LMFDB - Embedded newform 6005.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25928 q^{2} -0.374349 q^{3} +3.10434 q^{4} +1.00000 q^{5} +0.845758 q^{6} -3.16273 q^{7} -2.49501 q^{8} -2.85986 q^{9} +O(q^{10})$	\(q-2.25928 q^{2} -0.374349 q^{3} +3.10434 q^{4} +1.00000 q^{5} +0.845758 q^{6} -3.16273 q^{7} -2.49501 q^{8} -2.85986 q^{9} -2.25928 q^{10} +4.95137 q^{11} -1.16210 q^{12} -1.74623 q^{13} +7.14549 q^{14} -0.374349 q^{15} -0.571763 q^{16} -1.83143 q^{17} +6.46123 q^{18} +7.86216 q^{19} +3.10434 q^{20} +1.18396 q^{21} -11.1865 q^{22} +1.27327 q^{23} +0.934002 q^{24} +1.00000 q^{25} +3.94523 q^{26} +2.19363 q^{27} -9.81819 q^{28} -9.15593 q^{29} +0.845758 q^{30} -2.84202 q^{31} +6.28178 q^{32} -1.85354 q^{33} +4.13771 q^{34} -3.16273 q^{35} -8.87798 q^{36} +5.12296 q^{37} -17.7628 q^{38} +0.653700 q^{39} -2.49501 q^{40} +0.299311 q^{41} -2.67491 q^{42} -9.53903 q^{43} +15.3707 q^{44} -2.85986 q^{45} -2.87667 q^{46} -1.72106 q^{47} +0.214039 q^{48} +3.00287 q^{49} -2.25928 q^{50} +0.685594 q^{51} -5.42090 q^{52} -5.39322 q^{53} -4.95603 q^{54} +4.95137 q^{55} +7.89103 q^{56} -2.94319 q^{57} +20.6858 q^{58} +4.80614 q^{59} -1.16210 q^{60} +10.5115 q^{61} +6.42091 q^{62} +9.04498 q^{63} -13.0488 q^{64} -1.74623 q^{65} +4.18766 q^{66} +2.96639 q^{67} -5.68538 q^{68} -0.476646 q^{69} +7.14549 q^{70} +3.87703 q^{71} +7.13537 q^{72} -6.56592 q^{73} -11.5742 q^{74} -0.374349 q^{75} +24.4068 q^{76} -15.6598 q^{77} -1.47689 q^{78} +11.2427 q^{79} -0.571763 q^{80} +7.75841 q^{81} -0.676226 q^{82} -5.49815 q^{83} +3.67543 q^{84} -1.83143 q^{85} +21.5513 q^{86} +3.42751 q^{87} -12.3537 q^{88} -6.20061 q^{89} +6.46123 q^{90} +5.52287 q^{91} +3.95265 q^{92} +1.06391 q^{93} +3.88836 q^{94} +7.86216 q^{95} -2.35158 q^{96} +3.40123 q^{97} -6.78432 q^{98} -14.1602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−2.25928	−1.59755	−0.798775	−	0.601629i	$-0.794518\pi$
$2$	−2.25928	−1.59755	−0.798775	+	0.601629i	$0.794518\pi$
$3$	−0.374349	−0.216130	−0.108065	−	0.994144i	$-0.534466\pi$
$3$	−0.374349	−0.216130	−0.108065	+	0.994144i	$0.534466\pi$
$4$	3.10434	1.55217
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.845758	0.345279
$7$	−3.16273	−1.19540	−0.597700	−	0.801720i	$-0.703919\pi$
$7$	−3.16273	−1.19540	−0.597700	+	0.801720i	$0.703919\pi$
$8$	−2.49501	−0.882118
$9$	−2.85986	−0.953288
$10$	−2.25928	−0.714446
$11$	4.95137	1.49289	0.746447	−	0.665445i	$-0.231758\pi$
$11$	4.95137	1.49289	0.746447	+	0.665445i	$0.231758\pi$
$12$	−1.16210	−0.335471
$13$	−1.74623	−0.484318	−0.242159	−	0.970237i	$-0.577856\pi$
$13$	−1.74623	−0.484318	−0.242159	+	0.970237i	$0.577856\pi$
$14$	7.14549	1.90971
$15$	−0.374349	−0.0966564
$16$	−0.571763	−0.142941
$17$	−1.83143	−0.444187	−0.222094	−	0.975025i	$-0.571289\pi$
$17$	−1.83143	−0.444187	−0.222094	+	0.975025i	$0.571289\pi$
$18$	6.46123	1.52293
$19$	7.86216	1.80370	0.901852	−	0.432045i	$-0.142208\pi$
$19$	7.86216	1.80370	0.901852	+	0.432045i	$0.142208\pi$
$20$	3.10434	0.694151
$21$	1.18396	0.258362
$22$	−11.1865	−2.38497
$23$	1.27327	0.265495	0.132747	−	0.991150i	$-0.457620\pi$
$23$	1.27327	0.265495	0.132747	+	0.991150i	$0.457620\pi$
$24$	0.934002	0.190652
$25$	1.00000	0.200000
$26$	3.94523	0.773723
$27$	2.19363	0.422165
$28$	−9.81819	−1.85546
$29$	−9.15593	−1.70021	−0.850107	−	0.526610i	$-0.823463\pi$
$29$	−9.15593	−1.70021	−0.850107	+	0.526610i	$0.823463\pi$
$30$	0.845758	0.154414
$31$	−2.84202	−0.510442	−0.255221	−	0.966883i	$-0.582148\pi$
$31$	−2.84202	−0.510442	−0.255221	+	0.966883i	$0.582148\pi$
$32$	6.28178	1.11047
$33$	−1.85354	−0.322660
$34$	4.13771	0.709612
$35$	−3.16273	−0.534599
$36$	−8.87798	−1.47966
$37$	5.12296	0.842210	0.421105	−	0.907012i	$-0.361642\pi$
$37$	5.12296	0.842210	0.421105	+	0.907012i	$0.361642\pi$
$38$	−17.7628	−2.88151
$39$	0.653700	0.104676
$40$	−2.49501	−0.394495
$41$	0.299311	0.0467445	0.0233722	−	0.999727i	$-0.492560\pi$
$41$	0.299311	0.0467445	0.0233722	+	0.999727i	$0.492560\pi$
$42$	−2.67491	−0.412747
$43$	−9.53903	−1.45469	−0.727344	−	0.686273i	$-0.759246\pi$
$43$	−9.53903	−1.45469	−0.727344	+	0.686273i	$0.759246\pi$
$44$	15.3707	2.31722
$45$	−2.85986	−0.426323
$46$	−2.87667	−0.424141
$47$	−1.72106	−0.251043	−0.125521	−	0.992091i	$-0.540060\pi$
$47$	−1.72106	−0.251043	−0.125521	+	0.992091i	$0.540060\pi$
$48$	0.214039	0.0308939
$49$	3.00287	0.428982
$50$	−2.25928	−0.319510
$51$	0.685594	0.0960023
$52$	−5.42090	−0.751744
$53$	−5.39322	−0.740816	−0.370408	−	0.928869i	$-0.620782\pi$
$53$	−5.39322	−0.740816	−0.370408	+	0.928869i	$0.620782\pi$
$54$	−4.95603	−0.674430
$55$	4.95137	0.667642
$56$	7.89103	1.05448
$57$	−2.94319	−0.389835
$58$	20.6858	2.71618
$59$	4.80614	0.625706	0.312853	−	0.949802i	$-0.398715\pi$
$59$	4.80614	0.625706	0.312853	+	0.949802i	$0.398715\pi$
$60$	−1.16210	−0.150027
$61$	10.5115	1.34586	0.672930	−	0.739706i	$-0.265035\pi$
$61$	10.5115	1.34586	0.672930	+	0.739706i	$0.265035\pi$
$62$	6.42091	0.815457
$63$	9.04498	1.13956
$64$	−13.0488	−1.63110
$65$	−1.74623	−0.216594
$66$	4.18766	0.515465
$67$	2.96639	0.362403	0.181201	−	0.983446i	$-0.442001\pi$
$67$	2.96639	0.362403	0.181201	+	0.983446i	$0.442001\pi$
$68$	−5.68538	−0.689454
$69$	−0.476646	−0.0573815
$70$	7.14549	0.854049
$71$	3.87703	0.460119	0.230059	−	0.973177i	$-0.426108\pi$
$71$	3.87703	0.460119	0.230059	+	0.973177i	$0.426108\pi$
$72$	7.13537	0.840912
$73$	−6.56592	−0.768482	−0.384241	−	0.923233i	$-0.625537\pi$
$73$	−6.56592	−0.768482	−0.384241	+	0.923233i	$0.625537\pi$
$74$	−11.5742	−1.34547
$75$	−0.374349	−0.0432261
$76$	24.4068	2.79965
$77$	−15.6598	−1.78461
$78$	−1.47689	−0.167225
$79$	11.2427	1.26490	0.632452	−	0.774600i	$-0.282049\pi$
$79$	11.2427	1.26490	0.632452	+	0.774600i	$0.282049\pi$
$80$	−0.571763	−0.0639251
$81$	7.75841	0.862045
$82$	−0.676226	−0.0746767
$83$	−5.49815	−0.603500	−0.301750	−	0.953387i	$-0.597571\pi$
$83$	−5.49815	−0.603500	−0.301750	+	0.953387i	$0.597571\pi$
$84$	3.67543	0.401022
$85$	−1.83143	−0.198647
$86$	21.5513	2.32394
$87$	3.42751	0.367468
$88$	−12.3537	−1.31691
$89$	−6.20061	−0.657264	−0.328632	−	0.944458i	$-0.606588\pi$
$89$	−6.20061	−0.657264	−0.328632	+	0.944458i	$0.606588\pi$
$90$	6.46123	0.681073
$91$	5.52287	0.578954
$92$	3.95265	0.412093
$93$	1.06391	0.110322
$94$	3.88836	0.401054
$95$	7.86216	0.806641
$96$	−2.35158	−0.240007
$97$	3.40123	0.345342	0.172671	−	0.984980i	$-0.444760\pi$
$97$	3.40123	0.345342	0.172671	+	0.984980i	$0.444760\pi$
$98$	−6.78432	−0.685320
$99$	−14.1602	−1.42316
$100$	3.10434	0.310434
$101$	6.37894	0.634728	0.317364	−	0.948304i	$-0.397202\pi$
$101$	6.37894	0.634728	0.317364	+	0.948304i	$0.397202\pi$
$102$	−1.54895	−0.153369
$103$	14.9437	1.47244	0.736222	−	0.676740i	$-0.236608\pi$
$103$	14.9437	1.47244	0.736222	+	0.676740i	$0.236608\pi$
$104$	4.35686	0.427226
$105$	1.18396	0.115543
$106$	12.1848	1.18349
$107$	4.02443	0.389056	0.194528	−	0.980897i	$-0.437682\pi$
$107$	4.02443	0.389056	0.194528	+	0.980897i	$0.437682\pi$
$108$	6.80977	0.655271
$109$	−11.9384	−1.14349	−0.571743	−	0.820433i	$-0.693733\pi$
$109$	−11.9384	−1.14349	−0.571743	+	0.820433i	$0.693733\pi$
$110$	−11.1865	−1.06659
$111$	−1.91777	−0.182027
$112$	1.80833	0.170872
$113$	−17.9563	−1.68919	−0.844593	−	0.535409i	$-0.820157\pi$
$113$	−17.9563	−1.68919	−0.844593	+	0.535409i	$0.820157\pi$
$114$	6.64949	0.622781
$115$	1.27327	0.118733
$116$	−28.4231	−2.63902
$117$	4.99399	0.461695
$118$	−10.8584	−0.999597
$119$	5.79232	0.530982
$120$	0.934002	0.0852623
$121$	13.5160	1.22873
$122$	−23.7484	−2.15008
$123$	−0.112047	−0.0101029
$124$	−8.82259	−0.792292
$125$	1.00000	0.0894427
$126$	−20.4351	−1.82051
$127$	−9.59640	−0.851543	−0.425771	−	0.904831i	$-0.639997\pi$
$127$	−9.59640	−0.851543	−0.425771	+	0.904831i	$0.639997\pi$
$128$	16.9172	1.49529
$129$	3.57092	0.314402
$130$	3.94523	0.346019
$131$	1.89859	0.165881	0.0829404	−	0.996555i	$-0.473569\pi$
$131$	1.89859	0.165881	0.0829404	+	0.996555i	$0.473569\pi$
$132$	−5.75401	−0.500822
$133$	−24.8659	−2.15615
$134$	−6.70191	−0.578957
$135$	2.19363	0.188798
$136$	4.56943	0.391825
$137$	−5.27552	−0.450718	−0.225359	−	0.974276i	$-0.572356\pi$
$137$	−5.27552	−0.450718	−0.225359	+	0.974276i	$0.572356\pi$
$138$	1.07688	0.0916698
$139$	6.54939	0.555512	0.277756	−	0.960652i	$-0.410409\pi$
$139$	6.54939	0.555512	0.277756	+	0.960652i	$0.410409\pi$
$140$	−9.81819	−0.829788
$141$	0.644278	0.0542580
$142$	−8.75929	−0.735063
$143$	−8.64625	−0.723035
$144$	1.63517	0.136264
$145$	−9.15593	−0.760359
$146$	14.8342	1.22769
$147$	−1.12412	−0.0927160
$148$	15.9034	1.30725
$149$	−0.606962	−0.0497243	−0.0248621	−	0.999691i	$-0.507915\pi$
$149$	−0.606962	−0.0497243	−0.0248621	+	0.999691i	$0.507915\pi$
$150$	0.845758	0.0690558
$151$	24.5332	1.99648	0.998242	−	0.0592724i	$-0.0188781\pi$
$151$	24.5332	1.99648	0.998242	+	0.0592724i	$0.0188781\pi$
$152$	−19.6161	−1.59108
$153$	5.23764	0.423438
$154$	35.3799	2.85100
$155$	−2.84202	−0.228276
$156$	2.02931	0.162475
$157$	3.52873	0.281623	0.140812	−	0.990036i	$-0.455029\pi$
$157$	3.52873	0.281623	0.140812	+	0.990036i	$0.455029\pi$
$158$	−25.4004	−2.02075
$159$	2.01895	0.160113
$160$	6.28178	0.496619
$161$	−4.02700	−0.317372
$162$	−17.5284	−1.37716
$163$	−13.0842	−1.02483	−0.512417	−	0.858736i	$-0.671250\pi$
$163$	−13.0842	−1.02483	−0.512417	+	0.858736i	$0.671250\pi$
$164$	0.929161	0.0725553
$165$	−1.85354	−0.144298
$166$	12.4218	0.964122
$167$	−17.1422	−1.32650	−0.663252	−	0.748396i	$-0.730824\pi$
$167$	−17.1422	−1.32650	−0.663252	+	0.748396i	$0.730824\pi$
$168$	−2.95400	−0.227906
$169$	−9.95067	−0.765436
$170$	4.13771	0.317348
$171$	−22.4847	−1.71945
$172$	−29.6124	−2.25792
$173$	8.40065	0.638690	0.319345	−	0.947639i	$-0.396537\pi$
$173$	8.40065	0.638690	0.319345	+	0.947639i	$0.396537\pi$
$174$	−7.74370	−0.587049
$175$	−3.16273	−0.239080
$176$	−2.83101	−0.213395
$177$	−1.79917	−0.135234
$178$	14.0089	1.05001
$179$	−3.38882	−0.253292	−0.126646	−	0.991948i	$-0.540421\pi$
$179$	−3.38882	−0.253292	−0.126646	+	0.991948i	$0.540421\pi$
$180$	−8.87798	−0.661726
$181$	−12.7443	−0.947278	−0.473639	−	0.880719i	$-0.657060\pi$
$181$	−12.7443	−0.947278	−0.473639	+	0.880719i	$0.657060\pi$
$182$	−12.4777	−0.924909
$183$	−3.93497	−0.290881
$184$	−3.17681	−0.234198
$185$	5.12296	0.376648
$186$	−2.40366	−0.176245
$187$	−9.06809	−0.663124
$188$	−5.34276	−0.389661
$189$	−6.93787	−0.504656
$190$	−17.7628	−1.28865
$191$	20.3261	1.47074	0.735371	−	0.677664i	$-0.237008\pi$
$191$	20.3261	1.47074	0.735371	+	0.677664i	$0.237008\pi$
$192$	4.88479	0.352529
$193$	15.7531	1.13393	0.566967	−	0.823740i	$-0.308117\pi$
$193$	15.7531	1.13393	0.566967	+	0.823740i	$0.308117\pi$
$194$	−7.68432	−0.551702
$195$	0.653700	0.0468125
$196$	9.32193	0.665852
$197$	8.46836	0.603345	0.301673	−	0.953412i	$-0.402455\pi$
$197$	8.46836	0.603345	0.301673	+	0.953412i	$0.402455\pi$
$198$	31.9919	2.27357
$199$	−12.8830	−0.913254	−0.456627	−	0.889658i	$-0.650943\pi$
$199$	−12.8830	−0.913254	−0.456627	+	0.889658i	$0.650943\pi$
$200$	−2.49501	−0.176424
$201$	−1.11047	−0.0783262
$202$	−14.4118	−1.01401
$203$	28.9578	2.03244
$204$	2.12831	0.149012
$205$	0.299311	0.0209048
$206$	−33.7619	−2.35230
$207$	−3.64137	−0.253093
$208$	0.998433	0.0692289
$209$	38.9285	2.69274
$210$	−2.67491	−0.184586
$211$	−23.8168	−1.63961	−0.819807	−	0.572639i	$-0.805920\pi$
$211$	−23.8168	−1.63961	−0.819807	+	0.572639i	$0.805920\pi$
$212$	−16.7424	−1.14987
$213$	−1.45136	−0.0994456
$214$	−9.09230	−0.621537
$215$	−9.53903	−0.650557
$216$	−5.47312	−0.372399
$217$	8.98854	0.610182
$218$	26.9721	1.82678
$219$	2.45794	0.166092
$220$	15.3707	1.03629
$221$	3.19811	0.215128
$222$	4.33279	0.290798
$223$	−22.8073	−1.52729	−0.763644	−	0.645637i	$-0.776592\pi$
$223$	−22.8073	−1.52729	−0.763644	+	0.645637i	$0.776592\pi$
$224$	−19.8676	−1.32746
$225$	−2.85986	−0.190658
$226$	40.5682	2.69856
$227$	14.7683	0.980208	0.490104	−	0.871664i	$-0.336959\pi$
$227$	14.7683	0.980208	0.490104	+	0.871664i	$0.336959\pi$
$228$	−9.13666	−0.605090
$229$	−25.9623	−1.71564	−0.857818	−	0.513954i	$-0.828180\pi$
$229$	−25.9623	−1.71564	−0.857818	+	0.513954i	$0.828180\pi$
$230$	−2.87667	−0.189682
$231$	5.86224	0.385707
$232$	22.8441	1.49979
$233$	9.23151	0.604776	0.302388	−	0.953185i	$-0.402216\pi$
$233$	9.23151	0.604776	0.302388	+	0.953185i	$0.402216\pi$
$234$	−11.2828	−0.737581
$235$	−1.72106	−0.112270
$236$	14.9199	0.971201
$237$	−4.20869	−0.273384
$238$	−13.0865	−0.848270
$239$	11.8649	0.767478	0.383739	−	0.923442i	$-0.374636\pi$
$239$	11.8649	0.767478	0.383739	+	0.923442i	$0.374636\pi$
$240$	0.214039	0.0138162
$241$	2.32413	0.149711	0.0748553	−	0.997194i	$-0.476151\pi$
$241$	2.32413	0.149711	0.0748553	+	0.997194i	$0.476151\pi$
$242$	−30.5365	−1.96296
$243$	−9.48525	−0.608479
$244$	32.6313	2.08900
$245$	3.00287	0.191846
$246$	0.253144	0.0161399
$247$	−13.7292	−0.873567
$248$	7.09085	0.450270
$249$	2.05822	0.130435
$250$	−2.25928	−0.142889
$251$	13.0994	0.826825	0.413413	−	0.910544i	$-0.364337\pi$
$251$	13.0994	0.826825	0.413413	+	0.910544i	$0.364337\pi$
$252$	28.0787	1.76879
$253$	6.30442	0.396355
$254$	21.6809	1.36038
$255$	0.685594	0.0429335
$256$	−12.1232	−0.757700
$257$	10.2696	0.640599	0.320300	−	0.947316i	$-0.396216\pi$
$257$	10.2696	0.640599	0.320300	+	0.947316i	$0.396216\pi$
$258$	−8.06771	−0.502274
$259$	−16.2026	−1.00678
$260$	−5.42090	−0.336190
$261$	26.1847	1.62079
$262$	−4.28945	−0.265003
$263$	19.8618	1.22473	0.612366	−	0.790574i	$-0.290218\pi$
$263$	19.8618	1.22473	0.612366	+	0.790574i	$0.290218\pi$
$264$	4.62459	0.284624
$265$	−5.39322	−0.331303
$266$	56.1790	3.44456
$267$	2.32119	0.142055
$268$	9.20869	0.562510
$269$	10.1672	0.619903	0.309952	−	0.950752i	$-0.399687\pi$
$269$	10.1672	0.619903	0.309952	+	0.950752i	$0.399687\pi$
$270$	−4.95603	−0.301614
$271$	−23.2065	−1.40970	−0.704848	−	0.709358i	$-0.748985\pi$
$271$	−23.2065	−1.40970	−0.704848	+	0.709358i	$0.748985\pi$
$272$	1.04715	0.0634925
$273$	−2.06748	−0.125130
$274$	11.9189	0.720045
$275$	4.95137	0.298579
$276$	−1.47967	−0.0890657
$277$	−25.6230	−1.53954	−0.769768	−	0.638323i	$-0.779628\pi$
$277$	−25.6230	−1.53954	−0.769768	+	0.638323i	$0.779628\pi$
$278$	−14.7969	−0.887458
$279$	8.12779	0.486598
$280$	7.89103	0.471579
$281$	−19.9547	−1.19040	−0.595198	−	0.803579i	$-0.702927\pi$
$281$	−19.9547	−1.19040	−0.595198	+	0.803579i	$0.702927\pi$
$282$	−1.45560	−0.0866799
$283$	16.0354	0.953208	0.476604	−	0.879118i	$-0.341868\pi$
$283$	16.0354	0.953208	0.476604	+	0.879118i	$0.341868\pi$
$284$	12.0356	0.714182
$285$	−2.94319	−0.174340
$286$	19.5343	1.15509
$287$	−0.946639	−0.0558783
$288$	−17.9650	−1.05860
$289$	−13.6459	−0.802698
$290$	20.6858	1.21471
$291$	−1.27325	−0.0746389
$292$	−20.3828	−1.19281
$293$	14.3426	0.837905	0.418952	−	0.908008i	$-0.362397\pi$
$293$	14.3426	0.837905	0.418952	+	0.908008i	$0.362397\pi$
$294$	2.53970	0.148118
$295$	4.80614	0.279824
$296$	−12.7818	−0.742928
$297$	10.8615	0.630247
$298$	1.37130	0.0794370
$299$	−2.22342	−0.128584
$300$	−1.16210	−0.0670941
$301$	30.1694	1.73894
$302$	−55.4273	−3.18948
$303$	−2.38795	−0.137184
$304$	−4.49530	−0.257823
$305$	10.5115	0.601887
$306$	−11.8333	−0.676464
$307$	−14.4362	−0.823918	−0.411959	−	0.911202i	$-0.635155\pi$
$307$	−14.4362	−0.823918	−0.411959	+	0.911202i	$0.635155\pi$
$308$	−48.6134	−2.77001
$309$	−5.59415	−0.318240
$310$	6.42091	0.364683
$311$	−12.5719	−0.712886	−0.356443	−	0.934317i	$-0.616011\pi$
$311$	−12.5719	−0.712886	−0.356443	+	0.934317i	$0.616011\pi$
$312$	−1.63099	−0.0923364
$313$	−24.6019	−1.39058	−0.695292	−	0.718728i	$-0.744725\pi$
$313$	−24.6019	−1.39058	−0.695292	+	0.718728i	$0.744725\pi$
$314$	−7.97239	−0.449908
$315$	9.04498	0.509627
$316$	34.9012	1.96334
$317$	−4.64315	−0.260785	−0.130393	−	0.991462i	$-0.541624\pi$
$317$	−4.64315	−0.260785	−0.130393	+	0.991462i	$0.541624\pi$
$318$	−4.56136	−0.255788
$319$	−45.3344	−2.53824
$320$	−13.0488	−0.729448
$321$	−1.50654	−0.0840869
$322$	9.09812	0.507019
$323$	−14.3990	−0.801182
$324$	24.0847	1.33804
$325$	−1.74623	−0.0968636
$326$	29.5609	1.63723
$327$	4.46911	0.247142
$328$	−0.746782	−0.0412341
$329$	5.44326	0.300097
$330$	4.18766	0.230523
$331$	23.6259	1.29860	0.649298	−	0.760534i	$-0.275063\pi$
$331$	23.6259	1.29860	0.649298	+	0.760534i	$0.275063\pi$
$332$	−17.0681	−0.936734
$333$	−14.6510	−0.802868
$334$	38.7290	2.11916
$335$	2.96639	0.162071
$336$	−0.676948	−0.0369305
$337$	10.2596	0.558877	0.279438	−	0.960164i	$-0.409852\pi$
$337$	10.2596	0.558877	0.279438	+	0.960164i	$0.409852\pi$
$338$	22.4813	1.22282
$339$	6.72191	0.365084
$340$	−5.68538	−0.308333
$341$	−14.0719	−0.762035
$342$	50.7992	2.74691
$343$	12.6418	0.682595
$344$	23.7999	1.28321
$345$	−0.476646	−0.0256618
$346$	−18.9794	−1.02034
$347$	14.1150	0.757731	0.378865	−	0.925452i	$-0.376314\pi$
$347$	14.1150	0.757731	0.378865	+	0.925452i	$0.376314\pi$
$348$	10.6402	0.570372
$349$	−16.7653	−0.897425	−0.448713	−	0.893676i	$-0.648117\pi$
$349$	−16.7653	−0.897425	−0.448713	+	0.893676i	$0.648117\pi$
$350$	7.14549	0.381943
$351$	−3.83060	−0.204462
$352$	31.1034	1.65782
$353$	−24.5283	−1.30551	−0.652756	−	0.757568i	$-0.726387\pi$
$353$	−24.5283	−1.30551	−0.652756	+	0.757568i	$0.726387\pi$
$354$	4.06483	0.216043
$355$	3.87703	0.205771
$356$	−19.2488	−1.02018
$357$	−2.16835	−0.114761
$358$	7.65629	0.404647
$359$	−1.01906	−0.0537838	−0.0268919	−	0.999638i	$-0.508561\pi$
$359$	−1.01906	−0.0537838	−0.0268919	+	0.999638i	$0.508561\pi$
$360$	7.13537	0.376067
$361$	42.8136	2.25335
$362$	28.7930	1.51332
$363$	−5.05971	−0.265566
$364$	17.1449	0.898634
$365$	−6.56592	−0.343676
$366$	8.89019	0.464698
$367$	19.9745	1.04266	0.521331	−	0.853355i	$-0.325436\pi$
$367$	19.9745	1.04266	0.521331	+	0.853355i	$0.325436\pi$
$368$	−0.728008	−0.0379500
$369$	−0.855987	−0.0445609
$370$	−11.5742	−0.601714
$371$	17.0573	0.885571
$372$	3.30272	0.171238
$373$	−23.2826	−1.20553	−0.602765	−	0.797919i	$-0.705934\pi$
$373$	−23.2826	−1.20553	−0.602765	+	0.797919i	$0.705934\pi$
$374$	20.4873	1.05937
$375$	−0.374349	−0.0193313
$376$	4.29406	0.221449
$377$	15.9884	0.823445
$378$	15.6746	0.806213
$379$	8.83897	0.454027	0.227014	−	0.973892i	$-0.427104\pi$
$379$	8.83897	0.454027	0.227014	+	0.973892i	$0.427104\pi$
$380$	24.4068	1.25204
$381$	3.59240	0.184044
$382$	−45.9222	−2.34959
$383$	−12.3535	−0.631235	−0.315617	−	0.948887i	$-0.602212\pi$
$383$	−12.3535	−0.631235	−0.315617	+	0.948887i	$0.602212\pi$
$384$	−6.33294	−0.323177
$385$	−15.6598	−0.798100
$386$	−35.5907	−1.81152
$387$	27.2803	1.38674
$388$	10.5586	0.536030
$389$	−0.154675	−0.00784234	−0.00392117	−	0.999992i	$-0.501248\pi$
$389$	−0.154675	−0.00784234	−0.00392117	+	0.999992i	$0.501248\pi$
$390$	−1.47689	−0.0747853
$391$	−2.33190	−0.117929
$392$	−7.49218	−0.378412
$393$	−0.710735	−0.0358519
$394$	−19.1324	−0.963875
$395$	11.2427	0.565682
$396$	−43.9581	−2.20898
$397$	18.3806	0.922497	0.461249	−	0.887271i	$-0.347402\pi$
$397$	18.3806	0.922497	0.461249	+	0.887271i	$0.347402\pi$
$398$	29.1063	1.45897
$399$	9.30852	0.466009
$400$	−0.571763	−0.0285882
$401$	−15.5934	−0.778698	−0.389349	−	0.921090i	$-0.627300\pi$
$401$	−15.5934	−0.778698	−0.389349	+	0.921090i	$0.627300\pi$
$402$	2.50885	0.125130
$403$	4.96283	0.247216
$404$	19.8024	0.985205
$405$	7.75841	0.385518
$406$	−65.4236	−3.24692
$407$	25.3657	1.25733
$408$	−1.71056	−0.0846854
$409$	−27.0771	−1.33888	−0.669439	−	0.742867i	$-0.733465\pi$
$409$	−27.0771	−1.33888	−0.669439	+	0.742867i	$0.733465\pi$
$410$	−0.676226	−0.0333964
$411$	1.97488	0.0974139
$412$	46.3902	2.28548
$413$	−15.2005	−0.747969
$414$	8.22687	0.404329
$415$	−5.49815	−0.269894
$416$	−10.9695	−0.537822
$417$	−2.45176	−0.120063
$418$	−87.9502	−4.30179
$419$	−4.45326	−0.217556	−0.108778	−	0.994066i	$-0.534694\pi$
$419$	−4.45326	−0.217556	−0.108778	+	0.994066i	$0.534694\pi$
$420$	3.67543	0.179342
$421$	28.7465	1.40102	0.700508	−	0.713644i	$-0.252957\pi$
$421$	28.7465	1.40102	0.700508	+	0.713644i	$0.252957\pi$
$422$	53.8087	2.61937
$423$	4.92201	0.239316
$424$	13.4561	0.653487
$425$	−1.83143	−0.0888374
$426$	3.27903	0.158869
$427$	−33.2451	−1.60884
$428$	12.4932	0.603881
$429$	3.23671	0.156270
$430$	21.5513	1.03930
$431$	−6.92346	−0.333491	−0.166746	−	0.986000i	$-0.553326\pi$
$431$	−6.92346	−0.333491	−0.166746	+	0.986000i	$0.553326\pi$
$432$	−1.25424	−0.0603446
$433$	−28.6389	−1.37630	−0.688149	−	0.725569i	$-0.741577\pi$
$433$	−28.6389	−1.37630	−0.688149	+	0.725569i	$0.741577\pi$
$434$	−20.3076	−0.974797
$435$	3.42751	0.164337
$436$	−37.0607	−1.77488
$437$	10.0106	0.478874
$438$	−5.55318	−0.265341
$439$	18.2491	0.870984	0.435492	−	0.900193i	$-0.356574\pi$
$439$	18.2491	0.870984	0.435492	+	0.900193i	$0.356574\pi$
$440$	−12.3537	−0.588939
$441$	−8.58780	−0.408943
$442$	−7.22541	−0.343678
$443$	−12.7156	−0.604135	−0.302067	−	0.953287i	$-0.597677\pi$
$443$	−12.7156	−0.604135	−0.302067	+	0.953287i	$0.597677\pi$
$444$	−5.95342	−0.282537
$445$	−6.20061	−0.293937
$446$	51.5280	2.43992
$447$	0.227215	0.0107469
$448$	41.2698	1.94981
$449$	−9.54184	−0.450307	−0.225154	−	0.974323i	$-0.572288\pi$
$449$	−9.54184	−0.450307	−0.225154	+	0.974323i	$0.572288\pi$
$450$	6.46123	0.304585
$451$	1.48200	0.0697845
$452$	−55.7424	−2.62190
$453$	−9.18397	−0.431501
$454$	−33.3658	−1.56593
$455$	5.52287	0.258916
$456$	7.34328	0.343880
$457$	12.9827	0.607306	0.303653	−	0.952783i	$-0.401794\pi$
$457$	12.9827	0.607306	0.303653	+	0.952783i	$0.401794\pi$
$458$	58.6560	2.74081
$459$	−4.01749	−0.187520
$460$	3.95265	0.184293
$461$	−22.3204	−1.03956	−0.519781	−	0.854299i	$-0.673987\pi$
$461$	−22.3204	−1.03956	−0.519781	+	0.854299i	$0.673987\pi$
$462$	−13.2444	−0.616187
$463$	22.5091	1.04608	0.523042	−	0.852307i	$-0.324797\pi$
$463$	22.5091	1.04608	0.523042	+	0.852307i	$0.324797\pi$
$464$	5.23503	0.243030
$465$	1.06391	0.0493375
$466$	−20.8566	−0.966161
$467$	−25.7764	−1.19279	−0.596395	−	0.802691i	$-0.703401\pi$
$467$	−25.7764	−1.19279	−0.596395	+	0.802691i	$0.703401\pi$
$468$	15.5030	0.716628
$469$	−9.38191	−0.433216
$470$	3.88836	0.179357
$471$	−1.32098	−0.0608674
$472$	−11.9913	−0.551946
$473$	−47.2313	−2.17170
$474$	9.50861	0.436745
$475$	7.86216	0.360741
$476$	17.9813	0.824173
$477$	15.4239	0.706211
$478$	−26.8062	−1.22609
$479$	−13.0630	−0.596863	−0.298431	−	0.954431i	$-0.596463\pi$
$479$	−13.0630	−0.596863	−0.298431	+	0.954431i	$0.596463\pi$
$480$	−2.35158	−0.107334
$481$	−8.94589	−0.407898
$482$	−5.25086	−0.239170
$483$	1.50750	0.0685938
$484$	41.9583	1.90720
$485$	3.40123	0.154442
$486$	21.4298	0.972076
$487$	−39.6663	−1.79745	−0.898726	−	0.438511i	$-0.855506\pi$
$487$	−39.6663	−1.79745	−0.898726	+	0.438511i	$0.855506\pi$
$488$	−26.2263	−1.18721
$489$	4.89806	0.221498
$490$	−6.78432	−0.306484
$491$	13.4424	0.606648	0.303324	−	0.952887i	$-0.401904\pi$
$491$	13.4424	0.606648	0.303324	+	0.952887i	$0.401904\pi$
$492$	−0.347830	−0.0156814
$493$	16.7685	0.755213
$494$	31.0180	1.39557
$495$	−14.1602	−0.636455
$496$	1.62496	0.0729630
$497$	−12.2620	−0.550026
$498$	−4.65010	−0.208376
$499$	−11.9646	−0.535607	−0.267804	−	0.963474i	$-0.586298\pi$
$499$	−11.9646	−0.535607	−0.267804	+	0.963474i	$0.586298\pi$
$500$	3.10434	0.138830
$501$	6.41717	0.286698
$502$	−29.5951	−1.32090
$503$	−11.1401	−0.496714	−0.248357	−	0.968669i	$-0.579891\pi$
$503$	−11.1401	−0.496714	−0.248357	+	0.968669i	$0.579891\pi$
$504$	−22.5673	−1.00523
$505$	6.37894	0.283859
$506$	−14.2434	−0.633198
$507$	3.72502	0.165434
$508$	−29.7905	−1.32174
$509$	23.7608	1.05318	0.526590	−	0.850119i	$-0.323470\pi$
$509$	23.7608	1.05318	0.526590	+	0.850119i	$0.323470\pi$
$510$	−1.54895	−0.0685885
$511$	20.7662	0.918644
$512$	−6.44480	−0.284823
$513$	17.2467	0.761460
$514$	−23.2018	−1.02339
$515$	14.9437	0.658497
$516$	11.0854	0.488006
$517$	−8.52162	−0.374780
$518$	36.6061	1.60838
$519$	−3.14477	−0.138040
$520$	4.35686	0.191061
$521$	16.5956	0.727065	0.363532	−	0.931582i	$-0.381571\pi$
$521$	16.5956	0.727065	0.363532	+	0.931582i	$0.381571\pi$
$522$	−59.1586	−2.58930
$523$	−13.3440	−0.583492	−0.291746	−	0.956496i	$-0.594236\pi$
$523$	−13.3440	−0.583492	−0.291746	+	0.956496i	$0.594236\pi$
$524$	5.89387	0.257475
$525$	1.18396	0.0516724
$526$	−44.8734	−1.95657
$527$	5.20496	0.226732
$528$	1.05979	0.0461212
$529$	−21.3788	−0.929513
$530$	12.1848	0.529273
$531$	−13.7449	−0.596478
$532$	−77.1922	−3.34671
$533$	−0.522666	−0.0226392
$534$	−5.24422	−0.226940
$535$	4.02443	0.173991
$536$	−7.40117	−0.319682
$537$	1.26860	0.0547441
$538$	−22.9705	−0.990327
$539$	14.8683	0.640424
$540$	6.80977	0.293046
$541$	−0.278310	−0.0119655	−0.00598275	−	0.999982i	$-0.501904\pi$
$541$	−0.278310	−0.0119655	−0.00598275	+	0.999982i	$0.501904\pi$
$542$	52.4300	2.25206
$543$	4.77082	0.204736
$544$	−11.5047	−0.493258
$545$	−11.9384	−0.511383
$546$	4.67101	0.199901
$547$	7.22603	0.308963	0.154481	−	0.987996i	$-0.450629\pi$
$547$	7.22603	0.308963	0.154481	+	0.987996i	$0.450629\pi$
$548$	−16.3770	−0.699591
$549$	−30.0615	−1.28299
$550$	−11.1865	−0.476995
$551$	−71.9854	−3.06668
$552$	1.18923	0.0506172
$553$	−35.5577	−1.51207
$554$	57.8895	2.45949
$555$	−1.91777	−0.0814050
$556$	20.3315	0.862248
$557$	23.4311	0.992807	0.496403	−	0.868092i	$-0.334654\pi$
$557$	23.4311	0.992807	0.496403	+	0.868092i	$0.334654\pi$
$558$	−18.3629	−0.777365
$559$	16.6574	0.704532
$560$	1.80833	0.0764161
$561$	3.39463	0.143321
$562$	45.0832	1.90172
$563$	−23.5995	−0.994600	−0.497300	−	0.867579i	$-0.665675\pi$
$563$	−23.5995	−0.994600	−0.497300	+	0.867579i	$0.665675\pi$
$564$	2.00006	0.0842176
$565$	−17.9563	−0.755427
$566$	−36.2285	−1.52280
$567$	−24.5378	−1.03049
$568$	−9.67321	−0.405879
$569$	−40.5462	−1.69979	−0.849893	−	0.526956i	$-0.823333\pi$
$569$	−40.5462	−1.69979	−0.849893	+	0.526956i	$0.823333\pi$
$570$	6.64949	0.278516
$571$	−11.3160	−0.473560	−0.236780	−	0.971563i	$-0.576092\pi$
$571$	−11.3160	−0.473560	−0.236780	+	0.971563i	$0.576092\pi$
$572$	−26.8409	−1.12227
$573$	−7.60904	−0.317872
$574$	2.13872	0.0892685
$575$	1.27327	0.0530989
$576$	37.3177	1.55490
$577$	−34.6631	−1.44304	−0.721522	−	0.692392i	$-0.756557\pi$
$577$	−34.6631	−1.44304	−0.721522	+	0.692392i	$0.756557\pi$
$578$	30.8298	1.28235
$579$	−5.89716	−0.245078
$580$	−28.4231	−1.18021
$581$	17.3892	0.721424
$582$	2.87661	0.119240
$583$	−26.7038	−1.10596
$584$	16.3820	0.677892
$585$	4.99399	0.206476
$586$	−32.4040	−1.33860
$587$	17.6532	0.728625	0.364313	−	0.931277i	$-0.381304\pi$
$587$	17.6532	0.728625	0.364313	+	0.931277i	$0.381304\pi$
$588$	−3.48965	−0.143911
$589$	−22.3444	−0.920686
$590$	−10.8584	−0.447033
$591$	−3.17012	−0.130401
$592$	−2.92912	−0.120386
$593$	−11.4673	−0.470906	−0.235453	−	0.971886i	$-0.575657\pi$
$593$	−11.4673	−0.470906	−0.235453	+	0.971886i	$0.575657\pi$
$594$	−24.5391	−1.00685
$595$	5.79232	0.237462
$596$	−1.88421	−0.0771804
$597$	4.82275	0.197382
$598$	5.02333	0.205419
$599$	15.0404	0.614535	0.307268	−	0.951623i	$-0.400585\pi$
$599$	15.0404	0.614535	0.307268	+	0.951623i	$0.400585\pi$
$600$	0.934002	0.0381305
$601$	15.0230	0.612802	0.306401	−	0.951902i	$-0.400875\pi$
$601$	15.0230	0.612802	0.306401	+	0.951902i	$0.400875\pi$
$602$	−68.1611	−2.77804
$603$	−8.48348	−0.345474
$604$	76.1593	3.09888
$605$	13.5160	0.549505
$606$	5.39504	0.219158
$607$	−35.1728	−1.42762	−0.713809	−	0.700340i	$-0.753032\pi$
$607$	−35.1728	−1.42762	−0.713809	+	0.700340i	$0.753032\pi$
$608$	49.3884	2.00296
$609$	−10.8403	−0.439271
$610$	−23.7484	−0.961546
$611$	3.00538	0.121585
$612$	16.2594	0.657248
$613$	−24.9196	−1.00649	−0.503247	−	0.864143i	$-0.667861\pi$
$613$	−24.9196	−1.00649	−0.503247	+	0.864143i	$0.667861\pi$
$614$	32.6154	1.31625
$615$	−0.112047	−0.00451815
$616$	39.0714	1.57423
$617$	−48.7643	−1.96318	−0.981588	−	0.191011i	$-0.938823\pi$
$617$	−48.7643	−1.96318	−0.981588	+	0.191011i	$0.938823\pi$
$618$	12.6387	0.508404
$619$	−43.7305	−1.75768	−0.878838	−	0.477121i	$-0.841680\pi$
$619$	−43.7305	−1.75768	−0.878838	+	0.477121i	$0.841680\pi$
$620$	−8.82259	−0.354324
$621$	2.79308	0.112082
$622$	28.4034	1.13887
$623$	19.6109	0.785693
$624$	−0.373762	−0.0149625
$625$	1.00000	0.0400000
$626$	55.5826	2.22153
$627$	−14.5728	−0.581982
$628$	10.9544	0.437127
$629$	−9.38235	−0.374099
$630$	−20.4351	−0.814155
$631$	−44.4466	−1.76939	−0.884696	−	0.466169i	$-0.845634\pi$
$631$	−44.4466	−1.76939	−0.884696	+	0.466169i	$0.845634\pi$
$632$	−28.0506	−1.11579
$633$	8.91578	0.354370
$634$	10.4902	0.416617
$635$	−9.59640	−0.380822
$636$	6.26749	0.248522
$637$	−5.24372	−0.207764
$638$	102.423	4.05496
$639$	−11.0878	−0.438626
$640$	16.9172	0.668712
$641$	−19.3891	−0.765825	−0.382913	−	0.923785i	$-0.625079\pi$
$641$	−19.3891	−0.765825	−0.382913	+	0.923785i	$0.625079\pi$
$642$	3.40369	0.134333
$643$	−14.0619	−0.554545	−0.277273	−	0.960791i	$-0.589431\pi$
$643$	−14.0619	−0.554545	−0.277273	+	0.960791i	$0.589431\pi$
$644$	−12.5012	−0.492616
$645$	3.57092	0.140605
$646$	32.5314	1.27993
$647$	−36.7609	−1.44522	−0.722610	−	0.691255i	$-0.757058\pi$
$647$	−36.7609	−1.44522	−0.722610	+	0.691255i	$0.757058\pi$
$648$	−19.3573	−0.760425
$649$	23.7970	0.934112
$650$	3.94523	0.154745
$651$	−3.36485	−0.131879
$652$	−40.6178	−1.59072
$653$	−20.0312	−0.783880	−0.391940	−	0.919991i	$-0.628196\pi$
$653$	−20.0312	−0.783880	−0.391940	+	0.919991i	$0.628196\pi$
$654$	−10.0970	−0.394822
$655$	1.89859	0.0741841
$656$	−0.171135	−0.00668170
$657$	18.7776	0.732585
$658$	−12.2978	−0.479420
$659$	6.78215	0.264195	0.132098	−	0.991237i	$-0.457829\pi$
$659$	6.78215	0.264195	0.132098	+	0.991237i	$0.457829\pi$
$660$	−5.75401	−0.223974
$661$	5.90681	0.229748	0.114874	−	0.993380i	$-0.463354\pi$
$661$	5.90681	0.229748	0.114874	+	0.993380i	$0.463354\pi$
$662$	−53.3775	−2.07457
$663$	−1.19721	−0.0464957
$664$	13.7179	0.532358
$665$	−24.8659	−0.964259
$666$	33.1006	1.28262
$667$	−11.6580	−0.451398
$668$	−53.2152	−2.05896
$669$	8.53788	0.330093
$670$	−6.70191	−0.258917
$671$	52.0463	2.00923
$672$	7.43741	0.286904
$673$	−15.1161	−0.582682	−0.291341	−	0.956619i	$-0.594101\pi$
$673$	−15.1161	−0.582682	−0.291341	+	0.956619i	$0.594101\pi$
$674$	−23.1793	−0.892834
$675$	2.19363	0.0844329
$676$	−30.8902	−1.18809
$677$	−7.15669	−0.275054	−0.137527	−	0.990498i	$-0.543915\pi$
$677$	−7.15669	−0.275054	−0.137527	+	0.990498i	$0.543915\pi$
$678$	−15.1867	−0.583241
$679$	−10.7572	−0.412822
$680$	4.56943	0.175230
$681$	−5.52850	−0.211853
$682$	31.7923	1.21739
$683$	−3.10782	−0.118917	−0.0594587	−	0.998231i	$-0.518937\pi$
$683$	−3.10782	−0.118917	−0.0594587	+	0.998231i	$0.518937\pi$
$684$	−69.8001	−2.66887
$685$	−5.27552	−0.201567
$686$	−28.5614	−1.09048
$687$	9.71894	0.370801
$688$	5.45407	0.207934
$689$	9.41783	0.358791
$690$	1.07688	0.0409960
$691$	−43.0298	−1.63693	−0.818465	−	0.574557i	$-0.805174\pi$
$691$	−43.0298	−1.63693	−0.818465	+	0.574557i	$0.805174\pi$
$692$	26.0785	0.991354
$693$	44.7850	1.70124
$694$	−31.8896	−1.21051
$695$	6.54939	0.248432
$696$	−8.55166	−0.324150
$697$	−0.548167	−0.0207633
$698$	37.8774	1.43368
$699$	−3.45580	−0.130711
$700$	−9.81819	−0.371093
$701$	30.6158	1.15634	0.578171	−	0.815916i	$-0.303767\pi$
$701$	30.6158	1.15634	0.578171	+	0.815916i	$0.303767\pi$
$702$	8.65438	0.326639
$703$	40.2776	1.51910
$704$	−64.6093	−2.43505
$705$	0.644278	0.0242649
$706$	55.4163	2.08562
$707$	−20.1749	−0.758754
$708$	−5.58524	−0.209906
$709$	7.39104	0.277576	0.138788	−	0.990322i	$-0.455679\pi$
$709$	7.39104	0.277576	0.138788	+	0.990322i	$0.455679\pi$
$710$	−8.75929	−0.328730
$711$	−32.1526	−1.20582
$712$	15.4706	0.579784
$713$	−3.61865	−0.135520
$714$	4.89890	0.183337
$715$	−8.64625	−0.323351
$716$	−10.5200	−0.393152
$717$	−4.44162	−0.165875
$718$	2.30234	0.0859224
$719$	−10.8976	−0.406414	−0.203207	−	0.979136i	$-0.565136\pi$
$719$	−10.8976	−0.406414	−0.203207	+	0.979136i	$0.565136\pi$
$720$	1.63517	0.0609390
$721$	−47.2628	−1.76016
$722$	−96.7279	−3.59984
$723$	−0.870036	−0.0323570
$724$	−39.5627	−1.47034
$725$	−9.15593	−0.340043
$726$	11.4313	0.424255
$727$	20.6174	0.764655	0.382328	−	0.924027i	$-0.375123\pi$
$727$	20.6174	0.764655	0.382328	+	0.924027i	$0.375123\pi$
$728$	−13.7796	−0.510706
$729$	−19.7244	−0.730534
$730$	14.8342	0.549040
$731$	17.4701	0.646154
$732$	−12.2155	−0.451497
$733$	35.7931	1.32205	0.661024	−	0.750365i	$-0.270122\pi$
$733$	35.7931	1.32205	0.661024	+	0.750365i	$0.270122\pi$
$734$	−45.1280	−1.66570
$735$	−1.12412	−0.0414638
$736$	7.99839	0.294825
$737$	14.6877	0.541028
$738$	1.93391	0.0711883
$739$	−36.6491	−1.34816	−0.674080	−	0.738659i	$-0.735460\pi$
$739$	−36.6491	−1.34816	−0.674080	+	0.738659i	$0.735460\pi$
$740$	15.9034	0.584621
$741$	5.13950	0.188804
$742$	−38.5372	−1.41475
$743$	7.04682	0.258523	0.129261	−	0.991611i	$-0.458739\pi$
$743$	7.04682	0.258523	0.129261	+	0.991611i	$0.458739\pi$
$744$	−2.65445	−0.0973169
$745$	−0.606962	−0.0222374
$746$	52.6020	1.92589
$747$	15.7240	0.575309
$748$	−28.1504	−1.02928
$749$	−12.7282	−0.465078
$750$	0.845758	0.0308827
$751$	2.92078	0.106581	0.0532905	−	0.998579i	$-0.483029\pi$
$751$	2.92078	0.106581	0.0532905	+	0.998579i	$0.483029\pi$
$752$	0.984041	0.0358843
$753$	−4.90374	−0.178702
$754$	−36.1222	−1.31549
$755$	24.5332	0.892855
$756$	−21.5375	−0.783311
$757$	34.7591	1.26334	0.631671	−	0.775236i	$-0.282369\pi$
$757$	34.7591	1.26334	0.631671	+	0.775236i	$0.282369\pi$
$758$	−19.9697	−0.725332
$759$	−2.36005	−0.0856644
$760$	−19.6161	−0.711552
$761$	−26.4957	−0.960468	−0.480234	−	0.877140i	$-0.659448\pi$
$761$	−26.4957	−0.960468	−0.480234	+	0.877140i	$0.659448\pi$
$762$	−8.11623	−0.294020
$763$	37.7578	1.36692
$764$	63.0990	2.28284
$765$	5.23764	0.189367
$766$	27.9100	1.00843
$767$	−8.39264	−0.303041
$768$	4.53830	0.163762
$769$	−35.9547	−1.29656	−0.648281	−	0.761402i	$-0.724512\pi$
$769$	−35.9547	−1.29656	−0.648281	+	0.761402i	$0.724512\pi$
$770$	35.3799	1.27500
$771$	−3.84441	−0.138453
$772$	48.9030	1.76006
$773$	45.6465	1.64179	0.820895	−	0.571079i	$-0.193475\pi$
$773$	45.6465	1.64179	0.820895	+	0.571079i	$0.193475\pi$
$774$	−61.6338	−2.21538
$775$	−2.84202	−0.102088
$776$	−8.48608	−0.304633
$777$	6.06541	0.217595
$778$	0.349454	0.0125285
$779$	2.35323	0.0843132
$780$	2.02931	0.0726608
$781$	19.1966	0.686908
$782$	5.26842	0.188398
$783$	−20.0847	−0.717770
$784$	−1.71693	−0.0613190
$785$	3.52873	0.125946
$786$	1.60575	0.0572752
$787$	−39.4132	−1.40493	−0.702465	−	0.711718i	$-0.747917\pi$
$787$	−39.4132	−1.40493	−0.702465	+	0.711718i	$0.747917\pi$
$788$	26.2886	0.936494
$789$	−7.43524	−0.264702
$790$	−25.4004	−0.903706
$791$	56.7909	2.01925
$792$	35.3299	1.25539
$793$	−18.3556	−0.651825
$794$	−41.5270	−1.47374
$795$	2.01895	0.0716046
$796$	−39.9933	−1.41752
$797$	−26.1576	−0.926549	−0.463274	−	0.886215i	$-0.653326\pi$
$797$	−26.1576	−0.926549	−0.463274	+	0.886215i	$0.653326\pi$
$798$	−21.0305	−0.744473
$799$	3.15201	0.111510
$800$	6.28178	0.222095
$801$	17.7329	0.626562
$802$	35.2298	1.24401
$803$	−32.5103	−1.14726
$804$	−3.44726	−0.121575
$805$	−4.02700	−0.141933
$806$	−11.2124	−0.394941
$807$	−3.80607	−0.133980
$808$	−15.9155	−0.559905
$809$	9.65978	0.339620	0.169810	−	0.985477i	$-0.445685\pi$
$809$	9.65978	0.339620	0.169810	+	0.985477i	$0.445685\pi$
$810$	−17.5284	−0.615885
$811$	−33.8332	−1.18805	−0.594023	−	0.804448i	$-0.702461\pi$
$811$	−33.8332	−1.18805	−0.594023	+	0.804448i	$0.702461\pi$
$812$	89.8947	3.15468
$813$	8.68733	0.304678
$814$	−57.3081	−2.00865
$815$	−13.0842	−0.458320
$816$	−0.391997	−0.0137227
$817$	−74.9974	−2.62383
$818$	61.1748	2.13893
$819$	−15.7947	−0.551910
$820$	0.929161	0.0324477
$821$	11.8993	0.415287	0.207644	−	0.978205i	$-0.433421\pi$
$821$	11.8993	0.415287	0.207644	+	0.978205i	$0.433421\pi$
$822$	−4.46181	−0.155624
$823$	−24.7328	−0.862131	−0.431065	−	0.902321i	$-0.641862\pi$
$823$	−24.7328	−0.862131	−0.431065	+	0.902321i	$0.641862\pi$
$824$	−37.2846	−1.29887
$825$	−1.85354	−0.0645319
$826$	34.3422	1.19492
$827$	2.39264	0.0832003	0.0416002	−	0.999134i	$-0.486754\pi$
$827$	2.39264	0.0832003	0.0416002	+	0.999134i	$0.486754\pi$
$828$	−11.3040	−0.392843
$829$	11.0601	0.384132	0.192066	−	0.981382i	$-0.438481\pi$
$829$	11.0601	0.384132	0.192066	+	0.981382i	$0.438481\pi$
$830$	12.4218	0.431169
$831$	9.59193	0.332741
$832$	22.7862	0.789970
$833$	−5.49955	−0.190548
$834$	5.53920	0.191807
$835$	−17.1422	−0.593231
$836$	120.847	4.17958
$837$	−6.23435	−0.215490
$838$	10.0612	0.347557
$839$	−29.5707	−1.02089	−0.510447	−	0.859909i	$-0.670520\pi$
$839$	−29.5707	−1.02089	−0.510447	+	0.859909i	$0.670520\pi$
$840$	−2.95400	−0.101923
$841$	54.8311	1.89073
$842$	−64.9462	−2.23820
$843$	7.47001	0.257281
$844$	−73.9353	−2.54496
$845$	−9.95067	−0.342313
$846$	−11.1202	−0.382320
$847$	−42.7476	−1.46882
$848$	3.08365	0.105893
$849$	−6.00285	−0.206017
$850$	4.13771	0.141922
$851$	6.52290	0.223602
$852$	−4.50552	−0.154356
$853$	36.2096	1.23979	0.619897	−	0.784683i	$-0.287174\pi$
$853$	36.2096	1.23979	0.619897	+	0.784683i	$0.287174\pi$
$854$	75.1099	2.57021
$855$	−22.4847	−0.768961
$856$	−10.0410	−0.343193
$857$	−18.9613	−0.647704	−0.323852	−	0.946108i	$-0.604978\pi$
$857$	−18.9613	−0.647704	−0.323852	+	0.946108i	$0.604978\pi$
$858$	−7.31263	−0.249649
$859$	−30.4368	−1.03849	−0.519246	−	0.854625i	$-0.673787\pi$
$859$	−30.4368	−1.03849	−0.519246	+	0.854625i	$0.673787\pi$
$860$	−29.6124	−1.00977
$861$	0.354373	0.0120770
$862$	15.6420	0.532769
$863$	−43.7245	−1.48840	−0.744200	−	0.667957i	$-0.767169\pi$
$863$	−43.7245	−1.48840	−0.744200	+	0.667957i	$0.767169\pi$
$864$	13.7799	0.468803
$865$	8.40065	0.285631
$866$	64.7033	2.19871
$867$	5.10831	0.173487
$868$	27.9035	0.947106
$869$	55.6668	1.88837
$870$	−7.74370	−0.262536
$871$	−5.18002	−0.175518
$872$	29.7863	1.00869
$873$	−9.72704	−0.329211
$874$	−22.6168	−0.765025
$875$	−3.16273	−0.106920
$876$	7.63028	0.257803
$877$	−49.0482	−1.65624	−0.828120	−	0.560552i	$-0.810589\pi$
$877$	−49.0482	−1.65624	−0.828120	+	0.560552i	$0.810589\pi$
$878$	−41.2299	−1.39144
$879$	−5.36914	−0.181097
$880$	−2.83101	−0.0954334
$881$	−8.11090	−0.273263	−0.136632	−	0.990622i	$-0.543628\pi$
$881$	−8.11090	−0.273263	−0.136632	+	0.990622i	$0.543628\pi$
$882$	19.4022	0.653307
$883$	16.3936	0.551687	0.275843	−	0.961203i	$-0.411043\pi$
$883$	16.3936	0.551687	0.275843	+	0.961203i	$0.411043\pi$
$884$	9.92800	0.333915
$885$	−1.79917	−0.0604785
$886$	28.7280	0.965136
$887$	37.9683	1.27485	0.637425	−	0.770512i	$-0.279999\pi$
$887$	37.9683	1.27485	0.637425	+	0.770512i	$0.279999\pi$
$888$	4.78486	0.160569
$889$	30.3508	1.01793
$890$	14.0089	0.469580
$891$	38.4147	1.28694
$892$	−70.8015	−2.37061
$893$	−13.5313	−0.452807
$894$	−0.513343	−0.0171688
$895$	−3.38882	−0.113276
$896$	−53.5047	−1.78747
$897$	0.832336	0.0277909
$898$	21.5577	0.719389
$899$	26.0213	0.867860
$900$	−8.87798	−0.295933
$901$	9.87731	0.329061
$902$	−3.34824	−0.111484
$903$	−11.2939	−0.375837
$904$	44.8010	1.49006
$905$	−12.7443	−0.423636
$906$	20.7491	0.689344
$907$	−26.5945	−0.883055	−0.441528	−	0.897248i	$-0.645563\pi$
$907$	−26.5945	−0.883055	−0.441528	+	0.897248i	$0.645563\pi$
$908$	45.8459	1.52145
$909$	−18.2429	−0.605078
$910$	−12.4777	−0.413632
$911$	36.6552	1.21444	0.607221	−	0.794533i	$-0.292284\pi$
$911$	36.6552	1.21444	0.607221	+	0.794533i	$0.292284\pi$
$912$	1.68281	0.0557234
$913$	−27.2234	−0.900961
$914$	−29.3316	−0.970203
$915$	−3.93497	−0.130086
$916$	−80.5957	−2.66296
$917$	−6.00474	−0.198294
$918$	9.07662	0.299573
$919$	−28.0979	−0.926865	−0.463432	−	0.886132i	$-0.653382\pi$
$919$	−28.0979	−0.926865	−0.463432	+	0.886132i	$0.653382\pi$
$920$	−3.17681	−0.104736
$921$	5.40418	0.178074
$922$	50.4279	1.66075
$923$	−6.77020	−0.222844
$924$	18.1984	0.598683
$925$	5.12296	0.168442
$926$	−50.8542	−1.67117
$927$	−42.7369	−1.40366
$928$	−57.5156	−1.88804
$929$	59.0563	1.93757	0.968787	−	0.247895i	$-0.0797387\pi$
$929$	59.0563	1.93757	0.968787	+	0.247895i	$0.0797387\pi$
$930$	−2.40366	−0.0788191
$931$	23.6091	0.773756
$932$	28.6577	0.938715
$933$	4.70627	0.154076
$934$	58.2361	1.90554
$935$	−9.06809	−0.296558
$936$	−12.4600	−0.407269
$937$	42.3874	1.38474	0.692368	−	0.721544i	$-0.256567\pi$
$937$	42.3874	1.38474	0.692368	+	0.721544i	$0.256567\pi$
$938$	21.1963	0.692085
$939$	9.20970	0.300547
$940$	−5.34276	−0.174262
$941$	21.3095	0.694671	0.347335	−	0.937741i	$-0.387087\pi$
$941$	21.3095	0.694671	0.347335	+	0.937741i	$0.387087\pi$
$942$	2.98445	0.0972387
$943$	0.381103	0.0124104
$944$	−2.74797	−0.0894389
$945$	−6.93787	−0.225689
$946$	106.709	3.46939
$947$	4.01348	0.130421	0.0652103	−	0.997872i	$-0.479228\pi$
$947$	4.01348	0.130421	0.0652103	+	0.997872i	$0.479228\pi$
$948$	−13.0652	−0.424338
$949$	11.4656	0.372190
$950$	−17.7628	−0.576302
$951$	1.73816	0.0563636
$952$	−14.4519	−0.468388
$953$	−38.6113	−1.25074	−0.625371	−	0.780328i	$-0.715052\pi$
$953$	−38.6113	−1.25074	−0.625371	+	0.780328i	$0.715052\pi$
$954$	−34.8468	−1.12821
$955$	20.3261	0.657736
$956$	36.8327	1.19126
$957$	16.9709	0.548590
$958$	29.5129	0.953519
$959$	16.6851	0.538789
$960$	4.88479	0.157656
$961$	−22.9229	−0.739449
$962$	20.2113	0.651637
$963$	−11.5093	−0.370883
$964$	7.21489	0.232376
$965$	15.7531	0.507111
$966$	−3.40587	−0.109582
$967$	5.33035	0.171413	0.0857063	−	0.996320i	$-0.472685\pi$
$967$	5.33035	0.171413	0.0857063	+	0.996320i	$0.472685\pi$
$968$	−33.7226	−1.08389
$969$	5.39025	0.173160
$970$	−7.68432	−0.246729
$971$	−29.3694	−0.942508	−0.471254	−	0.881998i	$-0.656198\pi$
$971$	−29.3694	−0.942508	−0.471254	+	0.881998i	$0.656198\pi$
$972$	−29.4454	−0.944462
$973$	−20.7140	−0.664059
$974$	89.6172	2.87152
$975$	0.653700	0.0209352
$976$	−6.01010	−0.192379
$977$	−1.16130	−0.0371532	−0.0185766	−	0.999827i	$-0.505913\pi$
$977$	−1.16130	−0.0371532	−0.0185766	+	0.999827i	$0.505913\pi$
$978$	−11.0661	−0.353854
$979$	−30.7015	−0.981225
$980$	9.32193	0.297778
$981$	34.1421	1.09007
$982$	−30.3702	−0.969151
$983$	14.1772	0.452182	0.226091	−	0.974106i	$-0.427405\pi$
$983$	14.1772	0.452182	0.226091	+	0.974106i	$0.427405\pi$
$984$	0.279557	0.00891194
$985$	8.46836	0.269824
$986$	−37.8846	−1.20649
$987$	−2.03768	−0.0648600
$988$	−42.6200	−1.35592
$989$	−12.1457	−0.386212
$990$	31.9919	1.01677
$991$	−7.63678	−0.242590	−0.121295	−	0.992616i	$-0.538705\pi$
$991$	−7.63678	−0.242590	−0.121295	+	0.992616i	$0.538705\pi$
$992$	−17.8530	−0.566832
$993$	−8.84432	−0.280666
$994$	27.7033	0.878695
$995$	−12.8830	−0.408420
$996$	6.38942	0.202457
$997$	36.7273	1.16317	0.581583	−	0.813487i	$-0.302433\pi$
$997$	36.7273	1.16317	0.581583	+	0.813487i	$0.302433\pi$
$998$	27.0313	0.855660
$999$	11.2379	0.355551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.12	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.12	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25928 q^{2} -0.374349 q^{3} +3.10434 q^{4} +1.00000 q^{5} +0.845758 q^{6} -3.16273 q^{7} -2.49501 q^{8} -2.85986 q^{9} +O(q^{10})\)	\(q-2.25928 q^{2} -0.374349 q^{3} +3.10434 q^{4} +1.00000 q^{5} +0.845758 q^{6} -3.16273 q^{7} -2.49501 q^{8} -2.85986 q^{9} -2.25928 q^{10} +4.95137 q^{11} -1.16210 q^{12} -1.74623 q^{13} +7.14549 q^{14} -0.374349 q^{15} -0.571763 q^{16} -1.83143 q^{17} +6.46123 q^{18} +7.86216 q^{19} +3.10434 q^{20} +1.18396 q^{21} -11.1865 q^{22} +1.27327 q^{23} +0.934002 q^{24} +1.00000 q^{25} +3.94523 q^{26} +2.19363 q^{27} -9.81819 q^{28} -9.15593 q^{29} +0.845758 q^{30} -2.84202 q^{31} +6.28178 q^{32} -1.85354 q^{33} +4.13771 q^{34} -3.16273 q^{35} -8.87798 q^{36} +5.12296 q^{37} -17.7628 q^{38} +0.653700 q^{39} -2.49501 q^{40} +0.299311 q^{41} -2.67491 q^{42} -9.53903 q^{43} +15.3707 q^{44} -2.85986 q^{45} -2.87667 q^{46} -1.72106 q^{47} +0.214039 q^{48} +3.00287 q^{49} -2.25928 q^{50} +0.685594 q^{51} -5.42090 q^{52} -5.39322 q^{53} -4.95603 q^{54} +4.95137 q^{55} +7.89103 q^{56} -2.94319 q^{57} +20.6858 q^{58} +4.80614 q^{59} -1.16210 q^{60} +10.5115 q^{61} +6.42091 q^{62} +9.04498 q^{63} -13.0488 q^{64} -1.74623 q^{65} +4.18766 q^{66} +2.96639 q^{67} -5.68538 q^{68} -0.476646 q^{69} +7.14549 q^{70} +3.87703 q^{71} +7.13537 q^{72} -6.56592 q^{73} -11.5742 q^{74} -0.374349 q^{75} +24.4068 q^{76} -15.6598 q^{77} -1.47689 q^{78} +11.2427 q^{79} -0.571763 q^{80} +7.75841 q^{81} -0.676226 q^{82} -5.49815 q^{83} +3.67543 q^{84} -1.83143 q^{85} +21.5513 q^{86} +3.42751 q^{87} -12.3537 q^{88} -6.20061 q^{89} +6.46123 q^{90} +5.52287 q^{91} +3.95265 q^{92} +1.06391 q^{93} +3.88836 q^{94} +7.86216 q^{95} -2.35158 q^{96} +3.40123 q^{97} -6.78432 q^{98} -14.1602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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