LMFDB - Embedded newform 6013.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68013 q^{2} -1.39322 q^{3} +5.18311 q^{4} -1.95866 q^{5} +3.73403 q^{6} +1.00000 q^{7} -8.53117 q^{8} -1.05892 q^{9} +O(q^{10})$	\(q-2.68013 q^{2} -1.39322 q^{3} +5.18311 q^{4} -1.95866 q^{5} +3.73403 q^{6} +1.00000 q^{7} -8.53117 q^{8} -1.05892 q^{9} +5.24948 q^{10} +3.16031 q^{11} -7.22124 q^{12} -4.40301 q^{13} -2.68013 q^{14} +2.72886 q^{15} +12.4984 q^{16} +6.08653 q^{17} +2.83806 q^{18} -1.39963 q^{19} -10.1520 q^{20} -1.39322 q^{21} -8.47005 q^{22} -2.84554 q^{23} +11.8858 q^{24} -1.16363 q^{25} +11.8007 q^{26} +5.65499 q^{27} +5.18311 q^{28} -1.07171 q^{29} -7.31371 q^{30} -5.79804 q^{31} -16.4352 q^{32} -4.40302 q^{33} -16.3127 q^{34} -1.95866 q^{35} -5.48853 q^{36} +9.61262 q^{37} +3.75120 q^{38} +6.13439 q^{39} +16.7097 q^{40} -5.96335 q^{41} +3.73403 q^{42} +2.29228 q^{43} +16.3802 q^{44} +2.07408 q^{45} +7.62642 q^{46} +8.07149 q^{47} -17.4131 q^{48} +1.00000 q^{49} +3.11869 q^{50} -8.47991 q^{51} -22.8213 q^{52} +2.14724 q^{53} -15.1561 q^{54} -6.18999 q^{55} -8.53117 q^{56} +1.95000 q^{57} +2.87234 q^{58} +11.7345 q^{59} +14.1440 q^{60} -15.5384 q^{61} +15.5395 q^{62} -1.05892 q^{63} +19.0515 q^{64} +8.62403 q^{65} +11.8007 q^{66} -1.96948 q^{67} +31.5472 q^{68} +3.96447 q^{69} +5.24948 q^{70} -7.48822 q^{71} +9.03387 q^{72} -10.2051 q^{73} -25.7631 q^{74} +1.62120 q^{75} -7.25446 q^{76} +3.16031 q^{77} -16.4410 q^{78} -7.65424 q^{79} -24.4803 q^{80} -4.70191 q^{81} +15.9826 q^{82} -10.5248 q^{83} -7.22124 q^{84} -11.9215 q^{85} -6.14361 q^{86} +1.49314 q^{87} -26.9611 q^{88} +16.6674 q^{89} -5.55881 q^{90} -4.40301 q^{91} -14.7487 q^{92} +8.07798 q^{93} -21.6327 q^{94} +2.74141 q^{95} +22.8979 q^{96} +0.202424 q^{97} -2.68013 q^{98} -3.34653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) $ 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * 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 $

$2$	−2.68013	−1.89514	−0.947570	−	0.319548i	$-0.896469\pi$
$2$	−2.68013	−1.89514	−0.947570	+	0.319548i	$0.896469\pi$
$3$	−1.39322	−0.804379	−0.402189	−	0.915556i	$-0.631751\pi$
$3$	−1.39322	−0.804379	−0.402189	+	0.915556i	$0.631751\pi$
$4$	5.18311	2.59156
$5$	−1.95866	−0.875942	−0.437971	−	0.898989i	$-0.644303\pi$
$5$	−1.95866	−0.875942	−0.437971	+	0.898989i	$0.644303\pi$
$6$	3.73403	1.52441
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.53117	−3.01622
$9$	−1.05892	−0.352975
$10$	5.24948	1.66003
$11$	3.16031	0.952869	0.476435	−	0.879210i	$-0.341929\pi$
$11$	3.16031	0.952869	0.476435	+	0.879210i	$0.341929\pi$
$12$	−7.22124	−2.08459
$13$	−4.40301	−1.22118	−0.610588	−	0.791948i	$-0.709067\pi$
$13$	−4.40301	−1.22118	−0.610588	+	0.791948i	$0.709067\pi$
$14$	−2.68013	−0.716296
$15$	2.72886	0.704589
$16$	12.4984	3.12461
$17$	6.08653	1.47620	0.738101	−	0.674691i	$-0.235723\pi$
$17$	6.08653	1.47620	0.738101	+	0.674691i	$0.235723\pi$
$18$	2.83806	0.668937
$19$	−1.39963	−0.321098	−0.160549	−	0.987028i	$-0.551326\pi$
$19$	−1.39963	−0.321098	−0.160549	+	0.987028i	$0.551326\pi$
$20$	−10.1520	−2.27005
$21$	−1.39322	−0.304027
$22$	−8.47005	−1.80582
$23$	−2.84554	−0.593335	−0.296668	−	0.954981i	$-0.595875\pi$
$23$	−2.84554	−0.593335	−0.296668	+	0.954981i	$0.595875\pi$
$24$	11.8858	2.42619
$25$	−1.16363	−0.232726
$26$	11.8007	2.31430
$27$	5.65499	1.08830
$28$	5.18311	0.979517
$29$	−1.07171	−0.199012	−0.0995061	−	0.995037i	$-0.531726\pi$
$29$	−1.07171	−0.199012	−0.0995061	+	0.995037i	$0.531726\pi$
$30$	−7.31371	−1.33529
$31$	−5.79804	−1.04136	−0.520680	−	0.853752i	$-0.674321\pi$
$31$	−5.79804	−1.04136	−0.520680	+	0.853752i	$0.674321\pi$
$32$	−16.4352	−2.90535
$33$	−4.40302	−0.766468
$34$	−16.3127	−2.79761
$35$	−1.95866	−0.331075
$36$	−5.48853	−0.914754
$37$	9.61262	1.58031	0.790153	−	0.612910i	$-0.210001\pi$
$37$	9.61262	1.58031	0.790153	+	0.612910i	$0.210001\pi$
$38$	3.75120	0.608525
$39$	6.13439	0.982288
$40$	16.7097	2.64204
$41$	−5.96335	−0.931318	−0.465659	−	0.884964i	$-0.654183\pi$
$41$	−5.96335	−0.931318	−0.465659	+	0.884964i	$0.654183\pi$
$42$	3.73403	0.576173
$43$	2.29228	0.349569	0.174784	−	0.984607i	$-0.444077\pi$
$43$	2.29228	0.349569	0.174784	+	0.984607i	$0.444077\pi$
$44$	16.3802	2.46941
$45$	2.07408	0.309185
$46$	7.62642	1.12445
$47$	8.07149	1.17735	0.588674	−	0.808371i	$-0.299650\pi$
$47$	8.07149	1.17735	0.588674	+	0.808371i	$0.299650\pi$
$48$	−17.4131	−2.51337
$49$	1.00000	0.142857
$50$	3.11869	0.441049
$51$	−8.47991	−1.18742
$52$	−22.8213	−3.16475
$53$	2.14724	0.294946	0.147473	−	0.989066i	$-0.452886\pi$
$53$	2.14724	0.294946	0.147473	+	0.989066i	$0.452886\pi$
$54$	−15.1561	−2.06249
$55$	−6.18999	−0.834658
$56$	−8.53117	−1.14003
$57$	1.95000	0.258284
$58$	2.87234	0.377156
$59$	11.7345	1.52770	0.763851	−	0.645392i	$-0.223306\pi$
$59$	11.7345	1.52770	0.763851	+	0.645392i	$0.223306\pi$
$60$	14.1440	1.82598
$61$	−15.5384	−1.98949	−0.994746	−	0.102372i	$-0.967357\pi$
$61$	−15.5384	−1.98949	−0.994746	+	0.102372i	$0.967357\pi$
$62$	15.5395	1.97352
$63$	−1.05892	−0.133412
$64$	19.0515	2.38144
$65$	8.62403	1.06968
$66$	11.8007	1.45256
$67$	−1.96948	−0.240610	−0.120305	−	0.992737i	$-0.538387\pi$
$67$	−1.96948	−0.240610	−0.120305	+	0.992737i	$0.538387\pi$
$68$	31.5472	3.82566
$69$	3.96447	0.477266
$70$	5.24948	0.627433
$71$	−7.48822	−0.888688	−0.444344	−	0.895856i	$-0.646563\pi$
$71$	−7.48822	−0.888688	−0.444344	+	0.895856i	$0.646563\pi$
$72$	9.03387	1.06465
$73$	−10.2051	−1.19442	−0.597211	−	0.802084i	$-0.703724\pi$
$73$	−10.2051	−1.19442	−0.597211	+	0.802084i	$0.703724\pi$
$74$	−25.7631	−2.99490
$75$	1.62120	0.187200
$76$	−7.25446	−0.832143
$77$	3.16031	0.360151
$78$	−16.4410	−1.86157
$79$	−7.65424	−0.861170	−0.430585	−	0.902550i	$-0.641693\pi$
$79$	−7.65424	−0.861170	−0.430585	+	0.902550i	$0.641693\pi$
$80$	−24.4803	−2.73698
$81$	−4.70191	−0.522434
$82$	15.9826	1.76498
$83$	−10.5248	−1.15524	−0.577621	−	0.816305i	$-0.696019\pi$
$83$	−10.5248	−1.15524	−0.577621	+	0.816305i	$0.696019\pi$
$84$	−7.22124	−0.787902
$85$	−11.9215	−1.29307
$86$	−6.14361	−0.662482
$87$	1.49314	0.160081
$88$	−26.9611	−2.87407
$89$	16.6674	1.76674	0.883370	−	0.468676i	$-0.155269\pi$
$89$	16.6674	1.76674	0.883370	+	0.468676i	$0.155269\pi$
$90$	−5.55881	−0.585950
$91$	−4.40301	−0.461561
$92$	−14.7487	−1.53766
$93$	8.07798	0.837647
$94$	−21.6327	−2.23124
$95$	2.74141	0.281263
$96$	22.8979	2.33700
$97$	0.202424	0.0205530	0.0102765	−	0.999947i	$-0.496729\pi$
$97$	0.202424	0.0205530	0.0102765	+	0.999947i	$0.496729\pi$
$98$	−2.68013	−0.270734
$99$	−3.34653	−0.336339
$100$	−6.03124	−0.603124
$101$	18.3111	1.82202	0.911010	−	0.412385i	$-0.135304\pi$
$101$	18.3111	1.82202	0.911010	+	0.412385i	$0.135304\pi$
$102$	22.7273	2.25034
$103$	17.8337	1.75721	0.878605	−	0.477550i	$-0.158475\pi$
$103$	17.8337	1.75721	0.878605	+	0.477550i	$0.158475\pi$
$104$	37.5629	3.68334
$105$	2.72886	0.266310
$106$	−5.75489	−0.558964
$107$	−7.12014	−0.688330	−0.344165	−	0.938909i	$-0.611838\pi$
$107$	−7.12014	−0.688330	−0.344165	+	0.938909i	$0.611838\pi$
$108$	29.3105	2.82040
$109$	−13.6740	−1.30973	−0.654866	−	0.755745i	$-0.727275\pi$
$109$	−13.6740	−1.30973	−0.654866	+	0.755745i	$0.727275\pi$
$110$	16.5900	1.58179
$111$	−13.3925	−1.27116
$112$	12.4984	1.18099
$113$	8.52998	0.802433	0.401216	−	0.915983i	$-0.368588\pi$
$113$	8.52998	0.802433	0.401216	+	0.915983i	$0.368588\pi$
$114$	−5.22627	−0.489485
$115$	5.57345	0.519727
$116$	−5.55481	−0.515752
$117$	4.66246	0.431044
$118$	−31.4500	−2.89521
$119$	6.08653	0.557952
$120$	−23.2804	−2.12520
$121$	−1.01245	−0.0920405
$122$	41.6451	3.77037
$123$	8.30828	0.749133
$124$	−30.0519	−2.69874
$125$	12.0725	1.07980
$126$	2.83806	0.252834
$127$	−18.3998	−1.63272	−0.816359	−	0.577544i	$-0.804011\pi$
$127$	−18.3998	−1.63272	−0.816359	+	0.577544i	$0.804011\pi$
$128$	−18.1903	−1.60781
$129$	−3.19366	−0.281186
$130$	−23.1135	−2.02719
$131$	−8.12854	−0.710194	−0.355097	−	0.934830i	$-0.615552\pi$
$131$	−8.12854	−0.710194	−0.355097	+	0.934830i	$0.615552\pi$
$132$	−22.8214	−1.98634
$133$	−1.39963	−0.121364
$134$	5.27846	0.455989
$135$	−11.0762	−0.953291
$136$	−51.9253	−4.45255
$137$	3.45778	0.295418	0.147709	−	0.989031i	$-0.452810\pi$
$137$	3.45778	0.295418	0.147709	+	0.989031i	$0.452810\pi$
$138$	−10.6253	−0.904487
$139$	4.14045	0.351189	0.175594	−	0.984463i	$-0.443815\pi$
$139$	4.14045	0.351189	0.175594	+	0.984463i	$0.443815\pi$
$140$	−10.1520	−0.857999
$141$	−11.2454	−0.947034
$142$	20.0694	1.68419
$143$	−13.9149	−1.16362
$144$	−13.2349	−1.10291
$145$	2.09913	0.174323
$146$	27.3511	2.26360
$147$	−1.39322	−0.114911
$148$	49.8233	4.09545
$149$	−17.2808	−1.41570	−0.707851	−	0.706362i	$-0.750335\pi$
$149$	−17.2808	−1.41570	−0.707851	+	0.706362i	$0.750335\pi$
$150$	−4.34503	−0.354771
$151$	11.9967	0.976281	0.488141	−	0.872765i	$-0.337675\pi$
$151$	11.9967	0.976281	0.488141	+	0.872765i	$0.337675\pi$
$152$	11.9405	0.968503
$153$	−6.44518	−0.521062
$154$	−8.47005	−0.682536
$155$	11.3564	0.912170
$156$	31.7952	2.54566
$157$	−0.516006	−0.0411818	−0.0205909	−	0.999788i	$-0.506555\pi$
$157$	−0.516006	−0.0411818	−0.0205909	+	0.999788i	$0.506555\pi$
$158$	20.5144	1.63204
$159$	−2.99159	−0.237248
$160$	32.1910	2.54492
$161$	−2.84554	−0.224260
$162$	12.6017	0.990086
$163$	3.92805	0.307669	0.153834	−	0.988097i	$-0.450838\pi$
$163$	3.92805	0.307669	0.153834	+	0.988097i	$0.450838\pi$
$164$	−30.9087	−2.41357
$165$	8.62404	0.671381
$166$	28.2077	2.18935
$167$	18.5392	1.43461	0.717304	−	0.696760i	$-0.245376\pi$
$167$	18.5392	1.43461	0.717304	+	0.696760i	$0.245376\pi$
$168$	11.8858	0.917013
$169$	6.38652	0.491271
$170$	31.9512	2.45054
$171$	1.48211	0.113339
$172$	11.8811	0.905928
$173$	22.1698	1.68554	0.842769	−	0.538276i	$-0.180924\pi$
$173$	22.1698	1.68554	0.842769	+	0.538276i	$0.180924\pi$
$174$	−4.00181	−0.303376
$175$	−1.16363	−0.0879623
$176$	39.4990	2.97735
$177$	−16.3488	−1.22885
$178$	−44.6708	−3.34822
$179$	−7.90161	−0.590594	−0.295297	−	0.955406i	$-0.595419\pi$
$179$	−7.90161	−0.590594	−0.295297	+	0.955406i	$0.595419\pi$
$180$	10.7502	0.801271
$181$	12.7349	0.946575	0.473287	−	0.880908i	$-0.343067\pi$
$181$	12.7349	0.946575	0.473287	+	0.880908i	$0.343067\pi$
$182$	11.8007	0.874723
$183$	21.6485	1.60031
$184$	24.2758	1.78963
$185$	−18.8279	−1.38425
$186$	−21.6501	−1.58746
$187$	19.2353	1.40663
$188$	41.8355	3.05116
$189$	5.65499	0.411340
$190$	−7.34735	−0.533033
$191$	−5.20944	−0.376942	−0.188471	−	0.982079i	$-0.560353\pi$
$191$	−5.20944	−0.376942	−0.188471	+	0.982079i	$0.560353\pi$
$192$	−26.5431	−1.91558
$193$	−1.62417	−0.116911	−0.0584553	−	0.998290i	$-0.518618\pi$
$193$	−1.62417	−0.116911	−0.0584553	+	0.998290i	$0.518618\pi$
$194$	−0.542523	−0.0389508
$195$	−12.0152	−0.860427
$196$	5.18311	0.370222
$197$	−21.1488	−1.50679	−0.753395	−	0.657568i	$-0.771585\pi$
$197$	−21.1488	−1.50679	−0.753395	+	0.657568i	$0.771585\pi$
$198$	8.96914	0.637409
$199$	−15.5558	−1.10272	−0.551359	−	0.834268i	$-0.685891\pi$
$199$	−15.5558	−1.10272	−0.551359	+	0.834268i	$0.685891\pi$
$200$	9.92714	0.701955
$201$	2.74392	0.193541
$202$	−49.0761	−3.45298
$203$	−1.07171	−0.0752196
$204$	−43.9523	−3.07728
$205$	11.6802	0.815781
$206$	−47.7968	−3.33016
$207$	3.01321	0.209432
$208$	−55.0308	−3.81570
$209$	−4.42327	−0.305964
$210$	−7.31371	−0.504694
$211$	−10.3364	−0.711589	−0.355794	−	0.934564i	$-0.615790\pi$
$211$	−10.3364	−0.711589	−0.355794	+	0.934564i	$0.615790\pi$
$212$	11.1294	0.764369
$213$	10.4328	0.714842
$214$	19.0829	1.30448
$215$	−4.48980	−0.306202
$216$	−48.2437	−3.28257
$217$	−5.79804	−0.393597
$218$	36.6482	2.48213
$219$	14.2181	0.960768
$220$	−32.0834	−2.16306
$221$	−26.7991	−1.80270
$222$	35.8938	2.40903
$223$	7.16388	0.479729	0.239864	−	0.970806i	$-0.422897\pi$
$223$	7.16388	0.479729	0.239864	+	0.970806i	$0.422897\pi$
$224$	−16.4352	−1.09812
$225$	1.23220	0.0821465
$226$	−22.8615	−1.52072
$227$	−22.2753	−1.47846	−0.739231	−	0.673452i	$-0.764811\pi$
$227$	−22.2753	−1.47846	−0.739231	+	0.673452i	$0.764811\pi$
$228$	10.1071	0.669358
$229$	−4.56823	−0.301877	−0.150939	−	0.988543i	$-0.548230\pi$
$229$	−4.56823	−0.301877	−0.150939	+	0.988543i	$0.548230\pi$
$230$	−14.9376	−0.984956
$231$	−4.40302	−0.289698
$232$	9.14297	0.600266
$233$	−11.2722	−0.738463	−0.369232	−	0.929337i	$-0.620379\pi$
$233$	−11.2722	−0.738463	−0.369232	+	0.929337i	$0.620379\pi$
$234$	−12.4960	−0.816890
$235$	−15.8093	−1.03129
$236$	60.8213	3.95913
$237$	10.6641	0.692707
$238$	−16.3127	−1.05740
$239$	−16.6779	−1.07880	−0.539401	−	0.842049i	$-0.681349\pi$
$239$	−16.6779	−1.07880	−0.539401	+	0.842049i	$0.681349\pi$
$240$	34.1065	2.20157
$241$	−4.52246	−0.291317	−0.145659	−	0.989335i	$-0.546530\pi$
$241$	−4.52246	−0.291317	−0.145659	+	0.989335i	$0.546530\pi$
$242$	2.71349	0.174430
$243$	−10.4142	−0.668069
$244$	−80.5375	−5.15588
$245$	−1.95866	−0.125135
$246$	−22.2673	−1.41971
$247$	6.16260	0.392117
$248$	49.4641	3.14097
$249$	14.6634	0.929252
$250$	−32.3559	−2.04637
$251$	−18.8636	−1.19066	−0.595331	−	0.803481i	$-0.702979\pi$
$251$	−18.8636	−1.19066	−0.595331	+	0.803481i	$0.702979\pi$
$252$	−5.48853	−0.345745
$253$	−8.99277	−0.565371
$254$	49.3139	3.09423
$255$	16.6093	1.04011
$256$	10.6494	0.665589
$257$	9.22294	0.575311	0.287656	−	0.957734i	$-0.407124\pi$
$257$	9.22294	0.575311	0.287656	+	0.957734i	$0.407124\pi$
$258$	8.55943	0.532887
$259$	9.61262	0.597299
$260$	44.6993	2.77213
$261$	1.13486	0.0702463
$262$	21.7856	1.34592
$263$	−11.1709	−0.688828	−0.344414	−	0.938818i	$-0.611922\pi$
$263$	−11.1709	−0.688828	−0.344414	+	0.938818i	$0.611922\pi$
$264$	37.5629	2.31184
$265$	−4.20572	−0.258355
$266$	3.75120	0.230001
$267$	−23.2214	−1.42113
$268$	−10.2080	−0.623554
$269$	7.07315	0.431258	0.215629	−	0.976475i	$-0.430820\pi$
$269$	7.07315	0.431258	0.215629	+	0.976475i	$0.430820\pi$
$270$	29.6858	1.80662
$271$	0.126639	0.00769276	0.00384638	−	0.999993i	$-0.498776\pi$
$271$	0.126639	0.00769276	0.00384638	+	0.999993i	$0.498776\pi$
$272$	76.0722	4.61256
$273$	6.13439	0.371270
$274$	−9.26732	−0.559859
$275$	−3.67744	−0.221758
$276$	20.5483	1.23686
$277$	9.54000	0.573203	0.286601	−	0.958050i	$-0.407474\pi$
$277$	9.54000	0.573203	0.286601	+	0.958050i	$0.407474\pi$
$278$	−11.0970	−0.665552
$279$	6.13969	0.367573
$280$	16.7097	0.998596
$281$	−4.88743	−0.291560	−0.145780	−	0.989317i	$-0.546569\pi$
$281$	−4.88743	−0.291560	−0.145780	+	0.989317i	$0.546569\pi$
$282$	30.1392	1.79476
$283$	−16.0486	−0.953989	−0.476994	−	0.878906i	$-0.658274\pi$
$283$	−16.0486	−0.953989	−0.476994	+	0.878906i	$0.658274\pi$
$284$	−38.8123	−2.30309
$285$	−3.81940	−0.226242
$286$	37.2937	2.20523
$287$	−5.96335	−0.352005
$288$	17.4036	1.02552
$289$	20.0459	1.17917
$290$	−5.62594	−0.330367
$291$	−0.282022	−0.0165324
$292$	−52.8944	−3.09541
$293$	−2.51941	−0.147185	−0.0735926	−	0.997288i	$-0.523446\pi$
$293$	−2.51941	−0.147185	−0.0735926	+	0.997288i	$0.523446\pi$
$294$	3.73403	0.217773
$295$	−22.9840	−1.33818
$296$	−82.0069	−4.76656
$297$	17.8715	1.03701
$298$	46.3149	2.68295
$299$	12.5289	0.724567
$300$	8.40287	0.485140
$301$	2.29228	0.132125
$302$	−32.1529	−1.85019
$303$	−25.5114	−1.46559
$304$	−17.4932	−1.00331
$305$	30.4346	1.74268
$306$	17.2739	0.987485
$307$	10.5303	0.600997	0.300499	−	0.953782i	$-0.402847\pi$
$307$	10.5303	0.600997	0.300499	+	0.953782i	$0.402847\pi$
$308$	16.3802	0.933351
$309$	−24.8464	−1.41346
$310$	−30.4367	−1.72869
$311$	−31.3907	−1.78000	−0.890001	−	0.455959i	$-0.849296\pi$
$311$	−31.3907	−1.78000	−0.890001	+	0.455959i	$0.849296\pi$
$312$	−52.3335	−2.96280
$313$	25.3611	1.43349	0.716746	−	0.697335i	$-0.245631\pi$
$313$	25.3611	1.43349	0.716746	+	0.697335i	$0.245631\pi$
$314$	1.38297	0.0780453
$315$	2.07408	0.116861
$316$	−39.6728	−2.23177
$317$	3.92501	0.220451	0.110225	−	0.993907i	$-0.464843\pi$
$317$	3.92501	0.220451	0.110225	+	0.993907i	$0.464843\pi$
$318$	8.01785	0.449619
$319$	−3.38695	−0.189633
$320$	−37.3156	−2.08600
$321$	9.91995	0.553678
$322$	7.62642	0.425004
$323$	−8.51891	−0.474005
$324$	−24.3705	−1.35392
$325$	5.12349	0.284200
$326$	−10.5277	−0.583075
$327$	19.0510	1.05352
$328$	50.8743	2.80907
$329$	8.07149	0.444996
$330$	−23.1136	−1.27236
$331$	−12.7784	−0.702364	−0.351182	−	0.936307i	$-0.614220\pi$
$331$	−12.7784	−0.702364	−0.351182	+	0.936307i	$0.614220\pi$
$332$	−54.5510	−2.99388
$333$	−10.1790	−0.557808
$334$	−49.6876	−2.71878
$335$	3.85754	0.210760
$336$	−17.4131	−0.949965
$337$	27.1724	1.48017	0.740086	−	0.672512i	$-0.234785\pi$
$337$	27.1724	1.48017	0.740086	+	0.672512i	$0.234785\pi$
$338$	−17.1167	−0.931028
$339$	−11.8842	−0.645460
$340$	−61.7904	−3.35105
$341$	−18.3236	−0.992279
$342$	−3.97224	−0.214794
$343$	1.00000	0.0539949
$344$	−19.5558	−1.05438
$345$	−7.76507	−0.418057
$346$	−59.4180	−3.19433
$347$	33.6195	1.80479	0.902393	−	0.430913i	$-0.141808\pi$
$347$	33.6195	1.80479	0.902393	+	0.430913i	$0.141808\pi$
$348$	7.73911	0.414860
$349$	24.2099	1.29593	0.647964	−	0.761671i	$-0.275621\pi$
$349$	24.2099	1.29593	0.647964	+	0.761671i	$0.275621\pi$
$350$	3.11869	0.166701
$351$	−24.8990	−1.32901
$352$	−51.9402	−2.76842
$353$	−32.4831	−1.72890	−0.864451	−	0.502717i	$-0.832334\pi$
$353$	−32.4831	−1.72890	−0.864451	+	0.502717i	$0.832334\pi$
$354$	43.8170	2.32885
$355$	14.6669	0.778439
$356$	86.3890	4.57861
$357$	−8.47991	−0.448804
$358$	21.1774	1.11926
$359$	−16.9757	−0.895942	−0.447971	−	0.894048i	$-0.647853\pi$
$359$	−16.9757	−0.895942	−0.447971	+	0.894048i	$0.647853\pi$
$360$	−17.6943	−0.932572
$361$	−17.0410	−0.896896
$362$	−34.1311	−1.79389
$363$	1.41056	0.0740354
$364$	−22.8213	−1.19616
$365$	19.9885	1.04624
$366$	−58.0209	−3.03280
$367$	23.4115	1.22207	0.611035	−	0.791604i	$-0.290754\pi$
$367$	23.4115	1.22207	0.611035	+	0.791604i	$0.290754\pi$
$368$	−35.5648	−1.85394
$369$	6.31473	0.328732
$370$	50.4613	2.62336
$371$	2.14724	0.111479
$372$	41.8691	2.17081
$373$	−26.8145	−1.38840	−0.694200	−	0.719782i	$-0.744242\pi$
$373$	−26.8145	−1.38840	−0.694200	+	0.719782i	$0.744242\pi$
$374$	−51.5532	−2.66575
$375$	−16.8197	−0.868565
$376$	−68.8593	−3.55115
$377$	4.71877	0.243029
$378$	−15.1561	−0.779548
$379$	−16.5458	−0.849900	−0.424950	−	0.905217i	$-0.639708\pi$
$379$	−16.5458	−0.849900	−0.424950	+	0.905217i	$0.639708\pi$
$380$	14.2091	0.728909
$381$	25.6351	1.31332
$382$	13.9620	0.714358
$383$	24.8122	1.26784	0.633921	−	0.773398i	$-0.281444\pi$
$383$	24.8122	1.26784	0.633921	+	0.773398i	$0.281444\pi$
$384$	25.3432	1.29329
$385$	−6.18999	−0.315471
$386$	4.35300	0.221562
$387$	−2.42735	−0.123389
$388$	1.04919	0.0532643
$389$	20.2046	1.02441	0.512207	−	0.858862i	$-0.328828\pi$
$389$	20.2046	1.02441	0.512207	+	0.858862i	$0.328828\pi$
$390$	32.2024	1.63063
$391$	−17.3195	−0.875882
$392$	−8.53117	−0.430889
$393$	11.3249	0.571265
$394$	56.6816	2.85558
$395$	14.9921	0.754334
$396$	−17.3454	−0.871641
$397$	−22.5603	−1.13227	−0.566134	−	0.824313i	$-0.691562\pi$
$397$	−22.5603	−1.13227	−0.566134	+	0.824313i	$0.691562\pi$
$398$	41.6915	2.08981
$399$	1.95000	0.0976223
$400$	−14.5436	−0.727179
$401$	12.7210	0.635256	0.317628	−	0.948215i	$-0.397114\pi$
$401$	12.7210	0.635256	0.317628	+	0.948215i	$0.397114\pi$
$402$	−7.35408	−0.366788
$403$	25.5289	1.27168
$404$	94.9084	4.72187
$405$	9.20946	0.457622
$406$	2.87234	0.142552
$407$	30.3789	1.50582
$408$	72.3436	3.58154
$409$	27.9988	1.38445	0.692225	−	0.721682i	$-0.256631\pi$
$409$	27.9988	1.38445	0.692225	+	0.721682i	$0.256631\pi$
$410$	−31.3045	−1.54602
$411$	−4.81747	−0.237628
$412$	92.4343	4.55391
$413$	11.7345	0.577417
$414$	−8.07580	−0.396904
$415$	20.6145	1.01192
$416$	72.3642	3.54795
$417$	−5.76858	−0.282489
$418$	11.8550	0.579845
$419$	26.7656	1.30758	0.653792	−	0.756674i	$-0.273177\pi$
$419$	26.7656	1.30758	0.653792	+	0.756674i	$0.273177\pi$
$420$	14.1440	0.690156
$421$	−12.8328	−0.625430	−0.312715	−	0.949847i	$-0.601239\pi$
$421$	−12.8328	−0.625430	−0.312715	+	0.949847i	$0.601239\pi$
$422$	27.7030	1.34856
$423$	−8.54710	−0.415574
$424$	−18.3185	−0.889623
$425$	−7.08248	−0.343551
$426$	−27.9612	−1.35473
$427$	−15.5384	−0.751957
$428$	−36.9045	−1.78385
$429$	19.3866	0.935992
$430$	12.0333	0.580296
$431$	14.3157	0.689561	0.344781	−	0.938683i	$-0.387953\pi$
$431$	14.3157	0.689561	0.344781	+	0.938683i	$0.387953\pi$
$432$	70.6787	3.40053
$433$	−29.9093	−1.43735	−0.718674	−	0.695348i	$-0.755250\pi$
$433$	−29.9093	−1.43735	−0.718674	+	0.695348i	$0.755250\pi$
$434$	15.5395	0.745921
$435$	−2.92456	−0.140222
$436$	−70.8740	−3.39425
$437$	3.98271	0.190519
$438$	−38.1063	−1.82079
$439$	−11.1737	−0.533292	−0.266646	−	0.963795i	$-0.585915\pi$
$439$	−11.1737	−0.533292	−0.266646	+	0.963795i	$0.585915\pi$
$440$	52.8078	2.51752
$441$	−1.05892	−0.0504250
$442$	71.8251	3.41637
$443$	25.8068	1.22612	0.613058	−	0.790038i	$-0.289939\pi$
$443$	25.8068	1.22612	0.613058	+	0.790038i	$0.289939\pi$
$444$	−69.4151	−3.29429
$445$	−32.6458	−1.54756
$446$	−19.2002	−0.909154
$447$	24.0761	1.13876
$448$	19.0515	0.900100
$449$	12.7459	0.601518	0.300759	−	0.953700i	$-0.402760\pi$
$449$	12.7459	0.601518	0.300759	+	0.953700i	$0.402760\pi$
$450$	−3.30245	−0.155679
$451$	−18.8460	−0.887425
$452$	44.2118	2.07955
$453$	−16.7142	−0.785300
$454$	59.7007	2.80189
$455$	8.62403	0.404301
$456$	−16.6358	−0.779043
$457$	4.35040	0.203503	0.101752	−	0.994810i	$-0.467555\pi$
$457$	4.35040	0.203503	0.101752	+	0.994810i	$0.467555\pi$
$458$	12.2435	0.572100
$459$	34.4193	1.60656
$460$	28.8878	1.34690
$461$	−3.88858	−0.181109	−0.0905546	−	0.995891i	$-0.528864\pi$
$461$	−3.88858	−0.181109	−0.0905546	+	0.995891i	$0.528864\pi$
$462$	11.8007	0.549018
$463$	−7.88666	−0.366524	−0.183262	−	0.983064i	$-0.558666\pi$
$463$	−7.88666	−0.366524	−0.183262	+	0.983064i	$0.558666\pi$
$464$	−13.3948	−0.621836
$465$	−15.8220	−0.733730
$466$	30.2109	1.39949
$467$	−7.88541	−0.364893	−0.182447	−	0.983216i	$-0.558402\pi$
$467$	−7.88541	−0.364893	−0.182447	+	0.983216i	$0.558402\pi$
$468$	24.1661	1.11708
$469$	−1.96948	−0.0909420
$470$	42.3711	1.95444
$471$	0.718913	0.0331258
$472$	−100.109	−4.60789
$473$	7.24430	0.333093
$474$	−28.5812	−1.31278
$475$	1.62866	0.0747279
$476$	31.5472	1.44596
$477$	−2.27376	−0.104108
$478$	44.6989	2.04448
$479$	30.9629	1.41473	0.707364	−	0.706849i	$-0.249884\pi$
$479$	30.9629	1.41473	0.707364	+	0.706849i	$0.249884\pi$
$480$	−44.8493	−2.04708
$481$	−42.3245	−1.92983
$482$	12.1208	0.552087
$483$	3.96447	0.180390
$484$	−5.24762	−0.238528
$485$	−0.396480	−0.0180032
$486$	27.9114	1.26609
$487$	39.3587	1.78351	0.891756	−	0.452517i	$-0.149474\pi$
$487$	39.3587	1.78351	0.891756	+	0.452517i	$0.149474\pi$
$488$	132.561	6.00076
$489$	−5.47266	−0.247482
$490$	5.24948	0.237147
$491$	−5.27277	−0.237957	−0.118978	−	0.992897i	$-0.537962\pi$
$491$	−5.27277	−0.237957	−0.118978	+	0.992897i	$0.537962\pi$
$492$	43.0628	1.94142
$493$	−6.52302	−0.293782
$494$	−16.5166	−0.743117
$495$	6.55473	0.294613
$496$	−72.4665	−3.25384
$497$	−7.48822	−0.335893
$498$	−39.2997	−1.76106
$499$	26.5224	1.18731	0.593654	−	0.804721i	$-0.297685\pi$
$499$	26.5224	1.18731	0.593654	+	0.804721i	$0.297685\pi$
$500$	62.5731	2.79835
$501$	−25.8293	−1.15397
$502$	50.5570	2.25647
$503$	−20.8171	−0.928191	−0.464095	−	0.885785i	$-0.653620\pi$
$503$	−20.8171	−0.928191	−0.464095	+	0.885785i	$0.653620\pi$
$504$	9.03387	0.402400
$505$	−35.8652	−1.59598
$506$	24.1018	1.07146
$507$	−8.89787	−0.395168
$508$	−95.3683	−4.23128
$509$	−4.91285	−0.217758	−0.108879	−	0.994055i	$-0.534726\pi$
$509$	−4.91285	−0.217758	−0.108879	+	0.994055i	$0.534726\pi$
$510$	−44.5151	−1.97116
$511$	−10.2051	−0.451449
$512$	7.83877	0.346428
$513$	−7.91492	−0.349452
$514$	−24.7187	−1.09030
$515$	−34.9303	−1.53921
$516$	−16.5531	−0.728709
$517$	25.5084	1.12186
$518$	−25.7631	−1.13197
$519$	−30.8875	−1.35581
$520$	−73.5731	−3.22639
$521$	19.7543	0.865454	0.432727	−	0.901525i	$-0.357551\pi$
$521$	19.7543	0.865454	0.432727	+	0.901525i	$0.357551\pi$
$522$	−3.04159	−0.133127
$523$	24.2489	1.06033	0.530166	−	0.847894i	$-0.322130\pi$
$523$	24.2489	1.06033	0.530166	+	0.847894i	$0.322130\pi$
$524$	−42.1311	−1.84051
$525$	1.62120	0.0707550
$526$	29.9395	1.30543
$527$	−35.2900	−1.53726
$528$	−55.0309	−2.39491
$529$	−14.9029	−0.647953
$530$	11.2719	0.489620
$531$	−12.4260	−0.539240
$532$	−7.25446	−0.314521
$533$	26.2567	1.13730
$534$	62.2365	2.69324
$535$	13.9460	0.602937
$536$	16.8019	0.725733
$537$	11.0087	0.475061
$538$	−18.9570	−0.817294
$539$	3.16031	0.136124
$540$	−57.4094	−2.47051
$541$	0.754084	0.0324206	0.0162103	−	0.999869i	$-0.494840\pi$
$541$	0.754084	0.0324206	0.0162103	+	0.999869i	$0.494840\pi$
$542$	−0.339409	−0.0145789
$543$	−17.7425	−0.761405
$544$	−100.033	−4.28889
$545$	26.7828	1.14725
$546$	−16.4410	−0.703609
$547$	26.3705	1.12752	0.563761	−	0.825938i	$-0.309354\pi$
$547$	26.3705	1.12752	0.563761	+	0.825938i	$0.309354\pi$
$548$	17.9221	0.765593
$549$	16.4540	0.702241
$550$	9.85602	0.420262
$551$	1.50001	0.0639024
$552$	−33.8216	−1.43954
$553$	−7.65424	−0.325492
$554$	−25.5685	−1.08630
$555$	26.2315	1.11347
$556$	21.4604	0.910126
$557$	5.41085	0.229265	0.114632	−	0.993408i	$-0.463431\pi$
$557$	5.41085	0.229265	0.114632	+	0.993408i	$0.463431\pi$
$558$	−16.4552	−0.696603
$559$	−10.0929	−0.426885
$560$	−24.4803	−1.03448
$561$	−26.7991	−1.13146
$562$	13.0990	0.552547
$563$	−2.46042	−0.103694	−0.0518472	−	0.998655i	$-0.516511\pi$
$563$	−2.46042	−0.103694	−0.0518472	+	0.998655i	$0.516511\pi$
$564$	−58.2862	−2.45429
$565$	−16.7074	−0.702884
$566$	43.0123	1.80794
$567$	−4.70191	−0.197461
$568$	63.8833	2.68048
$569$	9.41749	0.394802	0.197401	−	0.980323i	$-0.436750\pi$
$569$	9.41749	0.394802	0.197401	+	0.980323i	$0.436750\pi$
$570$	10.2365	0.428760
$571$	14.2215	0.595150	0.297575	−	0.954698i	$-0.403822\pi$
$571$	14.2215	0.595150	0.297575	+	0.954698i	$0.403822\pi$
$572$	−72.1224	−3.01559
$573$	7.25792	0.303204
$574$	15.9826	0.667099
$575$	3.31116	0.138085
$576$	−20.1741	−0.840589
$577$	−7.54076	−0.313926	−0.156963	−	0.987604i	$-0.550170\pi$
$577$	−7.54076	−0.313926	−0.156963	+	0.987604i	$0.550170\pi$
$578$	−53.7257	−2.23469
$579$	2.26284	0.0940405
$580$	10.8800	0.451768
$581$	−10.5248	−0.436640
$582$	0.755856	0.0313312
$583$	6.78594	0.281045
$584$	87.0618	3.60264
$585$	−9.13219	−0.377570
$586$	6.75235	0.278937
$587$	38.0896	1.57213	0.786064	−	0.618146i	$-0.212116\pi$
$587$	38.0896	1.57213	0.786064	+	0.618146i	$0.212116\pi$
$588$	−7.22124	−0.297799
$589$	8.11513	0.334378
$590$	61.6001	2.53604
$591$	29.4650	1.21203
$592$	120.143	4.93784
$593$	2.95334	0.121279	0.0606396	−	0.998160i	$-0.480686\pi$
$593$	2.95334	0.121279	0.0606396	+	0.998160i	$0.480686\pi$
$594$	−47.8981	−1.96528
$595$	−11.9215	−0.488733
$596$	−89.5686	−3.66887
$597$	21.6727	0.887003
$598$	−33.5792	−1.37316
$599$	33.2450	1.35835	0.679176	−	0.733975i	$-0.262337\pi$
$599$	33.2450	1.35835	0.679176	+	0.733975i	$0.262337\pi$
$600$	−13.8307	−0.564638
$601$	27.2304	1.11075	0.555375	−	0.831600i	$-0.312575\pi$
$601$	27.2304	1.11075	0.555375	+	0.831600i	$0.312575\pi$
$602$	−6.14361	−0.250395
$603$	2.08553	0.0849292
$604$	62.1805	2.53009
$605$	1.98304	0.0806221
$606$	68.3740	2.77751
$607$	−15.7646	−0.639867	−0.319934	−	0.947440i	$-0.603661\pi$
$607$	−15.7646	−0.639867	−0.319934	+	0.947440i	$0.603661\pi$
$608$	23.0032	0.932903
$609$	1.49314	0.0605050
$610$	−81.5687	−3.30262
$611$	−35.5389	−1.43775
$612$	−33.4061	−1.35036
$613$	−9.18060	−0.370801	−0.185400	−	0.982663i	$-0.559358\pi$
$613$	−9.18060	−0.370801	−0.185400	+	0.982663i	$0.559358\pi$
$614$	−28.2227	−1.13897
$615$	−16.2731	−0.656197
$616$	−26.9611	−1.08630
$617$	2.77151	0.111577	0.0557884	−	0.998443i	$-0.482233\pi$
$617$	2.77151	0.111577	0.0557884	+	0.998443i	$0.482233\pi$
$618$	66.5916	2.67871
$619$	−18.3602	−0.737958	−0.368979	−	0.929438i	$-0.620293\pi$
$619$	−18.3602	−0.737958	−0.368979	+	0.929438i	$0.620293\pi$
$620$	58.8616	2.36394
$621$	−16.0915	−0.645729
$622$	84.1312	3.37335
$623$	16.6674	0.667765
$624$	76.6703	3.06927
$625$	−17.8278	−0.713112
$626$	−67.9710	−2.71667
$627$	6.16261	0.246111
$628$	−2.67452	−0.106725
$629$	58.5075	2.33285
$630$	−5.55881	−0.221468
$631$	7.67239	0.305433	0.152717	−	0.988270i	$-0.451198\pi$
$631$	7.67239	0.305433	0.152717	+	0.988270i	$0.451198\pi$
$632$	65.2997	2.59748
$633$	14.4010	0.572387
$634$	−10.5196	−0.417785
$635$	36.0391	1.43017
$636$	−15.5057	−0.614842
$637$	−4.40301	−0.174454
$638$	9.07747	0.359380
$639$	7.92946	0.313685
$640$	35.6287	1.40835
$641$	−6.47833	−0.255879	−0.127939	−	0.991782i	$-0.540836\pi$
$641$	−6.47833	−0.255879	−0.127939	+	0.991782i	$0.540836\pi$
$642$	−26.5868	−1.04930
$643$	−14.7911	−0.583302	−0.291651	−	0.956525i	$-0.594205\pi$
$643$	−14.7911	−0.583302	−0.291651	+	0.956525i	$0.594205\pi$
$644$	−14.7487	−0.581182
$645$	6.25530	0.246302
$646$	22.8318	0.898306
$647$	−27.2236	−1.07027	−0.535136	−	0.844766i	$-0.679739\pi$
$647$	−27.2236	−1.07027	−0.535136	+	0.844766i	$0.679739\pi$
$648$	40.1128	1.57578
$649$	37.0847	1.45570
$650$	−13.7316	−0.538599
$651$	8.07798	0.316601
$652$	20.3595	0.797341
$653$	31.0232	1.21403	0.607015	−	0.794690i	$-0.292367\pi$
$653$	31.0232	1.21403	0.607015	+	0.794690i	$0.292367\pi$
$654$	−51.0591	−1.99657
$655$	15.9211	0.622088
$656$	−74.5326	−2.91001
$657$	10.8065	0.421601
$658$	−21.6327	−0.843329
$659$	9.23802	0.359862	0.179931	−	0.983679i	$-0.442413\pi$
$659$	9.23802	0.359862	0.179931	+	0.983679i	$0.442413\pi$
$660$	44.6994	1.73992
$661$	37.7580	1.46862	0.734308	−	0.678816i	$-0.237507\pi$
$661$	37.7580	1.46862	0.734308	+	0.678816i	$0.237507\pi$
$662$	34.2478	1.33108
$663$	37.3372	1.45006
$664$	89.7885	3.48447
$665$	2.74141	0.106307
$666$	27.2812	1.05712
$667$	3.04960	0.118081
$668$	96.0909	3.71787
$669$	−9.98090	−0.385884
$670$	−10.3387	−0.399420
$671$	−49.1062	−1.89573
$672$	22.8979	0.883305
$673$	37.9894	1.46438	0.732191	−	0.681099i	$-0.238498\pi$
$673$	37.9894	1.46438	0.732191	+	0.681099i	$0.238498\pi$
$674$	−72.8256	−2.80514
$675$	−6.58033	−0.253277
$676$	33.1021	1.27316
$677$	−24.7663	−0.951847	−0.475923	−	0.879487i	$-0.657886\pi$
$677$	−24.7663	−0.951847	−0.475923	+	0.879487i	$0.657886\pi$
$678$	31.8512	1.22324
$679$	0.202424	0.00776831
$680$	101.704	3.90018
$681$	31.0345	1.18924
$682$	49.1097	1.88051
$683$	51.7117	1.97869	0.989347	−	0.145578i	$-0.0465041\pi$
$683$	51.7117	1.97869	0.989347	+	0.145578i	$0.0465041\pi$
$684$	7.68192	0.293726
$685$	−6.77264	−0.258769
$686$	−2.68013	−0.102328
$687$	6.36457	0.242824
$688$	28.6499	1.09227
$689$	−9.45432	−0.360181
$690$	20.8114	0.792278
$691$	21.2304	0.807643	0.403822	−	0.914838i	$-0.367682\pi$
$691$	21.2304	0.807643	0.403822	+	0.914838i	$0.367682\pi$
$692$	114.909	4.36817
$693$	−3.34653	−0.127124
$694$	−90.1046	−3.42032
$695$	−8.10976	−0.307621
$696$	−12.7382	−0.482841
$697$	−36.2961	−1.37481
$698$	−64.8858	−2.45597
$699$	15.7046	0.594004
$700$	−6.03124	−0.227959
$701$	2.41580	0.0912436	0.0456218	−	0.998959i	$-0.485473\pi$
$701$	2.41580	0.0912436	0.0456218	+	0.998959i	$0.485473\pi$
$702$	66.7327	2.51866
$703$	−13.4541	−0.507432
$704$	60.2087	2.26920
$705$	22.0260	0.829546
$706$	87.0591	3.27651
$707$	18.3111	0.688659
$708$	−84.7377	−3.18464
$709$	42.9755	1.61398	0.806990	−	0.590566i	$-0.201095\pi$
$709$	42.9755	1.61398	0.806990	+	0.590566i	$0.201095\pi$
$710$	−39.3093	−1.47525
$711$	8.10526	0.303971
$712$	−142.192	−5.32889
$713$	16.4985	0.617875
$714$	22.7273	0.850547
$715$	27.2546	1.01926
$716$	−40.9549	−1.53056
$717$	23.2360	0.867766
$718$	45.4971	1.69794
$719$	−27.7567	−1.03515	−0.517575	−	0.855638i	$-0.673165\pi$
$719$	−27.7567	−1.03515	−0.517575	+	0.855638i	$0.673165\pi$
$720$	25.9228	0.966084
$721$	17.8337	0.664163
$722$	45.6722	1.69974
$723$	6.30081	0.234329
$724$	66.0062	2.45310
$725$	1.24708	0.0463154
$726$	−3.78050	−0.140307
$727$	−14.1591	−0.525131	−0.262565	−	0.964914i	$-0.584569\pi$
$727$	−14.1591	−0.525131	−0.262565	+	0.964914i	$0.584569\pi$
$728$	37.5629	1.39217
$729$	28.6150	1.05981
$730$	−53.5717	−1.98278
$731$	13.9520	0.516034
$732$	112.207	4.14728
$733$	43.1190	1.59263	0.796317	−	0.604879i	$-0.206779\pi$
$733$	43.1190	1.59263	0.796317	+	0.604879i	$0.206779\pi$
$734$	−62.7459	−2.31599
$735$	2.72886	0.100656
$736$	46.7669	1.72385
$737$	−6.22415	−0.229270
$738$	−16.9243	−0.622993
$739$	49.0645	1.80487	0.902433	−	0.430831i	$-0.141779\pi$
$739$	49.0645	1.80487	0.902433	+	0.430831i	$0.141779\pi$
$740$	−97.5872	−3.58738
$741$	−8.58589	−0.315411
$742$	−5.75489	−0.211268
$743$	16.7717	0.615294	0.307647	−	0.951501i	$-0.400458\pi$
$743$	16.7717	0.615294	0.307647	+	0.951501i	$0.400458\pi$
$744$	−68.9146	−2.52653
$745$	33.8474	1.24007
$746$	71.8663	2.63121
$747$	11.1449	0.407771
$748$	99.6989	3.64535
$749$	−7.12014	−0.260164
$750$	45.0790	1.64605
$751$	−18.7172	−0.683002	−0.341501	−	0.939881i	$-0.610935\pi$
$751$	−18.7172	−0.683002	−0.341501	+	0.939881i	$0.610935\pi$
$752$	100.881	3.67876
$753$	26.2813	0.957743
$754$	−12.6469	−0.460574
$755$	−23.4976	−0.855165
$756$	29.3105	1.06601
$757$	−26.7918	−0.973765	−0.486883	−	0.873467i	$-0.661866\pi$
$757$	−26.7918	−0.973765	−0.486883	+	0.873467i	$0.661866\pi$
$758$	44.3449	1.61068
$759$	12.5290	0.454772
$760$	−23.3875	−0.848352
$761$	31.3164	1.13522	0.567608	−	0.823299i	$-0.307869\pi$
$761$	31.3164	1.13522	0.567608	+	0.823299i	$0.307869\pi$
$762$	−68.7054	−2.48893
$763$	−13.6740	−0.495032
$764$	−27.0011	−0.976866
$765$	12.6239	0.456420
$766$	−66.4999	−2.40274
$767$	−51.6672	−1.86559
$768$	−14.8370	−0.535386
$769$	−41.5683	−1.49899	−0.749495	−	0.662009i	$-0.769704\pi$
$769$	−41.5683	−1.49899	−0.749495	+	0.662009i	$0.769704\pi$
$770$	16.5900	0.597862
$771$	−12.8496	−0.462768
$772$	−8.41828	−0.302981
$773$	−20.4651	−0.736078	−0.368039	−	0.929810i	$-0.619971\pi$
$773$	−20.4651	−0.736078	−0.368039	+	0.929810i	$0.619971\pi$
$774$	6.50562	0.233840
$775$	6.74678	0.242352
$776$	−1.72691	−0.0619925
$777$	−13.3925	−0.480455
$778$	−54.1511	−1.94141
$779$	8.34650	0.299044
$780$	−62.2762	−2.22985
$781$	−23.6651	−0.846804
$782$	46.4184	1.65992
$783$	−6.06053	−0.216586
$784$	12.4984	0.446373
$785$	1.01068	0.0360728
$786$	−30.3522	−1.08263
$787$	−3.29602	−0.117490	−0.0587452	−	0.998273i	$-0.518710\pi$
$787$	−3.29602	−0.117490	−0.0587452	+	0.998273i	$0.518710\pi$
$788$	−109.617	−3.90493
$789$	15.5636	0.554079
$790$	−40.1808	−1.42957
$791$	8.52998	0.303291
$792$	28.5498	1.01447
$793$	68.4159	2.42952
$794$	60.4646	2.14581
$795$	5.85951	0.207816
$796$	−80.6272	−2.85776
$797$	8.93980	0.316664	0.158332	−	0.987386i	$-0.449388\pi$
$797$	8.93980	0.316664	0.158332	+	0.987386i	$0.449388\pi$
$798$	−5.22627	−0.185008
$799$	49.1274	1.73800
$800$	19.1245	0.676152
$801$	−17.6495	−0.623615
$802$	−34.0940	−1.20390
$803$	−32.2514	−1.13813
$804$	14.2221	0.501574
$805$	5.57345	0.196438
$806$	−68.4207	−2.41002
$807$	−9.85449	−0.346894
$808$	−156.215	−5.49562
$809$	49.2414	1.73124	0.865618	−	0.500705i	$-0.166926\pi$
$809$	49.2414	1.73124	0.865618	+	0.500705i	$0.166926\pi$
$810$	−24.6826	−0.867257
$811$	50.9127	1.78779	0.893893	−	0.448280i	$-0.147963\pi$
$811$	50.9127	1.78779	0.893893	+	0.448280i	$0.147963\pi$
$812$	−5.55481	−0.194936
$813$	−0.176436	−0.00618790
$814$	−81.4194	−2.85375
$815$	−7.69373	−0.269500
$816$	−105.986	−3.71024
$817$	−3.20835	−0.112246
$818$	−75.0404	−2.62373
$819$	4.66246	0.162919
$820$	60.5398	2.11414
$821$	−29.9395	−1.04490	−0.522448	−	0.852671i	$-0.674981\pi$
$821$	−29.9395	−1.04490	−0.522448	+	0.852671i	$0.674981\pi$
$822$	12.9115	0.450339
$823$	−14.8680	−0.518267	−0.259134	−	0.965842i	$-0.583437\pi$
$823$	−14.8680	−0.518267	−0.259134	+	0.965842i	$0.583437\pi$
$824$	−152.143	−5.30014
$825$	5.12350	0.178377
$826$	−31.4500	−1.09429
$827$	17.0459	0.592745	0.296372	−	0.955072i	$-0.404223\pi$
$827$	17.0459	0.592745	0.296372	+	0.955072i	$0.404223\pi$
$828$	15.6178	0.542756
$829$	19.3414	0.671753	0.335877	−	0.941906i	$-0.390967\pi$
$829$	19.3414	0.671753	0.335877	+	0.941906i	$0.390967\pi$
$830$	−55.2495	−1.91774
$831$	−13.2914	−0.461072
$832$	−83.8842	−2.90816
$833$	6.08653	0.210886
$834$	15.4606	0.535356
$835$	−36.3121	−1.25663
$836$	−22.9263	−0.792924
$837$	−32.7879	−1.13332
$838$	−71.7353	−2.47806
$839$	23.7747	0.820794	0.410397	−	0.911907i	$-0.365390\pi$
$839$	23.7747	0.820794	0.410397	+	0.911907i	$0.365390\pi$
$840$	−23.2804	−0.803249
$841$	−27.8514	−0.960394
$842$	34.3935	1.18528
$843$	6.80929	0.234525
$844$	−53.5749	−1.84412
$845$	−12.5091	−0.430325
$846$	22.9074	0.787571
$847$	−1.01245	−0.0347880
$848$	26.8371	0.921591
$849$	22.3593	0.767368
$850$	18.9820	0.651077
$851$	−27.3531	−0.937651
$852$	54.0743	1.85255
$853$	26.6843	0.913652	0.456826	−	0.889556i	$-0.348986\pi$
$853$	26.6843	0.913652	0.456826	+	0.889556i	$0.348986\pi$
$854$	41.6451	1.42506
$855$	−2.90295	−0.0992787
$856$	60.7431	2.07616
$857$	47.7397	1.63076	0.815378	−	0.578928i	$-0.196529\pi$
$857$	47.7397	1.63076	0.815378	+	0.578928i	$0.196529\pi$
$858$	−51.9586	−1.77384
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	−23.2712	−0.793540
$861$	8.30828	0.283146
$862$	−38.3679	−1.30682
$863$	7.15022	0.243396	0.121698	−	0.992567i	$-0.461166\pi$
$863$	7.15022	0.243396	0.121698	+	0.992567i	$0.461166\pi$
$864$	−92.9408	−3.16191
$865$	−43.4232	−1.47643
$866$	80.1608	2.72397
$867$	−27.9284	−0.948499
$868$	−30.0519	−1.02003
$869$	−24.1898	−0.820582
$870$	7.83820	0.265740
$871$	8.67163	0.293827
$872$	116.655	3.95045
$873$	−0.214351	−0.00725470
$874$	−10.6742	−0.361060
$875$	12.0725	0.408125
$876$	73.6938	2.48988
$877$	−0.548551	−0.0185233	−0.00926163	−	0.999957i	$-0.502948\pi$
$877$	−0.548551	−0.0185233	−0.00926163	+	0.999957i	$0.502948\pi$
$878$	29.9470	1.01066
$879$	3.51010	0.118393
$880$	−77.3652	−2.60798
$881$	−42.7183	−1.43922	−0.719608	−	0.694380i	$-0.755679\pi$
$881$	−42.7183	−1.43922	−0.719608	+	0.694380i	$0.755679\pi$
$882$	2.83806	0.0955624
$883$	−16.9624	−0.570830	−0.285415	−	0.958404i	$-0.592131\pi$
$883$	−16.9624	−0.570830	−0.285415	+	0.958404i	$0.592131\pi$
$884$	−138.903	−4.67180
$885$	32.0218	1.07640
$886$	−69.1655	−2.32366
$887$	32.2463	1.08273	0.541363	−	0.840789i	$-0.317909\pi$
$887$	32.2463	1.08273	0.541363	+	0.840789i	$0.317909\pi$
$888$	114.254	3.83412
$889$	−18.3998	−0.617110
$890$	87.4952	2.93285
$891$	−14.8595	−0.497811
$892$	37.1312	1.24325
$893$	−11.2971	−0.378044
$894$	−64.5271	−2.15811
$895$	15.4766	0.517326
$896$	−18.1903	−0.607696
$897$	−17.4556	−0.582826
$898$	−34.1608	−1.13996
$899$	6.21384	0.207243
$900$	6.38662	0.212887
$901$	13.0692	0.435399
$902$	50.5099	1.68179
$903$	−3.19366	−0.106278
$904$	−72.7707	−2.42032
$905$	−24.9433	−0.829144
$906$	44.7962	1.48825
$907$	31.1998	1.03597	0.517987	−	0.855389i	$-0.326682\pi$
$907$	31.1998	1.03597	0.517987	+	0.855389i	$0.326682\pi$
$908$	−115.455	−3.83152
$909$	−19.3900	−0.643127
$910$	−23.1135	−0.766207
$911$	40.2885	1.33482	0.667408	−	0.744692i	$-0.267404\pi$
$911$	40.2885	1.33482	0.667408	+	0.744692i	$0.267404\pi$
$912$	24.3720	0.807038
$913$	−33.2615	−1.10079
$914$	−11.6597	−0.385667
$915$	−42.4022	−1.40177
$916$	−23.6777	−0.782332
$917$	−8.12854	−0.268428
$918$	−92.2484	−3.04465
$919$	−7.26584	−0.239678	−0.119839	−	0.992793i	$-0.538238\pi$
$919$	−7.26584	−0.239678	−0.119839	+	0.992793i	$0.538238\pi$
$920$	−47.5481	−1.56761
$921$	−14.6711	−0.483429
$922$	10.4219	0.343227
$923$	32.9707	1.08524
$924$	−22.8214	−0.750768
$925$	−11.1855	−0.367779
$926$	21.1373	0.694615
$927$	−18.8846	−0.620251
$928$	17.6138	0.578201
$929$	−1.17296	−0.0384834	−0.0192417	−	0.999815i	$-0.506125\pi$
$929$	−1.17296	−0.0384834	−0.0192417	+	0.999815i	$0.506125\pi$
$930$	42.4052	1.39052
$931$	−1.39963	−0.0458711
$932$	−58.4249	−1.91377
$933$	43.7343	1.43180
$934$	21.1339	0.691524
$935$	−37.6756	−1.23212
$936$	−39.7762	−1.30013
$937$	1.77420	0.0579607	0.0289804	−	0.999580i	$-0.490774\pi$
$937$	1.77420	0.0579607	0.0289804	+	0.999580i	$0.490774\pi$
$938$	5.27846	0.172348
$939$	−35.3337	−1.15307
$940$	−81.9416	−2.67264
$941$	56.1805	1.83143	0.915716	−	0.401825i	$-0.131624\pi$
$941$	56.1805	1.83143	0.915716	+	0.401825i	$0.131624\pi$
$942$	−1.92678	−0.0627780
$943$	16.9689	0.552584
$944$	146.663	4.77348
$945$	−11.0762	−0.360310
$946$	−19.4157	−0.631259
$947$	−16.9707	−0.551474	−0.275737	−	0.961233i	$-0.588922\pi$
$947$	−16.9707	−0.551474	−0.275737	+	0.961233i	$0.588922\pi$
$948$	55.2732	1.79519
$949$	44.9334	1.45860
$950$	−4.36502	−0.141620
$951$	−5.46842	−0.177326
$952$	−51.9253	−1.68291
$953$	24.9602	0.808539	0.404270	−	0.914640i	$-0.367526\pi$
$953$	24.9602	0.808539	0.404270	+	0.914640i	$0.367526\pi$
$954$	6.09399	0.197300
$955$	10.2035	0.330179
$956$	−86.4433	−2.79578
$957$	4.71878	0.152536
$958$	−82.9846	−2.68111
$959$	3.45778	0.111658
$960$	51.9890	1.67794
$961$	2.61729	0.0844286
$962$	113.435	3.65730
$963$	7.53969	0.242963
$964$	−23.4404	−0.754966
$965$	3.18121	0.102407
$966$	−10.6253	−0.341864
$967$	17.0796	0.549243	0.274621	−	0.961552i	$-0.411448\pi$
$967$	17.0796	0.549243	0.274621	+	0.961552i	$0.411448\pi$
$968$	8.63734	0.277615
$969$	11.8688	0.381280
$970$	1.06262	0.0341187
$971$	52.1012	1.67201	0.836003	−	0.548724i	$-0.184886\pi$
$971$	52.1012	1.67201	0.836003	+	0.548724i	$0.184886\pi$
$972$	−53.9778	−1.73134
$973$	4.14045	0.132737
$974$	−105.486	−3.38001
$975$	−7.13817	−0.228604
$976$	−194.206	−6.21639
$977$	26.4834	0.847278	0.423639	−	0.905831i	$-0.360752\pi$
$977$	26.4834	0.847278	0.423639	+	0.905831i	$0.360752\pi$
$978$	14.6675	0.469013
$979$	52.6741	1.68347
$980$	−10.1520	−0.324293
$981$	14.4797	0.462303
$982$	14.1317	0.450962
$983$	−39.0034	−1.24401	−0.622007	−	0.783011i	$-0.713683\pi$
$983$	−39.0034	−1.24401	−0.622007	+	0.783011i	$0.713683\pi$
$984$	−70.8794	−2.25955
$985$	41.4234	1.31986
$986$	17.4826	0.556758
$987$	−11.2454	−0.357945
$988$	31.9415	1.01619
$989$	−6.52276	−0.207412
$990$	−17.5675	−0.558333
$991$	−44.5271	−1.41445	−0.707224	−	0.706989i	$-0.750053\pi$
$991$	−44.5271	−1.41445	−0.707224	+	0.706989i	$0.750053\pi$
$992$	95.2918	3.02552
$993$	17.8032	0.564966
$994$	20.0694	0.636564
$995$	30.4685	0.965917
$996$	76.0018	2.40821
$997$	20.1867	0.639319	0.319660	−	0.947532i	$-0.396431\pi$
$997$	20.1867	0.639319	0.319660	+	0.947532i	$0.396431\pi$
$998$	−71.0837	−2.25011
$999$	54.3593	1.71985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.2	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.2	✓	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68013 q^{2} -1.39322 q^{3} +5.18311 q^{4} -1.95866 q^{5} +3.73403 q^{6} +1.00000 q^{7} -8.53117 q^{8} -1.05892 q^{9} +O(q^{10})\)	\(q-2.68013 q^{2} -1.39322 q^{3} +5.18311 q^{4} -1.95866 q^{5} +3.73403 q^{6} +1.00000 q^{7} -8.53117 q^{8} -1.05892 q^{9} +5.24948 q^{10} +3.16031 q^{11} -7.22124 q^{12} -4.40301 q^{13} -2.68013 q^{14} +2.72886 q^{15} +12.4984 q^{16} +6.08653 q^{17} +2.83806 q^{18} -1.39963 q^{19} -10.1520 q^{20} -1.39322 q^{21} -8.47005 q^{22} -2.84554 q^{23} +11.8858 q^{24} -1.16363 q^{25} +11.8007 q^{26} +5.65499 q^{27} +5.18311 q^{28} -1.07171 q^{29} -7.31371 q^{30} -5.79804 q^{31} -16.4352 q^{32} -4.40302 q^{33} -16.3127 q^{34} -1.95866 q^{35} -5.48853 q^{36} +9.61262 q^{37} +3.75120 q^{38} +6.13439 q^{39} +16.7097 q^{40} -5.96335 q^{41} +3.73403 q^{42} +2.29228 q^{43} +16.3802 q^{44} +2.07408 q^{45} +7.62642 q^{46} +8.07149 q^{47} -17.4131 q^{48} +1.00000 q^{49} +3.11869 q^{50} -8.47991 q^{51} -22.8213 q^{52} +2.14724 q^{53} -15.1561 q^{54} -6.18999 q^{55} -8.53117 q^{56} +1.95000 q^{57} +2.87234 q^{58} +11.7345 q^{59} +14.1440 q^{60} -15.5384 q^{61} +15.5395 q^{62} -1.05892 q^{63} +19.0515 q^{64} +8.62403 q^{65} +11.8007 q^{66} -1.96948 q^{67} +31.5472 q^{68} +3.96447 q^{69} +5.24948 q^{70} -7.48822 q^{71} +9.03387 q^{72} -10.2051 q^{73} -25.7631 q^{74} +1.62120 q^{75} -7.25446 q^{76} +3.16031 q^{77} -16.4410 q^{78} -7.65424 q^{79} -24.4803 q^{80} -4.70191 q^{81} +15.9826 q^{82} -10.5248 q^{83} -7.22124 q^{84} -11.9215 q^{85} -6.14361 q^{86} +1.49314 q^{87} -26.9611 q^{88} +16.6674 q^{89} -5.55881 q^{90} -4.40301 q^{91} -14.7487 q^{92} +8.07798 q^{93} -21.6327 q^{94} +2.74141 q^{95} +22.8979 q^{96} +0.202424 q^{97} -2.68013 q^{98} -3.34653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

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