	0.482769	−	0.875748i	$-0.339631\pi$
$577$	23.1930	0.965539	0.482769	+	0.875748i	$0.339631\pi$
$578$	34.6916	1.44298
$579$	0.644591	0.0267883
$580$	−8.84148	−0.367123
$581$	−0.0270392	−0.00112178
$582$	1.36065	0.0564009
$583$	−10.4881	−0.434372
$584$	1.22419	0.0506573
$585$	−15.1866	−0.627891
$586$	27.1820	1.12288
$587$	−23.3168	−0.962387	−0.481194	−	0.876614i	$-0.659797\pi$
$587$	−23.3168	−0.962387	−0.481194	+	0.876614i	$0.659797\pi$
$588$	3.64797	0.150440
$589$	−26.5009	−1.09195
$590$	−41.7358	−1.71824
$591$	−4.11077	−0.169094
$592$	−3.16762	−0.130189
$593$	−36.8149	−1.51181	−0.755904	−	0.654682i	$-0.772802\pi$
$593$	−36.8149	−1.51181	−0.755904	+	0.654682i	$0.772802\pi$
$594$	−3.98722	−0.163598
$595$	0.112169	0.00459848
$596$	11.7023	0.479344
$597$	2.02985	0.0830761
$598$	26.9196	1.10082
$599$	−1.52089	−0.0621418	−0.0310709	−	0.999517i	$-0.509892\pi$
$599$	−1.52089	−0.0621418	−0.0310709	+	0.999517i	$0.509892\pi$
$600$	0.708181	0.0289114
$601$	−10.2214	−0.416940	−0.208470	−	0.978029i	$-0.566848\pi$
$601$	−10.2214	−0.416940	−0.208470	+	0.978029i	$0.566848\pi$
$602$	0.102242	0.00416709
$603$	−6.94220	−0.282708
$604$	45.6744	1.85846
$605$	−27.1849	−1.10522
$606$	−3.41718	−0.138813
$607$	−30.7746	−1.24910	−0.624551	−	0.780984i	$-0.714718\pi$
$607$	−30.7746	−1.24910	−0.624551	+	0.780984i	$0.714718\pi$
$608$	33.3088	1.35085
$609$	−0.0163643	−0.000663115 0
$610$	−19.6946	−0.797410
$611$	−2.22279	−0.0899244
$612$	4.24532	0.171607
$613$	−44.4078	−1.79361	−0.896807	−	0.442423i	$-0.854119\pi$
$613$	−44.4078	−1.79361	−0.896807	+	0.442423i	$0.854119\pi$
$614$	27.5766	1.11290
$615$	−3.31914	−0.133840
$616$	0.0642539	0.00258886
$617$	−16.3100	−0.656617	−0.328309	−	0.944570i	$-0.606479\pi$
$617$	−16.3100	−0.656617	−0.328309	+	0.944570i	$0.606479\pi$
$618$	−4.09649	−0.164785
$619$	−16.8898	−0.678858	−0.339429	−	0.940632i	$-0.610234\pi$
$619$	−16.8898	−0.678858	−0.339429	+	0.940632i	$0.610234\pi$
$620$	−46.2515	−1.85750
$621$	−10.0960	−0.405137
$622$	−10.7274	−0.430128
$623$	0.413550	0.0165685
$624$	1.18217	0.0473248
$625$	−27.8931	−1.11573
$626$	−16.5960	−0.663308
$627$	−1.32290	−0.0528317
$628$	−42.6525	−1.70202
$629$	−0.611238	−0.0243717
$630$	−1.12992	−0.0450171
$631$	−41.4701	−1.65090	−0.825449	−	0.564477i	$-0.809078\pi$
$631$	−41.4701	−1.65090	−0.825449	+	0.564477i	$0.809078\pi$
$632$	6.26605	0.249250
$633$	3.59218	0.142776
$634$	−24.2204	−0.961916
$635$	−11.4389	−0.453940
$636$	3.77267	0.149596
$637$	−11.7865	−0.467000
$638$	3.71914	0.147242
$639$	38.4136	1.51962
$640$	17.7518	0.701700
$641$	−35.1508	−1.38837	−0.694186	−	0.719796i	$-0.744235\pi$
$641$	−35.1508	−1.38837	−0.694186	+	0.719796i	$0.744235\pi$
$642$	7.80636	0.308092
$643$	26.4183	1.04184	0.520918	−	0.853607i	$-0.325590\pi$
$643$	26.4183	1.04184	0.520918	+	0.853607i	$0.325590\pi$
$644$	1.08279	0.0426677
$645$	−0.552025	−0.0217360
$646$	5.25419	0.206724
$647$	17.2754	0.679165	0.339582	−	0.940576i	$-0.389714\pi$
$647$	17.2754	0.679165	0.339582	+	0.940576i	$0.389714\pi$
$648$	−6.31705	−0.248157
$649$	9.49107	0.372557
$650$	−15.2281	−0.597294
$651$	−0.0856048	−0.00335512
$652$	2.35365	0.0921761
$653$	9.27760	0.363060	0.181530	−	0.983385i	$-0.441895\pi$
$653$	9.27760	0.363060	0.181530	+	0.983385i	$0.441895\pi$
$654$	−1.54574	−0.0604434
$655$	55.6358	2.17387
$656$	−15.5358	−0.606570
$657$	4.89556	0.190994
$658$	−0.165380	−0.00644719
$659$	33.3877	1.30060	0.650300	−	0.759678i	$-0.274643\pi$
$659$	33.3877	1.30060	0.650300	+	0.759678i	$0.274643\pi$
$660$	−2.30884	−0.0898713
$661$	19.9449	0.775765	0.387882	−	0.921709i	$-0.373207\pi$
$661$	19.9449	0.775765	0.387882	+	0.921709i	$0.373207\pi$
$662$	23.9983	0.932719
$663$	0.228117	0.00885933
$664$	−0.332144	−0.0128897
$665$	−0.756017	−0.0293171
$666$	6.15722	0.238588
$667$	9.41717	0.364634
$668$	−15.4549	−0.597968
$669$	−4.31816	−0.166950
$670$	−14.9954	−0.579322
$671$	4.47871	0.172899
$672$	0.107596	0.00415061
$673$	27.1249	1.04559	0.522793	−	0.852459i	$-0.324890\pi$
$673$	27.1249	1.04559	0.522793	+	0.852459i	$0.324890\pi$
$674$	17.1879	0.662052
$675$	5.71117	0.219823
$676$	−23.9176	−0.919909
$677$	31.3501	1.20488	0.602440	−	0.798164i	$-0.294195\pi$
$677$	31.3501	1.20488	0.602440	+	0.798164i	$0.294195\pi$
$678$	−4.26217	−0.163688
$679$	−0.176830	−0.00678613
$680$	1.37786	0.0528386
$681$	3.83745	0.147051
$682$	19.4555	0.744991
$683$	−29.0340	−1.11096	−0.555478	−	0.831531i	$-0.687465\pi$
$683$	−29.0340	−1.11096	−0.555478	+	0.831531i	$0.687465\pi$
$684$	−28.6134	−1.09406
$685$	−54.0924	−2.06677
$686$	−1.75434	−0.0669811
$687$	−4.55505	−0.173786
$688$	−2.58385	−0.0985082
$689$	−12.1894	−0.464381
$690$	−10.8139	−0.411678
$691$	6.65312	0.253097	0.126548	−	0.991960i	$-0.459610\pi$
$691$	6.65312	0.253097	0.126548	+	0.991960i	$0.459610\pi$
$692$	−52.8463	−2.00892
$693$	0.256953	0.00976084
$694$	−13.1163	−0.497888
$695$	−40.6493	−1.54191
$696$	−0.201016	−0.00761948
$697$	−2.99785	−0.113551
$698$	−64.3044	−2.43396
$699$	−3.91109	−0.147931
$700$	−0.612519	−0.0231510
$701$	−19.6411	−0.741834	−0.370917	−	0.928666i	$-0.620957\pi$
$701$	−19.6411	−0.741834	−0.370917	+	0.928666i	$0.620957\pi$
$702$	−4.63403	−0.174900
$703$	4.11973	0.155379
$704$	−15.2705	−0.575528
$705$	0.892918	0.0336293
$706$	−53.8361	−2.02615
$707$	0.444097	0.0167020
$708$	−3.41403	−0.128307
$709$	−20.9621	−0.787246	−0.393623	−	0.919272i	$-0.628779\pi$
$709$	−20.9621	−0.787246	−0.393623	+	0.919272i	$0.628779\pi$
$710$	82.9747	3.11398
$711$	25.0581	0.939752
$712$	5.07996	0.190379
$713$	49.2630	1.84491
$714$	0.0169724	0.000635177 0
$715$	7.45982	0.278981
$716$	12.2137	0.456447
$717$	−2.25869	−0.0843523
$718$	−20.6422	−0.770360
$719$	−25.6594	−0.956935	−0.478467	−	0.878105i	$-0.658808\pi$
$719$	−25.6594	−0.956935	−0.478467	+	0.878105i	$0.658808\pi$
$720$	28.5551	1.06418
$721$	0.532380	0.0198269
$722$	4.23113	0.157466
$723$	−4.54656	−0.169088
$724$	−22.8310	−0.848507
$725$	−5.32718	−0.197846
$726$	−4.11337	−0.152661
$727$	24.9254	0.924431	0.462215	−	0.886768i	$-0.347055\pi$
$727$	24.9254	0.924431	0.462215	+	0.886768i	$0.347055\pi$
$728$	0.0746771	0.00276772
$729$	−24.3859	−0.903182
$730$	10.5746	0.391383
$731$	−0.498590	−0.0184410
$732$	−1.61104	−0.0595456
$733$	37.7637	1.39483	0.697417	−	0.716666i	$-0.254333\pi$
$733$	37.7637	1.39483	0.697417	+	0.716666i	$0.254333\pi$
$734$	34.9577	1.29031
$735$	4.73479	0.174645
$736$	−61.9184	−2.28234
$737$	3.41007	0.125612
$738$	30.1984	1.11162
$739$	−15.0041	−0.551935	−0.275968	−	0.961167i	$-0.588998\pi$
$739$	−15.0041	−0.551935	−0.275968	+	0.961167i	$0.588998\pi$
$740$	7.19008	0.264313
$741$	−1.53750	−0.0564816
$742$	−0.906921	−0.0332941
$743$	−10.4780	−0.384400	−0.192200	−	0.981356i	$-0.561562\pi$
$743$	−10.4780	−0.384400	−0.192200	+	0.981356i	$0.561562\pi$
$744$	−1.05155	−0.0385517
$745$	15.1887	0.556469
$746$	−41.6806	−1.52603
$747$	−1.32825	−0.0485982
$748$	−2.08534	−0.0762477
$749$	−1.01451	−0.0370695
$750$	−0.943012	−0.0344339
$751$	21.2925	0.776973	0.388486	−	0.921454i	$-0.372998\pi$
$751$	21.2925	0.776973	0.388486	+	0.921454i	$0.372998\pi$
$752$	4.17945	0.152409
$753$	3.13446	0.114226
$754$	4.32246	0.157415
$755$	59.2818	2.15749
$756$	−0.186394	−0.00677910
$757$	39.4182	1.43268	0.716339	−	0.697752i	$-0.245816\pi$
$757$	39.4182	1.43268	0.716339	+	0.697752i	$0.245816\pi$
$758$	−61.3407	−2.22799
$759$	2.45917	0.0892622
$760$	−9.28675	−0.336866
$761$	8.50065	0.308148	0.154074	−	0.988059i	$-0.450761\pi$
$761$	8.50065	0.308148	0.154074	+	0.988059i	$0.450761\pi$
$762$	−1.73084	−0.0627016
$763$	0.200885	0.00727252
$764$	−17.6096	−0.637092
$765$	5.51011	0.199218
$766$	−14.4278	−0.521296
$767$	11.0307	0.398296
$768$	−1.98156	−0.0715033
$769$	19.1384	0.690148	0.345074	−	0.938575i	$-0.387854\pi$
$769$	19.1384	0.690148	0.345074	+	0.938575i	$0.387854\pi$
$770$	0.555027	0.0200018
$771$	2.76556	0.0995991
$772$	−6.84845	−0.246481
$773$	−13.9570	−0.501998	−0.250999	−	0.967987i	$-0.580759\pi$
$773$	−13.9570	−0.501998	−0.250999	+	0.967987i	$0.580759\pi$
$774$	5.02247	0.180529
$775$	−27.8675	−1.00103
$776$	−2.17215	−0.0779755
$777$	0.0133078	0.000477415 0
$778$	67.5509	2.42182
$779$	20.2054	0.723934
$780$	−2.68337	−0.0960802
$781$	−18.8691	−0.675191
$782$	−9.76711	−0.349271
$783$	−1.62110	−0.0579335
$784$	22.1619	0.791498
$785$	−55.3597	−1.97587
$786$	8.41831	0.300271
$787$	14.1215	0.503378	0.251689	−	0.967808i	$-0.419014\pi$
$787$	14.1215	0.503378	0.251689	+	0.967808i	$0.419014\pi$
$788$	43.6748	1.55585
$789$	−5.91601	−0.210616
$790$	54.1263	1.92573
$791$	0.553911	0.0196948
$792$	3.15636	0.112156
$793$	5.20524	0.184843
$794$	−47.1646	−1.67381
$795$	4.89663	0.173666
$796$	−21.5661	−0.764389
$797$	−14.5076	−0.513884	−0.256942	−	0.966427i	$-0.582715\pi$
$797$	−14.5076	−0.513884	−0.256942	+	0.966427i	$0.582715\pi$
$798$	−0.114394	−0.00404949
$799$	0.806484	0.0285314
$800$	35.0265	1.23837
$801$	20.3149	0.717791
$802$	55.0652	1.94442
$803$	−2.40475	−0.0848616
$804$	−1.22664	−0.0432602
$805$	1.40537	0.0495329
$806$	22.6116	0.796459
$807$	−3.87327	−0.136346
$808$	5.45519	0.191913
$809$	6.36609	0.223820	0.111910	−	0.993718i	$-0.464303\pi$
$809$	6.36609	0.223820	0.111910	+	0.993718i	$0.464303\pi$
$810$	−54.5668	−1.91728
$811$	−41.4296	−1.45479	−0.727396	−	0.686218i	$-0.759269\pi$
$811$	−41.4296	−1.45479	−0.727396	+	0.686218i	$0.759269\pi$
$812$	0.173862	0.00610137
$813$	−3.68983	−0.129408
$814$	−3.02448	−0.106008
$815$	3.05486	0.107007
$816$	−0.428923	−0.0150153
$817$	3.36048	0.117568
$818$	−30.3062	−1.05963
$819$	0.298636	0.0104352
$820$	35.2641	1.23147
$821$	−18.4352	−0.643392	−0.321696	−	0.946843i	$-0.604253\pi$
$821$	−18.4352	−0.643392	−0.321696	+	0.946843i	$0.604253\pi$
$822$	−8.18478	−0.285477
$823$	9.57187	0.333654	0.166827	−	0.985986i	$-0.446648\pi$
$823$	9.57187	0.333654	0.166827	+	0.985986i	$0.446648\pi$
$824$	6.53964	0.227819
$825$	−1.39112	−0.0484326
$826$	0.820708	0.0285561
$827$	−13.5675	−0.471789	−0.235895	−	0.971779i	$-0.575802\pi$
$827$	−13.5675	−0.471789	−0.235895	+	0.971779i	$0.575802\pi$
$828$	53.1899	1.84848
$829$	−0.533875	−0.0185422	−0.00927112	−	0.999957i	$-0.502951\pi$
$829$	−0.533875	−0.0185422	−0.00927112	+	0.999957i	$0.502951\pi$
$830$	−2.86907	−0.0995868
$831$	−4.29605	−0.149028
$832$	−17.7476	−0.615289
$833$	4.27646	0.148171
$834$	−6.15068	−0.212981
$835$	−20.0593	−0.694180
$836$	14.0552	0.486108
$837$	−8.48030	−0.293122
$838$	15.9047	0.549417
$839$	−28.2307	−0.974631	−0.487316	−	0.873226i	$-0.662024\pi$
$839$	−28.2307	−0.974631	−0.487316	+	0.873226i	$0.662024\pi$
$840$	−0.0299986	−0.00103505
$841$	−27.4879	−0.947858
$842$	33.0079	1.13753
$843$	7.25987	0.250043
$844$	−38.1650	−1.31369
$845$	−31.0432	−1.06792
$846$	−8.12401	−0.279309
$847$	0.534573	0.0183681
$848$	22.9195	0.787059
$849$	−2.10401	−0.0722094
$850$	5.52514	0.189511
$851$	−7.65824	−0.262521
$852$	6.78742	0.232533
$853$	−17.4245	−0.596604	−0.298302	−	0.954472i	$-0.596420\pi$
$853$	−17.4245	−0.596604	−0.298302	+	0.954472i	$0.596420\pi$
$854$	0.387281	0.0132525
$855$	−37.1380	−1.27009
$856$	−12.4621	−0.425945
$857$	41.3876	1.41377	0.706887	−	0.707326i	$-0.250099\pi$
$857$	41.3876	1.41377	0.706887	+	0.707326i	$0.250099\pi$
$858$	1.12875	0.0385350
$859$	−2.59027	−0.0883788	−0.0441894	−	0.999023i	$-0.514071\pi$
$859$	−2.59027	−0.0883788	−0.0441894	+	0.999023i	$0.514071\pi$
$860$	5.86498	0.199994
$861$	0.0652687	0.00222435
$862$	50.2475	1.71144
$863$	9.82929	0.334593	0.167297	−	0.985907i	$-0.446496\pi$
$863$	9.82929	0.334593	0.167297	+	0.985907i	$0.446496\pi$
$864$	10.6588	0.362621
$865$	−68.5905	−2.33215
$866$	6.84930	0.232749
$867$	3.68326	0.125090
$868$	0.909506	0.0308706
$869$	−12.3088	−0.417546
$870$	−1.73638	−0.0588688
$871$	3.96325	0.134290
$872$	2.46763	0.0835644
$873$	−8.68647	−0.293993
$874$	65.8301	2.22674
$875$	0.122554	0.00414307
$876$	0.865011	0.0292260
$877$	21.5326	0.727104	0.363552	−	0.931574i	$-0.381564\pi$
$877$	21.5326	0.727104	0.363552	+	0.931574i	$0.381564\pi$
$878$	−32.3390	−1.09139
$879$	2.88595	0.0973407
$880$	−14.0265	−0.472834
$881$	−30.0961	−1.01396	−0.506982	−	0.861957i	$-0.669239\pi$
$881$	−30.0961	−1.01396	−0.506982	+	0.861957i	$0.669239\pi$
$882$	−43.0783	−1.45052
$883$	40.5470	1.36451	0.682257	−	0.731112i	$-0.260998\pi$
$883$	40.5470	1.36451	0.682257	+	0.731112i	$0.260998\pi$
$884$	−2.42362	−0.0815153
$885$	−4.43116	−0.148952
$886$	−14.9676	−0.502846
$887$	−40.9806	−1.37599	−0.687996	−	0.725714i	$-0.741510\pi$
$887$	−40.9806	−1.37599	−0.687996	+	0.725714i	$0.741510\pi$
$888$	0.163470	0.00548570
$889$	0.224939	0.00754423
$890$	43.8808	1.47089
$891$	12.4089	0.415715
$892$	45.8782	1.53611
$893$	−5.43569	−0.181898
$894$	2.29821	0.0768637
$895$	15.8524	0.529889
$896$	−0.349077	−0.0116619
$897$	2.85809	0.0954289
$898$	61.8334	2.06341
$899$	7.91012	0.263817
$900$	−30.0889	−1.00296
$901$	4.42264	0.147340
$902$	−14.8337	−0.493909
$903$	0.0108552	0.000361239 0
$904$	6.80413	0.226302
$905$	−29.6329	−0.985030
$906$	8.96999	0.298008
$907$	45.5948	1.51395	0.756976	−	0.653443i	$-0.226676\pi$
$907$	45.5948	1.51395	0.756976	+	0.653443i	$0.226676\pi$
$908$	−40.7709	−1.35303
$909$	21.8154	0.723573
$910$	0.645063	0.0213836
$911$	37.3201	1.23647	0.618235	−	0.785993i	$-0.287848\pi$
$911$	37.3201	1.23647	0.618235	+	0.785993i	$0.287848\pi$
$912$	2.89093	0.0957282
$913$	0.652450	0.0215929
$914$	46.4327	1.53586
$915$	−2.09100	−0.0691264
$916$	48.3950	1.59902
$917$	−1.09404	−0.0361285
$918$	1.68134	0.0554926
$919$	29.5391	0.974406	0.487203	−	0.873289i	$-0.338017\pi$
$919$	29.5391	0.974406	0.487203	+	0.873289i	$0.338017\pi$
$920$	17.2633	0.569154
$921$	2.92785	0.0964758
$922$	75.8122	2.49674
$923$	−21.9301	−0.721837
$924$	0.0454018	0.00149361
$925$	4.33217	0.142441
$926$	14.4091	0.473512
$927$	26.1522	0.858951
$928$	−9.94219	−0.326368
$929$	44.9161	1.47365	0.736825	−	0.676084i	$-0.236324\pi$
$929$	44.9161	1.47365	0.736825	+	0.676084i	$0.236324\pi$
$930$	−9.08333	−0.297854
$931$	−28.8232	−0.944644
$932$	41.5532	1.36112
$933$	−1.13894	−0.0372872
$934$	52.7155	1.72490
$935$	−2.70661	−0.0885158
$936$	3.66838	0.119905
$937$	32.3946	1.05829	0.529143	−	0.848533i	$-0.322514\pi$
$937$	32.3946	1.05829	0.529143	+	0.848533i	$0.322514\pi$
$938$	0.294874	0.00962799
$939$	−1.76202	−0.0575013
$940$	−9.48679	−0.309425
$941$	2.12839	0.0693834	0.0346917	−	0.999398i	$-0.488955\pi$
$941$	2.12839	0.0693834	0.0346917	+	0.999398i	$0.488955\pi$
$942$	−8.37653	−0.272922
$943$	−37.5602	−1.22313
$944$	−20.7408	−0.675054
$945$	−0.241926	−0.00786984
$946$	−2.46709	−0.0802119
$947$	−50.9137	−1.65447	−0.827236	−	0.561854i	$-0.810088\pi$
$947$	−50.9137	−1.65447	−0.827236	+	0.561854i	$0.810088\pi$
$948$	4.42759	0.143801
$949$	−2.79484	−0.0907244
$950$	−37.2393	−1.20820
$951$	−2.57152	−0.0833872
$952$	−0.0270948	−0.000878146 0
$953$	−36.5773	−1.18485	−0.592427	−	0.805624i	$-0.701830\pi$
$953$	−36.5773	−1.18485	−0.592427	+	0.805624i	$0.701830\pi$
$954$	−44.5509	−1.44239
$955$	−22.8559	−0.739599
$956$	23.9974	0.776131
$957$	0.394867	0.0127642
$958$	−39.3655	−1.27184
$959$	1.06369	0.0343485
$960$	7.12943	0.230101
$961$	10.3793	0.334817
$962$	−3.51511	−0.113332
$963$	−49.8362	−1.60595
$964$	48.3048	1.55579
$965$	−8.88876	−0.286139
$966$	0.212648	0.00684185
$967$	−27.8878	−0.896810	−0.448405	−	0.893830i	$-0.648008\pi$
$967$	−27.8878	−0.896810	−0.448405	+	0.893830i	$0.648008\pi$
$968$	6.56658	0.211058
$969$	0.557846	0.0179206
$970$	−18.7631	−0.602446
$971$	−27.8115	−0.892513	−0.446257	−	0.894905i	$-0.647243\pi$
$971$	−27.8115	−0.892513	−0.446257	+	0.894905i	$0.647243\pi$
$972$	−13.7722	−0.441743
$973$	0.799342	0.0256257
$974$	−33.2021	−1.06386
$975$	−1.61679	−0.0517787
$976$	−9.78728	−0.313283
$977$	8.93163	0.285748	0.142874	−	0.989741i	$-0.454366\pi$
$977$	8.93163	0.285748	0.142874	+	0.989741i	$0.454366\pi$
$978$	0.462234	0.0147806
$979$	−9.97886	−0.318926
$980$	−50.3046	−1.60692
$981$	9.86811	0.315064
$982$	31.7272	1.01246
$983$	−14.2101	−0.453233	−0.226616	−	0.973984i	$-0.572766\pi$
$983$	−14.2101	−0.453233	−0.226616	+	0.973984i	$0.572766\pi$
$984$	0.801747	0.0255588
$985$	56.6865	1.80618
$986$	−1.56830	−0.0499448
$987$	−0.0175587	−0.000558899 0
$988$	16.3352	0.519691
$989$	−6.24686	−0.198639
$990$	27.2647	0.866529
$991$	−3.08982	−0.0981514	−0.0490757	−	0.998795i	$-0.515628\pi$
$991$	−3.08982	−0.0981514	−0.0490757	+	0.998795i	$0.515628\pi$
$992$	−52.0095	−1.65130
$993$	2.54793	0.0808562
$994$	−1.63164	−0.0517526
$995$	−27.9911	−0.887378
$996$	−0.234693	−0.00743653
$997$	11.0393	0.349617	0.174809	−	0.984602i	$-0.444069\pi$
$997$	11.0393	0.349617	0.174809	+	0.984602i	$0.444069\pi$
$998$	90.6952	2.87091
$999$	1.31832	0.0417096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.18	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.18	✓	109	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08654 q^{2} -0.221531 q^{3} +2.35365 q^{4} +3.05486 q^{5} +0.462234 q^{6} -0.0600719 q^{7} -0.737910 q^{8} -2.95092 q^{9} +O(q^{10})\)	\(q-2.08654 q^{2} -0.221531 q^{3} +2.35365 q^{4} +3.05486 q^{5} +0.462234 q^{6} -0.0600719 q^{7} -0.737910 q^{8} -2.95092 q^{9} -6.37409 q^{10} +1.44952 q^{11} -0.521407 q^{12} +1.68466 q^{13} +0.125342 q^{14} -0.676747 q^{15} -3.16762 q^{16} -0.611238 q^{17} +6.15722 q^{18} +4.11973 q^{19} +7.19008 q^{20} +0.0133078 q^{21} -3.02448 q^{22} -7.65824 q^{23} +0.163470 q^{24} +4.33217 q^{25} -3.51511 q^{26} +1.31832 q^{27} -0.141388 q^{28} -1.22968 q^{29} +1.41206 q^{30} -6.43268 q^{31} +8.08520 q^{32} -0.321114 q^{33} +1.27537 q^{34} -0.183511 q^{35} -6.94545 q^{36} +1.00000 q^{37} -8.59599 q^{38} -0.373205 q^{39} -2.25421 q^{40} +4.90455 q^{41} -0.0277673 q^{42} +0.815704 q^{43} +3.41167 q^{44} -9.01466 q^{45} +15.9792 q^{46} -1.31943 q^{47} +0.701728 q^{48} -6.99639 q^{49} -9.03926 q^{50} +0.135408 q^{51} +3.96511 q^{52} -7.23555 q^{53} -2.75072 q^{54} +4.42808 q^{55} +0.0443277 q^{56} -0.912649 q^{57} +2.56577 q^{58} +6.54773 q^{59} -1.59283 q^{60} +3.08978 q^{61} +13.4220 q^{62} +0.177268 q^{63} -10.5348 q^{64} +5.14640 q^{65} +0.670018 q^{66} +2.35255 q^{67} -1.43864 q^{68} +1.69654 q^{69} +0.382904 q^{70} -13.0175 q^{71} +2.17752 q^{72} -1.65899 q^{73} -2.08654 q^{74} -0.959711 q^{75} +9.69641 q^{76} -0.0870755 q^{77} +0.778707 q^{78} -8.49161 q^{79} -9.67665 q^{80} +8.56072 q^{81} -10.2335 q^{82} +0.450114 q^{83} +0.0313219 q^{84} -1.86725 q^{85} -1.70200 q^{86} +0.272412 q^{87} -1.06962 q^{88} -6.88425 q^{89} +18.8095 q^{90} -0.101201 q^{91} -18.0248 q^{92} +1.42504 q^{93} +2.75304 q^{94} +12.5852 q^{95} -1.79112 q^{96} +2.94365 q^{97} +14.5983 q^{98} -4.27743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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