LMFDB - Embedded newform 6034.2.a.o.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.655704 q^{3} +1.00000 q^{4} -2.51498 q^{5} +0.655704 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.57005 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.655704 q^{3} +1.00000 q^{4} -2.51498 q^{5} +0.655704 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.57005 q^{9} +2.51498 q^{10} +0.759055 q^{11} -0.655704 q^{12} -1.72048 q^{13} +1.00000 q^{14} +1.64909 q^{15} +1.00000 q^{16} -4.29161 q^{17} +2.57005 q^{18} -4.70144 q^{19} -2.51498 q^{20} +0.655704 q^{21} -0.759055 q^{22} +6.68093 q^{23} +0.655704 q^{24} +1.32515 q^{25} +1.72048 q^{26} +3.65231 q^{27} -1.00000 q^{28} +3.74766 q^{29} -1.64909 q^{30} +8.67327 q^{31} -1.00000 q^{32} -0.497716 q^{33} +4.29161 q^{34} +2.51498 q^{35} -2.57005 q^{36} +3.60257 q^{37} +4.70144 q^{38} +1.12813 q^{39} +2.51498 q^{40} +2.87528 q^{41} -0.655704 q^{42} +11.8519 q^{43} +0.759055 q^{44} +6.46364 q^{45} -6.68093 q^{46} -11.0367 q^{47} -0.655704 q^{48} +1.00000 q^{49} -1.32515 q^{50} +2.81402 q^{51} -1.72048 q^{52} +9.98268 q^{53} -3.65231 q^{54} -1.90901 q^{55} +1.00000 q^{56} +3.08275 q^{57} -3.74766 q^{58} -4.78535 q^{59} +1.64909 q^{60} -4.02184 q^{61} -8.67327 q^{62} +2.57005 q^{63} +1.00000 q^{64} +4.32698 q^{65} +0.497716 q^{66} -3.87525 q^{67} -4.29161 q^{68} -4.38071 q^{69} -2.51498 q^{70} +13.0874 q^{71} +2.57005 q^{72} -0.893285 q^{73} -3.60257 q^{74} -0.868903 q^{75} -4.70144 q^{76} -0.759055 q^{77} -1.12813 q^{78} +2.90350 q^{79} -2.51498 q^{80} +5.31532 q^{81} -2.87528 q^{82} -1.48801 q^{83} +0.655704 q^{84} +10.7933 q^{85} -11.8519 q^{86} -2.45735 q^{87} -0.759055 q^{88} -6.12726 q^{89} -6.46364 q^{90} +1.72048 q^{91} +6.68093 q^{92} -5.68710 q^{93} +11.0367 q^{94} +11.8240 q^{95} +0.655704 q^{96} +0.629236 q^{97} -1.00000 q^{98} -1.95081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.655704	−0.378571	−0.189285	−	0.981922i	$-0.560617\pi$
$3$	−0.655704	−0.378571	−0.189285	+	0.981922i	$0.560617\pi$
$4$	1.00000	0.500000
$5$	−2.51498	−1.12474	−0.562368	−	0.826887i	$-0.690109\pi$
$5$	−2.51498	−1.12474	−0.562368	+	0.826887i	$0.690109\pi$
$6$	0.655704	0.267690
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.57005	−0.856684
$10$	2.51498	0.795308
$11$	0.759055	0.228864	0.114432	−	0.993431i	$-0.463495\pi$
$11$	0.759055	0.228864	0.114432	+	0.993431i	$0.463495\pi$
$12$	−0.655704	−0.189285
$13$	−1.72048	−0.477176	−0.238588	−	0.971121i	$-0.576684\pi$
$13$	−1.72048	−0.477176	−0.238588	+	0.971121i	$0.576684\pi$
$14$	1.00000	0.267261
$15$	1.64909	0.425792
$16$	1.00000	0.250000
$17$	−4.29161	−1.04087	−0.520434	−	0.853902i	$-0.674230\pi$
$17$	−4.29161	−1.04087	−0.520434	+	0.853902i	$0.674230\pi$
$18$	2.57005	0.605767
$19$	−4.70144	−1.07858	−0.539292	−	0.842119i	$-0.681308\pi$
$19$	−4.70144	−1.07858	−0.539292	+	0.842119i	$0.681308\pi$
$20$	−2.51498	−0.562368
$21$	0.655704	0.143086
$22$	−0.759055	−0.161831
$23$	6.68093	1.39307	0.696535	−	0.717522i	$-0.254724\pi$
$23$	6.68093	1.39307	0.696535	+	0.717522i	$0.254724\pi$
$24$	0.655704	0.133845
$25$	1.32515	0.265029
$26$	1.72048	0.337414
$27$	3.65231	0.702887
$28$	−1.00000	−0.188982
$29$	3.74766	0.695922	0.347961	−	0.937509i	$-0.386874\pi$
$29$	3.74766	0.695922	0.347961	+	0.937509i	$0.386874\pi$
$30$	−1.64909	−0.301080
$31$	8.67327	1.55777	0.778883	−	0.627170i	$-0.215787\pi$
$31$	8.67327	1.55777	0.778883	+	0.627170i	$0.215787\pi$
$32$	−1.00000	−0.176777
$33$	−0.497716	−0.0866412
$34$	4.29161	0.736004
$35$	2.51498	0.425110
$36$	−2.57005	−0.428342
$37$	3.60257	0.592258	0.296129	−	0.955148i	$-0.404304\pi$
$37$	3.60257	0.592258	0.296129	+	0.955148i	$0.404304\pi$
$38$	4.70144	0.762674
$39$	1.12813	0.180645
$40$	2.51498	0.397654
$41$	2.87528	0.449044	0.224522	−	0.974469i	$-0.427918\pi$
$41$	2.87528	0.449044	0.224522	+	0.974469i	$0.427918\pi$
$42$	−0.655704	−0.101177
$43$	11.8519	1.80740	0.903701	−	0.428165i	$-0.140840\pi$
$43$	11.8519	1.80740	0.903701	+	0.428165i	$0.140840\pi$
$44$	0.759055	0.114432
$45$	6.46364	0.963543
$46$	−6.68093	−0.985050
$47$	−11.0367	−1.60987	−0.804936	−	0.593362i	$-0.797800\pi$
$47$	−11.0367	−1.60987	−0.804936	+	0.593362i	$0.797800\pi$
$48$	−0.655704	−0.0946427
$49$	1.00000	0.142857
$50$	−1.32515	−0.187404
$51$	2.81402	0.394042
$52$	−1.72048	−0.238588
$53$	9.98268	1.37123	0.685613	−	0.727966i	$-0.259534\pi$
$53$	9.98268	1.37123	0.685613	+	0.727966i	$0.259534\pi$
$54$	−3.65231	−0.497016
$55$	−1.90901	−0.257411
$56$	1.00000	0.133631
$57$	3.08275	0.408320
$58$	−3.74766	−0.492091
$59$	−4.78535	−0.622999	−0.311500	−	0.950246i	$-0.600831\pi$
$59$	−4.78535	−0.622999	−0.311500	+	0.950246i	$0.600831\pi$
$60$	1.64909	0.212896
$61$	−4.02184	−0.514944	−0.257472	−	0.966286i	$-0.582889\pi$
$61$	−4.02184	−0.514944	−0.257472	+	0.966286i	$0.582889\pi$
$62$	−8.67327	−1.10151
$63$	2.57005	0.323796
$64$	1.00000	0.125000
$65$	4.32698	0.536696
$66$	0.497716	0.0612646
$67$	−3.87525	−0.473438	−0.236719	−	0.971578i	$-0.576072\pi$
$67$	−3.87525	−0.473438	−0.236719	+	0.971578i	$0.576072\pi$
$68$	−4.29161	−0.520434
$69$	−4.38071	−0.527376
$70$	−2.51498	−0.300598
$71$	13.0874	1.55319	0.776594	−	0.630001i	$-0.216946\pi$
$71$	13.0874	1.55319	0.776594	+	0.630001i	$0.216946\pi$
$72$	2.57005	0.302884
$73$	−0.893285	−0.104551	−0.0522756	−	0.998633i	$-0.516647\pi$
$73$	−0.893285	−0.104551	−0.0522756	+	0.998633i	$0.516647\pi$
$74$	−3.60257	−0.418790
$75$	−0.868903	−0.100332
$76$	−4.70144	−0.539292
$77$	−0.759055	−0.0865024
$78$	−1.12813	−0.127735
$79$	2.90350	0.326669	0.163334	−	0.986571i	$-0.447775\pi$
$79$	2.90350	0.326669	0.163334	+	0.986571i	$0.447775\pi$
$80$	−2.51498	−0.281184
$81$	5.31532	0.590592
$82$	−2.87528	−0.317522
$83$	−1.48801	−0.163330	−0.0816652	−	0.996660i	$-0.526024\pi$
$83$	−1.48801	−0.163330	−0.0816652	+	0.996660i	$0.526024\pi$
$84$	0.655704	0.0715432
$85$	10.7933	1.17070
$86$	−11.8519	−1.27803
$87$	−2.45735	−0.263456
$88$	−0.759055	−0.0809156
$89$	−6.12726	−0.649489	−0.324744	−	0.945802i	$-0.605278\pi$
$89$	−6.12726	−0.649489	−0.324744	+	0.945802i	$0.605278\pi$
$90$	−6.46364	−0.681328
$91$	1.72048	0.180355
$92$	6.68093	0.696535
$93$	−5.68710	−0.589725
$94$	11.0367	1.13835
$95$	11.8240	1.21312
$96$	0.655704	0.0669225
$97$	0.629236	0.0638892	0.0319446	−	0.999490i	$-0.489830\pi$
$97$	0.629236	0.0638892	0.0319446	+	0.999490i	$0.489830\pi$
$98$	−1.00000	−0.101015
$99$	−1.95081	−0.196064
$100$	1.32515	0.132515
$101$	−16.2289	−1.61484	−0.807418	−	0.589979i	$-0.799136\pi$
$101$	−16.2289	−1.61484	−0.807418	+	0.589979i	$0.799136\pi$
$102$	−2.81402	−0.278630
$103$	0.0339062	0.00334087	0.00167044	−	0.999999i	$-0.499468\pi$
$103$	0.0339062	0.00334087	0.00167044	+	0.999999i	$0.499468\pi$
$104$	1.72048	0.168707
$105$	−1.64909	−0.160934
$106$	−9.98268	−0.969603
$107$	−10.6108	−1.02579	−0.512893	−	0.858453i	$-0.671426\pi$
$107$	−10.6108	−1.02579	−0.512893	+	0.858453i	$0.671426\pi$
$108$	3.65231	0.351443
$109$	−15.5115	−1.48574	−0.742868	−	0.669438i	$-0.766535\pi$
$109$	−15.5115	−1.48574	−0.742868	+	0.669438i	$0.766535\pi$
$110$	1.90901	0.182017
$111$	−2.36222	−0.224212
$112$	−1.00000	−0.0944911
$113$	−10.0968	−0.949830	−0.474915	−	0.880032i	$-0.657521\pi$
$113$	−10.0968	−0.949830	−0.474915	+	0.880032i	$0.657521\pi$
$114$	−3.08275	−0.288726
$115$	−16.8024	−1.56684
$116$	3.74766	0.347961
$117$	4.42173	0.408789
$118$	4.78535	0.440527
$119$	4.29161	0.393411
$120$	−1.64909	−0.150540
$121$	−10.4238	−0.947621
$122$	4.02184	0.364120
$123$	−1.88533	−0.169995
$124$	8.67327	0.778883
$125$	9.24220	0.826648
$126$	−2.57005	−0.228958
$127$	15.4038	1.36686	0.683432	−	0.730014i	$-0.260486\pi$
$127$	15.4038	1.36686	0.683432	+	0.730014i	$0.260486\pi$
$128$	−1.00000	−0.0883883
$129$	−7.77135	−0.684229
$130$	−4.32698	−0.379502
$131$	19.7518	1.72572	0.862862	−	0.505439i	$-0.168669\pi$
$131$	19.7518	1.72572	0.862862	+	0.505439i	$0.168669\pi$
$132$	−0.497716	−0.0433206
$133$	4.70144	0.407666
$134$	3.87525	0.334771
$135$	−9.18549	−0.790561
$136$	4.29161	0.368002
$137$	−16.0199	−1.36867	−0.684337	−	0.729166i	$-0.739908\pi$
$137$	−16.0199	−1.36867	−0.684337	+	0.729166i	$0.739908\pi$
$138$	4.38071	0.372911
$139$	−3.68155	−0.312265	−0.156133	−	0.987736i	$-0.549903\pi$
$139$	−3.68155	−0.312265	−0.156133	+	0.987736i	$0.549903\pi$
$140$	2.51498	0.212555
$141$	7.23682	0.609451
$142$	−13.0874	−1.09827
$143$	−1.30594	−0.109208
$144$	−2.57005	−0.214171
$145$	−9.42529	−0.782728
$146$	0.893285	0.0739288
$147$	−0.655704	−0.0540816
$148$	3.60257	0.296129
$149$	−0.539748	−0.0442179	−0.0221089	−	0.999756i	$-0.507038\pi$
$149$	−0.539748	−0.0442179	−0.0221089	+	0.999756i	$0.507038\pi$
$150$	0.868903	0.0709456
$151$	20.7956	1.69232	0.846160	−	0.532929i	$-0.178909\pi$
$151$	20.7956	1.69232	0.846160	+	0.532929i	$0.178909\pi$
$152$	4.70144	0.381337
$153$	11.0297	0.891695
$154$	0.759055	0.0611664
$155$	−21.8131	−1.75207
$156$	1.12813	0.0903224
$157$	23.6466	1.88720	0.943601	−	0.331085i	$-0.107415\pi$
$157$	23.6466	1.88720	0.943601	+	0.331085i	$0.107415\pi$
$158$	−2.90350	−0.230990
$159$	−6.54568	−0.519106
$160$	2.51498	0.198827
$161$	−6.68093	−0.526531
$162$	−5.31532	−0.417611
$163$	22.1317	1.73349	0.866745	−	0.498752i	$-0.166208\pi$
$163$	22.1317	1.73349	0.866745	+	0.498752i	$0.166208\pi$
$164$	2.87528	0.224522
$165$	1.25175	0.0974484
$166$	1.48801	0.115492
$167$	13.9098	1.07637	0.538184	−	0.842827i	$-0.319110\pi$
$167$	13.9098	1.07637	0.538184	+	0.842827i	$0.319110\pi$
$168$	−0.655704	−0.0505887
$169$	−10.0399	−0.772303
$170$	−10.7933	−0.827810
$171$	12.0829	0.924005
$172$	11.8519	0.903701
$173$	−4.09590	−0.311405	−0.155703	−	0.987804i	$-0.549764\pi$
$173$	−4.09590	−0.311405	−0.155703	+	0.987804i	$0.549764\pi$
$174$	2.45735	0.186291
$175$	−1.32515	−0.100172
$176$	0.759055	0.0572159
$177$	3.13777	0.235849
$178$	6.12726	0.459258
$179$	−13.6351	−1.01914	−0.509568	−	0.860430i	$-0.670195\pi$
$179$	−13.6351	−1.01914	−0.509568	+	0.860430i	$0.670195\pi$
$180$	6.46364	0.481771
$181$	2.29580	0.170646	0.0853229	−	0.996353i	$-0.472808\pi$
$181$	2.29580	0.170646	0.0853229	+	0.996353i	$0.472808\pi$
$182$	−1.72048	−0.127531
$183$	2.63714	0.194943
$184$	−6.68093	−0.492525
$185$	−9.06040	−0.666134
$186$	5.68710	0.416998
$187$	−3.25757	−0.238217
$188$	−11.0367	−0.804936
$189$	−3.65231	−0.265666
$190$	−11.8240	−0.857806
$191$	4.04753	0.292869	0.146434	−	0.989220i	$-0.453220\pi$
$191$	4.04753	0.292869	0.146434	+	0.989220i	$0.453220\pi$
$192$	−0.655704	−0.0473214
$193$	16.8130	1.21023	0.605113	−	0.796140i	$-0.293128\pi$
$193$	16.8130	1.21023	0.605113	+	0.796140i	$0.293128\pi$
$194$	−0.629236	−0.0451765
$195$	−2.83722	−0.203178
$196$	1.00000	0.0714286
$197$	−25.7491	−1.83454	−0.917272	−	0.398261i	$-0.869614\pi$
$197$	−25.7491	−1.83454	−0.917272	+	0.398261i	$0.869614\pi$
$198$	1.95081	0.138638
$199$	−16.2556	−1.15233	−0.576163	−	0.817335i	$-0.695451\pi$
$199$	−16.2556	−1.15233	−0.576163	+	0.817335i	$0.695451\pi$
$200$	−1.32515	−0.0937019
$201$	2.54102	0.179230
$202$	16.2289	1.14186
$203$	−3.74766	−0.263034
$204$	2.81402	0.197021
$205$	−7.23129	−0.505055
$206$	−0.0339062	−0.00236235
$207$	−17.1703	−1.19342
$208$	−1.72048	−0.119294
$209$	−3.56865	−0.246849
$210$	1.64909	0.113798
$211$	4.81076	0.331186	0.165593	−	0.986194i	$-0.447046\pi$
$211$	4.81076	0.331186	0.165593	+	0.986194i	$0.447046\pi$
$212$	9.98268	0.685613
$213$	−8.58146	−0.587992
$214$	10.6108	0.725340
$215$	−29.8074	−2.03285
$216$	−3.65231	−0.248508
$217$	−8.67327	−0.588780
$218$	15.5115	1.05057
$219$	0.585731	0.0395800
$220$	−1.90901	−0.128706
$221$	7.38363	0.496677
$222$	2.36222	0.158542
$223$	−18.0990	−1.21200	−0.605999	−	0.795465i	$-0.707227\pi$
$223$	−18.0990	−1.21200	−0.605999	+	0.795465i	$0.707227\pi$
$224$	1.00000	0.0668153
$225$	−3.40569	−0.227046
$226$	10.0968	0.671631
$227$	9.16802	0.608503	0.304251	−	0.952592i	$-0.401594\pi$
$227$	9.16802	0.608503	0.304251	+	0.952592i	$0.401594\pi$
$228$	3.08275	0.204160
$229$	−3.16196	−0.208948	−0.104474	−	0.994528i	$-0.533316\pi$
$229$	−3.16196	−0.208948	−0.104474	+	0.994528i	$0.533316\pi$
$230$	16.8024	1.10792
$231$	0.497716	0.0327473
$232$	−3.74766	−0.246046
$233$	−14.6050	−0.956803	−0.478402	−	0.878141i	$-0.658784\pi$
$233$	−14.6050	−0.956803	−0.478402	+	0.878141i	$0.658784\pi$
$234$	−4.42173	−0.289057
$235$	27.7572	1.81068
$236$	−4.78535	−0.311500
$237$	−1.90383	−0.123667
$238$	−4.29161	−0.278184
$239$	−23.1227	−1.49569	−0.747843	−	0.663876i	$-0.768910\pi$
$239$	−23.1227	−1.49569	−0.747843	+	0.663876i	$0.768910\pi$
$240$	1.64909	0.106448
$241$	−31.0035	−1.99711	−0.998554	−	0.0537557i	$-0.982881\pi$
$241$	−31.0035	−1.99711	−0.998554	+	0.0537557i	$0.982881\pi$
$242$	10.4238	0.670070
$243$	−14.4422	−0.926467
$244$	−4.02184	−0.257472
$245$	−2.51498	−0.160676
$246$	1.88533	0.120205
$247$	8.08873	0.514674
$248$	−8.67327	−0.550753
$249$	0.975695	0.0618321
$250$	−9.24220	−0.584528
$251$	28.6378	1.80760	0.903800	−	0.427955i	$-0.140766\pi$
$251$	28.6378	1.80760	0.903800	+	0.427955i	$0.140766\pi$
$252$	2.57005	0.161898
$253$	5.07120	0.318823
$254$	−15.4038	−0.966519
$255$	−7.07722	−0.443193
$256$	1.00000	0.0625000
$257$	−9.80758	−0.611780	−0.305890	−	0.952067i	$-0.598954\pi$
$257$	−9.80758	−0.611780	−0.305890	+	0.952067i	$0.598954\pi$
$258$	7.77135	0.483823
$259$	−3.60257	−0.223853
$260$	4.32698	0.268348
$261$	−9.63167	−0.596185
$262$	−19.7518	−1.22027
$263$	21.0246	1.29643	0.648217	−	0.761455i	$-0.275515\pi$
$263$	21.0246	1.29643	0.648217	+	0.761455i	$0.275515\pi$
$264$	0.497716	0.0306323
$265$	−25.1063	−1.54227
$266$	−4.70144	−0.288264
$267$	4.01767	0.245878
$268$	−3.87525	−0.236719
$269$	0.0870859	0.00530972	0.00265486	−	0.999996i	$-0.499155\pi$
$269$	0.0870859	0.00530972	0.00265486	+	0.999996i	$0.499155\pi$
$270$	9.18549	0.559011
$271$	4.00587	0.243339	0.121670	−	0.992571i	$-0.461175\pi$
$271$	4.00587	0.243339	0.121670	+	0.992571i	$0.461175\pi$
$272$	−4.29161	−0.260217
$273$	−1.12813	−0.0682773
$274$	16.0199	0.967799
$275$	1.00586	0.0606555
$276$	−4.38071	−0.263688
$277$	−13.0530	−0.784277	−0.392139	−	0.919906i	$-0.628265\pi$
$277$	−13.0530	−0.784277	−0.392139	+	0.919906i	$0.628265\pi$
$278$	3.68155	0.220805
$279$	−22.2908	−1.33451
$280$	−2.51498	−0.150299
$281$	8.86885	0.529071	0.264535	−	0.964376i	$-0.414781\pi$
$281$	8.86885	0.529071	0.264535	+	0.964376i	$0.414781\pi$
$282$	−7.23682	−0.430947
$283$	8.78185	0.522027	0.261013	−	0.965335i	$-0.415943\pi$
$283$	8.78185	0.522027	0.261013	+	0.965335i	$0.415943\pi$
$284$	13.0874	0.776594
$285$	−7.75307	−0.459252
$286$	1.30594	0.0772219
$287$	−2.87528	−0.169723
$288$	2.57005	0.151442
$289$	1.41788	0.0834049
$290$	9.42529	0.553472
$291$	−0.412592	−0.0241866
$292$	−0.893285	−0.0522756
$293$	8.58340	0.501448	0.250724	−	0.968059i	$-0.419331\pi$
$293$	8.58340	0.501448	0.250724	+	0.968059i	$0.419331\pi$
$294$	0.655704	0.0382414
$295$	12.0351	0.700709
$296$	−3.60257	−0.209395
$297$	2.77230	0.160865
$298$	0.539748	0.0312668
$299$	−11.4944	−0.664739
$300$	−0.868903	−0.0501661
$301$	−11.8519	−0.683133
$302$	−20.7956	−1.19665
$303$	10.6414	0.611330
$304$	−4.70144	−0.269646
$305$	10.1149	0.579175
$306$	−11.0297	−0.630523
$307$	−3.67327	−0.209645	−0.104822	−	0.994491i	$-0.533427\pi$
$307$	−3.67327	−0.209645	−0.104822	+	0.994491i	$0.533427\pi$
$308$	−0.759055	−0.0432512
$309$	−0.0222324	−0.00126476
$310$	21.8131	1.23890
$311$	−12.0271	−0.681993	−0.340997	−	0.940065i	$-0.610764\pi$
$311$	−12.0271	−0.681993	−0.340997	+	0.940065i	$0.610764\pi$
$312$	−1.12813	−0.0638676
$313$	−12.2290	−0.691226	−0.345613	−	0.938377i	$-0.612329\pi$
$313$	−12.2290	−0.691226	−0.345613	+	0.938377i	$0.612329\pi$
$314$	−23.6466	−1.33445
$315$	−6.46364	−0.364185
$316$	2.90350	0.163334
$317$	−14.5871	−0.819292	−0.409646	−	0.912245i	$-0.634348\pi$
$317$	−14.5871	−0.819292	−0.409646	+	0.912245i	$0.634348\pi$
$318$	6.54568	0.367064
$319$	2.84468	0.159271
$320$	−2.51498	−0.140592
$321$	6.95755	0.388332
$322$	6.68093	0.372314
$323$	20.1767	1.12266
$324$	5.31532	0.295296
$325$	−2.27989	−0.126465
$326$	−22.1317	−1.22576
$327$	10.1710	0.562456
$328$	−2.87528	−0.158761
$329$	11.0367	0.608474
$330$	−1.25175	−0.0689064
$331$	−29.8850	−1.64263	−0.821313	−	0.570478i	$-0.806758\pi$
$331$	−29.8850	−1.64263	−0.821313	+	0.570478i	$0.806758\pi$
$332$	−1.48801	−0.0816652
$333$	−9.25878	−0.507378
$334$	−13.9098	−0.761108
$335$	9.74620	0.532492
$336$	0.655704	0.0357716
$337$	20.8076	1.13346	0.566731	−	0.823903i	$-0.308208\pi$
$337$	20.8076	1.13346	0.566731	+	0.823903i	$0.308208\pi$
$338$	10.0399	0.546101
$339$	6.62053	0.359578
$340$	10.7933	0.585350
$341$	6.58349	0.356516
$342$	−12.0829	−0.653370
$343$	−1.00000	−0.0539949
$344$	−11.8519	−0.639013
$345$	11.0174	0.593158
$346$	4.09590	0.220197
$347$	−35.4782	−1.90457	−0.952286	−	0.305208i	$-0.901274\pi$
$347$	−35.4782	−1.90457	−0.952286	+	0.305208i	$0.901274\pi$
$348$	−2.45735	−0.131728
$349$	21.3832	1.14461	0.572307	−	0.820039i	$-0.306048\pi$
$349$	21.3832	1.14461	0.572307	+	0.820039i	$0.306048\pi$
$350$	1.32515	0.0708320
$351$	−6.28372	−0.335400
$352$	−0.759055	−0.0404578
$353$	5.06719	0.269699	0.134850	−	0.990866i	$-0.456945\pi$
$353$	5.06719	0.269699	0.134850	+	0.990866i	$0.456945\pi$
$354$	−3.13777	−0.166771
$355$	−32.9146	−1.74693
$356$	−6.12726	−0.324744
$357$	−2.81402	−0.148934
$358$	13.6351	0.720638
$359$	−12.9118	−0.681460	−0.340730	−	0.940161i	$-0.610674\pi$
$359$	−12.9118	−0.681460	−0.340730	+	0.940161i	$0.610674\pi$
$360$	−6.46364	−0.340664
$361$	3.10350	0.163342
$362$	−2.29580	−0.120665
$363$	6.83495	0.358742
$364$	1.72048	0.0901777
$365$	2.24660	0.117592
$366$	−2.63714	−0.137845
$367$	13.5713	0.708418	0.354209	−	0.935166i	$-0.384750\pi$
$367$	13.5713	0.708418	0.354209	+	0.935166i	$0.384750\pi$
$368$	6.68093	0.348268
$369$	−7.38962	−0.384688
$370$	9.06040	0.471028
$371$	−9.98268	−0.518275
$372$	−5.68710	−0.294862
$373$	−7.66902	−0.397087	−0.198544	−	0.980092i	$-0.563621\pi$
$373$	−7.66902	−0.397087	−0.198544	+	0.980092i	$0.563621\pi$
$374$	3.25757	0.168445
$375$	−6.06015	−0.312945
$376$	11.0367	0.569176
$377$	−6.44777	−0.332077
$378$	3.65231	0.187854
$379$	−9.09079	−0.466963	−0.233481	−	0.972361i	$-0.575012\pi$
$379$	−9.09079	−0.466963	−0.233481	+	0.972361i	$0.575012\pi$
$380$	11.8240	0.606560
$381$	−10.1003	−0.517455
$382$	−4.04753	−0.207090
$383$	−15.3153	−0.782577	−0.391288	−	0.920268i	$-0.627971\pi$
$383$	−15.3153	−0.782577	−0.391288	+	0.920268i	$0.627971\pi$
$384$	0.655704	0.0334613
$385$	1.90901	0.0972922
$386$	−16.8130	−0.855759
$387$	−30.4601	−1.54837
$388$	0.629236	0.0319446
$389$	33.5633	1.70173	0.850863	−	0.525387i	$-0.176080\pi$
$389$	33.5633	1.70173	0.850863	+	0.525387i	$0.176080\pi$
$390$	2.83722	0.143668
$391$	−28.6719	−1.45000
$392$	−1.00000	−0.0505076
$393$	−12.9513	−0.653309
$394$	25.7491	1.29722
$395$	−7.30225	−0.367416
$396$	−1.95081	−0.0980320
$397$	4.51987	0.226846	0.113423	−	0.993547i	$-0.463819\pi$
$397$	4.51987	0.226846	0.113423	+	0.993547i	$0.463819\pi$
$398$	16.2556	0.814818
$399$	−3.08275	−0.154331
$400$	1.32515	0.0662573
$401$	−5.55581	−0.277444	−0.138722	−	0.990331i	$-0.544299\pi$
$401$	−5.55581	−0.277444	−0.138722	+	0.990331i	$0.544299\pi$
$402$	−2.54102	−0.126735
$403$	−14.9222	−0.743328
$404$	−16.2289	−0.807418
$405$	−13.3680	−0.664259
$406$	3.74766	0.185993
$407$	2.73455	0.135546
$408$	−2.81402	−0.139315
$409$	29.6823	1.46769	0.733847	−	0.679315i	$-0.237723\pi$
$409$	29.6823	1.46769	0.733847	+	0.679315i	$0.237723\pi$
$410$	7.23129	0.357128
$411$	10.5043	0.518140
$412$	0.0339062	0.00167044
$413$	4.78535	0.235472
$414$	17.1703	0.843876
$415$	3.74232	0.183703
$416$	1.72048	0.0843535
$417$	2.41401	0.118215
$418$	3.56865	0.174548
$419$	15.7972	0.771744	0.385872	−	0.922552i	$-0.373901\pi$
$419$	15.7972	0.771744	0.385872	+	0.922552i	$0.373901\pi$
$420$	−1.64909	−0.0804671
$421$	34.1017	1.66202	0.831009	−	0.556259i	$-0.187764\pi$
$421$	34.1017	1.66202	0.831009	+	0.556259i	$0.187764\pi$
$422$	−4.81076	−0.234184
$423$	28.3650	1.37915
$424$	−9.98268	−0.484802
$425$	−5.68700	−0.275860
$426$	8.58146	0.415773
$427$	4.02184	0.194630
$428$	−10.6108	−0.512893
$429$	0.856310	0.0413431
$430$	29.8074	1.43744
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	3.65231	0.175722
$433$	35.6836	1.71484	0.857422	−	0.514614i	$-0.172065\pi$
$433$	35.6836	1.71484	0.857422	+	0.514614i	$0.172065\pi$
$434$	8.67327	0.416330
$435$	6.18020	0.296318
$436$	−15.5115	−0.742868
$437$	−31.4100	−1.50254
$438$	−0.585731	−0.0279873
$439$	−13.5828	−0.648271	−0.324135	−	0.946011i	$-0.605073\pi$
$439$	−13.5828	−0.648271	−0.324135	+	0.946011i	$0.605073\pi$
$440$	1.90901	0.0910086
$441$	−2.57005	−0.122383
$442$	−7.38363	−0.351203
$443$	−16.6069	−0.789017	−0.394508	−	0.918892i	$-0.629085\pi$
$443$	−16.6069	−0.789017	−0.394508	+	0.918892i	$0.629085\pi$
$444$	−2.36222	−0.112106
$445$	15.4100	0.730503
$446$	18.0990	0.857012
$447$	0.353915	0.0167396
$448$	−1.00000	−0.0472456
$449$	−3.85810	−0.182075	−0.0910375	−	0.995847i	$-0.529018\pi$
$449$	−3.85810	−0.182075	−0.0910375	+	0.995847i	$0.529018\pi$
$450$	3.40569	0.160546
$451$	2.18250	0.102770
$452$	−10.0968	−0.474915
$453$	−13.6357	−0.640663
$454$	−9.16802	−0.430277
$455$	−4.32698	−0.202852
$456$	−3.08275	−0.144363
$457$	24.0805	1.12644	0.563219	−	0.826308i	$-0.309563\pi$
$457$	24.0805	1.12644	0.563219	+	0.826308i	$0.309563\pi$
$458$	3.16196	0.147748
$459$	−15.6743	−0.731612
$460$	−16.8024	−0.783418
$461$	−32.0748	−1.49387	−0.746935	−	0.664897i	$-0.768476\pi$
$461$	−32.0748	−1.49387	−0.746935	+	0.664897i	$0.768476\pi$
$462$	−0.497716	−0.0231558
$463$	−10.4014	−0.483395	−0.241698	−	0.970352i	$-0.577704\pi$
$463$	−10.4014	−0.483395	−0.241698	+	0.970352i	$0.577704\pi$
$464$	3.74766	0.173981
$465$	14.3030	0.663284
$466$	14.6050	0.676562
$467$	7.71150	0.356846	0.178423	−	0.983954i	$-0.442901\pi$
$467$	7.71150	0.356846	0.178423	+	0.983954i	$0.442901\pi$
$468$	4.42173	0.204394
$469$	3.87525	0.178943
$470$	−27.7572	−1.28034
$471$	−15.5052	−0.714440
$472$	4.78535	0.220264
$473$	8.99626	0.413649
$474$	1.90383	0.0874460
$475$	−6.23008	−0.285856
$476$	4.29161	0.196705
$477$	−25.6560	−1.17471
$478$	23.1227	1.05761
$479$	−9.56556	−0.437062	−0.218531	−	0.975830i	$-0.570126\pi$
$479$	−9.56556	−0.437062	−0.218531	+	0.975830i	$0.570126\pi$
$480$	−1.64909	−0.0752701
$481$	−6.19815	−0.282611
$482$	31.0035	1.41217
$483$	4.38071	0.199329
$484$	−10.4238	−0.473811
$485$	−1.58252	−0.0718584
$486$	14.4422	0.655111
$487$	32.0631	1.45292	0.726460	−	0.687209i	$-0.241164\pi$
$487$	32.0631	1.45292	0.726460	+	0.687209i	$0.241164\pi$
$488$	4.02184	0.182060
$489$	−14.5119	−0.656249
$490$	2.51498	0.113615
$491$	−37.8419	−1.70778	−0.853892	−	0.520451i	$-0.825764\pi$
$491$	−37.8419	−1.70778	−0.853892	+	0.520451i	$0.825764\pi$
$492$	−1.88533	−0.0849974
$493$	−16.0835	−0.724363
$494$	−8.08873	−0.363929
$495$	4.90626	0.220520
$496$	8.67327	0.389441
$497$	−13.0874	−0.587050
$498$	−0.975695	−0.0437219
$499$	−31.0246	−1.38885	−0.694427	−	0.719564i	$-0.744342\pi$
$499$	−31.0246	−1.38885	−0.694427	+	0.719564i	$0.744342\pi$
$500$	9.24220	0.413324
$501$	−9.12068	−0.407482
$502$	−28.6378	−1.27817
$503$	−14.4330	−0.643538	−0.321769	−	0.946818i	$-0.604277\pi$
$503$	−14.4330	−0.643538	−0.321769	+	0.946818i	$0.604277\pi$
$504$	−2.57005	−0.114479
$505$	40.8155	1.81626
$506$	−5.07120	−0.225442
$507$	6.58323	0.292372
$508$	15.4038	0.683432
$509$	−21.2047	−0.939880	−0.469940	−	0.882698i	$-0.655724\pi$
$509$	−21.2047	−0.939880	−0.469940	+	0.882698i	$0.655724\pi$
$510$	7.07722	0.313385
$511$	0.893285	0.0395166
$512$	−1.00000	−0.0441942
$513$	−17.1711	−0.758122
$514$	9.80758	0.432594
$515$	−0.0852735	−0.00375760
$516$	−7.77135	−0.342115
$517$	−8.37748	−0.368441
$518$	3.60257	0.158288
$519$	2.68570	0.117889
$520$	−4.32698	−0.189751
$521$	−23.5837	−1.03322	−0.516611	−	0.856220i	$-0.672807\pi$
$521$	−23.5837	−1.03322	−0.516611	+	0.856220i	$0.672807\pi$
$522$	9.63167	0.421567
$523$	28.5971	1.25047	0.625233	−	0.780438i	$-0.285004\pi$
$523$	28.5971	1.25047	0.625233	+	0.780438i	$0.285004\pi$
$524$	19.7518	0.862862
$525$	0.868903	0.0379220
$526$	−21.0246	−0.916718
$527$	−37.2223	−1.62143
$528$	−0.497716	−0.0216603
$529$	21.6349	0.940646
$530$	25.1063	1.09055
$531$	12.2986	0.533714
$532$	4.70144	0.203833
$533$	−4.94687	−0.214273
$534$	−4.01767	−0.173862
$535$	26.6860	1.15374
$536$	3.87525	0.167385
$537$	8.94060	0.385815
$538$	−0.0870859	−0.00375454
$539$	0.759055	0.0326948
$540$	−9.18549	−0.395281
$541$	16.1683	0.695129	0.347564	−	0.937656i	$-0.387009\pi$
$541$	16.1683	0.695129	0.347564	+	0.937656i	$0.387009\pi$
$542$	−4.00587	−0.172067
$543$	−1.50537	−0.0646015
$544$	4.29161	0.184001
$545$	39.0113	1.67106
$546$	1.12813	0.0482794
$547$	20.6440	0.882672	0.441336	−	0.897342i	$-0.354505\pi$
$547$	20.6440	0.882672	0.441336	+	0.897342i	$0.354505\pi$
$548$	−16.0199	−0.684337
$549$	10.3363	0.441144
$550$	−1.00586	−0.0428899
$551$	−17.6194	−0.750610
$552$	4.38071	0.186456
$553$	−2.90350	−0.123469
$554$	13.0530	0.554568
$555$	5.94094	0.252179
$556$	−3.68155	−0.156133
$557$	−8.45622	−0.358302	−0.179151	−	0.983822i	$-0.557335\pi$
$557$	−8.45622	−0.358302	−0.179151	+	0.983822i	$0.557335\pi$
$558$	22.2908	0.943643
$559$	−20.3910	−0.862448
$560$	2.51498	0.106277
$561$	2.13600	0.0901820
$562$	−8.86885	−0.374110
$563$	3.90196	0.164448	0.0822240	−	0.996614i	$-0.473798\pi$
$563$	3.90196	0.164448	0.0822240	+	0.996614i	$0.473798\pi$
$564$	7.23682	0.304725
$565$	25.3934	1.06831
$566$	−8.78185	−0.369129
$567$	−5.31532	−0.223223
$568$	−13.0874	−0.549135
$569$	21.1404	0.886251	0.443126	−	0.896460i	$-0.353870\pi$
$569$	21.1404	0.886251	0.443126	+	0.896460i	$0.353870\pi$
$570$	7.75307	0.324740
$571$	1.55490	0.0650705	0.0325353	−	0.999471i	$-0.489642\pi$
$571$	1.55490	0.0650705	0.0325353	+	0.999471i	$0.489642\pi$
$572$	−1.30594	−0.0546041
$573$	−2.65398	−0.110872
$574$	2.87528	0.120012
$575$	8.85321	0.369204
$576$	−2.57005	−0.107086
$577$	−17.7042	−0.737035	−0.368518	−	0.929621i	$-0.620135\pi$
$577$	−17.7042	−0.737035	−0.368518	+	0.929621i	$0.620135\pi$
$578$	−1.41788	−0.0589762
$579$	−11.0244	−0.458156
$580$	−9.42529	−0.391364
$581$	1.48801	0.0617331
$582$	0.412592	0.0171025
$583$	7.57740	0.313824
$584$	0.893285	0.0369644
$585$	−11.1206	−0.459779
$586$	−8.58340	−0.354577
$587$	−9.41711	−0.388686	−0.194343	−	0.980934i	$-0.562257\pi$
$587$	−9.41711	−0.388686	−0.194343	+	0.980934i	$0.562257\pi$
$588$	−0.655704	−0.0270408
$589$	−40.7768	−1.68018
$590$	−12.0351	−0.495476
$591$	16.8838	0.694505
$592$	3.60257	0.148065
$593$	−22.9885	−0.944025	−0.472013	−	0.881592i	$-0.656472\pi$
$593$	−22.9885	−0.944025	−0.472013	+	0.881592i	$0.656472\pi$
$594$	−2.77230	−0.113749
$595$	−10.7933	−0.442483
$596$	−0.539748	−0.0221089
$597$	10.6588	0.436237
$598$	11.4944	0.470042
$599$	15.2756	0.624146	0.312073	−	0.950058i	$-0.398977\pi$
$599$	15.2756	0.624146	0.312073	+	0.950058i	$0.398977\pi$
$600$	0.868903	0.0354728
$601$	−0.671161	−0.0273772	−0.0136886	−	0.999906i	$-0.504357\pi$
$601$	−0.671161	−0.0273772	−0.0136886	+	0.999906i	$0.504357\pi$
$602$	11.8519	0.483048
$603$	9.95960	0.405586
$604$	20.7956	0.846160
$605$	26.2158	1.06582
$606$	−10.6414	−0.432276
$607$	10.5252	0.427204	0.213602	−	0.976921i	$-0.431480\pi$
$607$	10.5252	0.427204	0.213602	+	0.976921i	$0.431480\pi$
$608$	4.70144	0.190668
$609$	2.45735	0.0995770
$610$	−10.1149	−0.409539
$611$	18.9885	0.768191
$612$	11.0297	0.445847
$613$	35.8447	1.44775	0.723876	−	0.689930i	$-0.242359\pi$
$613$	35.8447	1.44775	0.723876	+	0.689930i	$0.242359\pi$
$614$	3.67327	0.148241
$615$	4.74158	0.191199
$616$	0.759055	0.0305832
$617$	−29.3122	−1.18007	−0.590033	−	0.807379i	$-0.700885\pi$
$617$	−29.3122	−1.18007	−0.590033	+	0.807379i	$0.700885\pi$
$618$	0.0222324	0.000894319 0
$619$	−7.15604	−0.287625	−0.143813	−	0.989605i	$-0.545936\pi$
$619$	−7.15604	−0.287625	−0.143813	+	0.989605i	$0.545936\pi$
$620$	−21.8131	−0.876037
$621$	24.4008	0.979171
$622$	12.0271	0.482242
$623$	6.12726	0.245484
$624$	1.12813	0.0451612
$625$	−29.8697	−1.19479
$626$	12.2290	0.488770
$627$	2.33998	0.0934497
$628$	23.6466	0.943601
$629$	−15.4608	−0.616462
$630$	6.46364	0.257518
$631$	−27.6739	−1.10168	−0.550840	−	0.834611i	$-0.685692\pi$
$631$	−27.6739	−1.10168	−0.550840	+	0.834611i	$0.685692\pi$
$632$	−2.90350	−0.115495
$633$	−3.15443	−0.125378
$634$	14.5871	0.579327
$635$	−38.7403	−1.53736
$636$	−6.54568	−0.259553
$637$	−1.72048	−0.0681679
$638$	−2.84468	−0.112622
$639$	−33.6353	−1.33059
$640$	2.51498	0.0994135
$641$	−8.41301	−0.332294	−0.166147	−	0.986101i	$-0.553133\pi$
$641$	−8.41301	−0.332294	−0.166147	+	0.986101i	$0.553133\pi$
$642$	−6.95755	−0.274592
$643$	−44.1936	−1.74283	−0.871413	−	0.490550i	$-0.836796\pi$
$643$	−44.1936	−1.74283	−0.871413	+	0.490550i	$0.836796\pi$
$644$	−6.68093	−0.263266
$645$	19.5448	0.769577
$646$	−20.1767	−0.793842
$647$	3.50494	0.137793	0.0688967	−	0.997624i	$-0.478052\pi$
$647$	3.50494	0.137793	0.0688967	+	0.997624i	$0.478052\pi$
$648$	−5.31532	−0.208806
$649$	−3.63234	−0.142582
$650$	2.27989	0.0894245
$651$	5.68710	0.222895
$652$	22.1317	0.866745
$653$	−32.3058	−1.26423	−0.632113	−	0.774876i	$-0.717812\pi$
$653$	−32.3058	−1.26423	−0.632113	+	0.774876i	$0.717812\pi$
$654$	−10.1710	−0.397717
$655$	−49.6755	−1.94098
$656$	2.87528	0.112261
$657$	2.29579	0.0895673
$658$	−11.0367	−0.430256
$659$	−7.45321	−0.290336	−0.145168	−	0.989407i	$-0.546372\pi$
$659$	−7.45321	−0.290336	−0.145168	+	0.989407i	$0.546372\pi$
$660$	1.25175	0.0487242
$661$	−24.0820	−0.936680	−0.468340	−	0.883548i	$-0.655148\pi$
$661$	−24.0820	−0.936680	−0.468340	+	0.883548i	$0.655148\pi$
$662$	29.8850	1.16151
$663$	−4.84147	−0.188027
$664$	1.48801	0.0577460
$665$	−11.8240	−0.458516
$666$	9.25878	0.358771
$667$	25.0378	0.969469
$668$	13.9098	0.538184
$669$	11.8676	0.458827
$670$	−9.74620	−0.376529
$671$	−3.05280	−0.117852
$672$	−0.655704	−0.0252943
$673$	−43.2347	−1.66658	−0.833288	−	0.552839i	$-0.813544\pi$
$673$	−43.2347	−1.66658	−0.833288	+	0.552839i	$0.813544\pi$
$674$	−20.8076	−0.801479
$675$	4.83984	0.186285
$676$	−10.0399	−0.386152
$677$	6.63594	0.255040	0.127520	−	0.991836i	$-0.459298\pi$
$677$	6.63594	0.255040	0.127520	+	0.991836i	$0.459298\pi$
$678$	−6.62053	−0.254260
$679$	−0.629236	−0.0241479
$680$	−10.7933	−0.413905
$681$	−6.01151	−0.230361
$682$	−6.58349	−0.252095
$683$	−49.7614	−1.90407	−0.952034	−	0.305992i	$-0.901012\pi$
$683$	−49.7614	−1.90407	−0.952034	+	0.305992i	$0.901012\pi$
$684$	12.0829	0.462003
$685$	40.2899	1.53940
$686$	1.00000	0.0381802
$687$	2.07331	0.0791016
$688$	11.8519	0.451850
$689$	−17.1750	−0.654316
$690$	−11.0174	−0.419426
$691$	−26.2763	−0.999598	−0.499799	−	0.866141i	$-0.666593\pi$
$691$	−26.2763	−0.999598	−0.499799	+	0.866141i	$0.666593\pi$
$692$	−4.09590	−0.155703
$693$	1.95081	0.0741052
$694$	35.4782	1.34674
$695$	9.25904	0.351216
$696$	2.45735	0.0931457
$697$	−12.3396	−0.467395
$698$	−21.3832	−0.809365
$699$	9.57654	0.362218
$700$	−1.32515	−0.0500858
$701$	27.4113	1.03531	0.517655	−	0.855589i	$-0.326805\pi$
$701$	27.4113	1.03531	0.517655	+	0.855589i	$0.326805\pi$
$702$	6.28372	0.237164
$703$	−16.9372	−0.638800
$704$	0.759055	0.0286080
$705$	−18.2005	−0.685470
$706$	−5.06719	−0.190706
$707$	16.2289	0.610351
$708$	3.13777	0.117925
$709$	−32.4301	−1.21794	−0.608970	−	0.793193i	$-0.708417\pi$
$709$	−32.4301	−1.21794	−0.608970	+	0.793193i	$0.708417\pi$
$710$	32.9146	1.23526
$711$	−7.46214	−0.279852
$712$	6.12726	0.229629
$713$	57.9455	2.17008
$714$	2.81402	0.105312
$715$	3.28442	0.122830
$716$	−13.6351	−0.509568
$717$	15.1617	0.566223
$718$	12.9118	0.481865
$719$	−24.0060	−0.895271	−0.447635	−	0.894216i	$-0.647734\pi$
$719$	−24.0060	−0.895271	−0.447635	+	0.894216i	$0.647734\pi$
$720$	6.46364	0.240886
$721$	−0.0339062	−0.00126273
$722$	−3.10350	−0.115500
$723$	20.3291	0.756047
$724$	2.29580	0.0853229
$725$	4.96619	0.184440
$726$	−6.83495	−0.253669
$727$	−52.0321	−1.92976	−0.964882	−	0.262685i	$-0.915392\pi$
$727$	−52.0321	−1.92976	−0.964882	+	0.262685i	$0.915392\pi$
$728$	−1.72048	−0.0637653
$729$	−6.47617	−0.239858
$730$	−2.24660	−0.0831503
$731$	−50.8638	−1.88126
$732$	2.63714	0.0974713
$733$	27.2504	1.00652	0.503258	−	0.864136i	$-0.332134\pi$
$733$	27.2504	1.00652	0.503258	+	0.864136i	$0.332134\pi$
$734$	−13.5713	−0.500927
$735$	1.64909	0.0608274
$736$	−6.68093	−0.246262
$737$	−2.94153	−0.108353
$738$	7.38962	0.272016
$739$	−9.98338	−0.367245	−0.183622	−	0.982997i	$-0.558782\pi$
$739$	−9.98338	−0.367245	−0.183622	+	0.982997i	$0.558782\pi$
$740$	−9.06040	−0.333067
$741$	−5.30381	−0.194840
$742$	9.98268	0.366476
$743$	21.7021	0.796174	0.398087	−	0.917348i	$-0.369674\pi$
$743$	21.7021	0.796174	0.398087	+	0.917348i	$0.369674\pi$
$744$	5.68710	0.208499
$745$	1.35746	0.0497334
$746$	7.66902	0.280783
$747$	3.82427	0.139923
$748$	−3.25757	−0.119108
$749$	10.6108	0.387710
$750$	6.06015	0.221285
$751$	49.9899	1.82416	0.912078	−	0.410017i	$-0.134477\pi$
$751$	49.9899	1.82416	0.912078	+	0.410017i	$0.134477\pi$
$752$	−11.0367	−0.402468
$753$	−18.7779	−0.684305
$754$	6.44777	0.234814
$755$	−52.3005	−1.90341
$756$	−3.65231	−0.132833
$757$	−9.67562	−0.351666	−0.175833	−	0.984420i	$-0.556262\pi$
$757$	−9.67562	−0.351666	−0.175833	+	0.984420i	$0.556262\pi$
$758$	9.09079	0.330192
$759$	−3.32520	−0.120697
$760$	−11.8240	−0.428903
$761$	−29.9475	−1.08560	−0.542799	−	0.839863i	$-0.682635\pi$
$761$	−29.9475	−1.08560	−0.542799	+	0.839863i	$0.682635\pi$
$762$	10.1003	0.365896
$763$	15.5115	0.561555
$764$	4.04753	0.146434
$765$	−27.7394	−1.00292
$766$	15.3153	0.553365
$767$	8.23310	0.297280
$768$	−0.655704	−0.0236607
$769$	26.4225	0.952820	0.476410	−	0.879223i	$-0.341938\pi$
$769$	26.4225	0.952820	0.476410	+	0.879223i	$0.341938\pi$
$770$	−1.90901	−0.0687960
$771$	6.43087	0.231602
$772$	16.8130	0.605113
$773$	−8.01126	−0.288145	−0.144073	−	0.989567i	$-0.546020\pi$
$773$	−8.01126	−0.288145	−0.144073	+	0.989567i	$0.546020\pi$
$774$	30.4601	1.09486
$775$	11.4933	0.412853
$776$	−0.629236	−0.0225882
$777$	2.36222	0.0847441
$778$	−33.5633	−1.20330
$779$	−13.5180	−0.484331
$780$	−2.83722	−0.101589
$781$	9.93406	0.355468
$782$	28.6719	1.02531
$783$	13.6876	0.489154
$784$	1.00000	0.0357143
$785$	−59.4707	−2.12260
$786$	12.9513	0.461959
$787$	35.5513	1.26727	0.633634	−	0.773633i	$-0.281563\pi$
$787$	35.5513	1.26727	0.633634	+	0.773633i	$0.281563\pi$
$788$	−25.7491	−0.917272
$789$	−13.7859	−0.490792
$790$	7.30225	0.259802
$791$	10.0968	0.359002
$792$	1.95081	0.0693191
$793$	6.91950	0.245719
$794$	−4.51987	−0.160404
$795$	16.4623	0.583857
$796$	−16.2556	−0.576163
$797$	−1.87570	−0.0664408	−0.0332204	−	0.999448i	$-0.510576\pi$
$797$	−1.87570	−0.0664408	−0.0332204	+	0.999448i	$0.510576\pi$
$798$	3.08275	0.109128
$799$	47.3653	1.67566
$800$	−1.32515	−0.0468510
$801$	15.7474	0.556407
$802$	5.55581	0.196183
$803$	−0.678053	−0.0239280
$804$	2.54102	0.0896149
$805$	16.8024	0.592208
$806$	14.9222	0.525612
$807$	−0.0571026	−0.00201011
$808$	16.2289	0.570931
$809$	3.29105	0.115707	0.0578536	−	0.998325i	$-0.481574\pi$
$809$	3.29105	0.115707	0.0578536	+	0.998325i	$0.481574\pi$
$810$	13.3680	0.469702
$811$	37.4634	1.31552	0.657760	−	0.753228i	$-0.271504\pi$
$811$	37.4634	1.31552	0.657760	+	0.753228i	$0.271504\pi$
$812$	−3.74766	−0.131517
$813$	−2.62666	−0.0921211
$814$	−2.73455	−0.0958458
$815$	−55.6609	−1.94972
$816$	2.81402	0.0985105
$817$	−55.7210	−1.94943
$818$	−29.6823	−1.03782
$819$	−4.42173	−0.154508
$820$	−7.23129	−0.252528
$821$	49.6584	1.73309	0.866546	−	0.499098i	$-0.166335\pi$
$821$	49.6584	1.73309	0.866546	+	0.499098i	$0.166335\pi$
$822$	−10.5043	−0.366381
$823$	−6.81750	−0.237643	−0.118822	−	0.992916i	$-0.537912\pi$
$823$	−6.81750	−0.237643	−0.118822	+	0.992916i	$0.537912\pi$
$824$	−0.0339062	−0.00118118
$825$	−0.659545	−0.0229624
$826$	−4.78535	−0.166504
$827$	−9.07869	−0.315697	−0.157849	−	0.987463i	$-0.550456\pi$
$827$	−9.07869	−0.315697	−0.157849	+	0.987463i	$0.550456\pi$
$828$	−17.1703	−0.596711
$829$	22.1586	0.769600	0.384800	−	0.923000i	$-0.374270\pi$
$829$	22.1586	0.769600	0.384800	+	0.923000i	$0.374270\pi$
$830$	−3.74232	−0.129898
$831$	8.55889	0.296905
$832$	−1.72048	−0.0596470
$833$	−4.29161	−0.148695
$834$	−2.41401	−0.0835903
$835$	−34.9828	−1.21063
$836$	−3.56865	−0.123424
$837$	31.6774	1.09493
$838$	−15.7972	−0.545706
$839$	−14.3565	−0.495643	−0.247822	−	0.968806i	$-0.579715\pi$
$839$	−14.3565	−0.495643	−0.247822	+	0.968806i	$0.579715\pi$
$840$	1.64909	0.0568988
$841$	−14.9551	−0.515692
$842$	−34.1017	−1.17522
$843$	−5.81534	−0.200291
$844$	4.81076	0.165593
$845$	25.2503	0.868637
$846$	−28.3650	−0.975207
$847$	10.4238	0.358167
$848$	9.98268	0.342806
$849$	−5.75829	−0.197624
$850$	5.68700	0.195063
$851$	24.0685	0.825058
$852$	−8.58146	−0.293996
$853$	6.56315	0.224718	0.112359	−	0.993668i	$-0.464159\pi$
$853$	6.56315	0.224718	0.112359	+	0.993668i	$0.464159\pi$
$854$	−4.02184	−0.137624
$855$	−30.3884	−1.03926
$856$	10.6108	0.362670
$857$	−29.4242	−1.00511	−0.502555	−	0.864545i	$-0.667607\pi$
$857$	−29.4242	−1.00511	−0.502555	+	0.864545i	$0.667607\pi$
$858$	−0.856310	−0.0292340
$859$	−38.3638	−1.30896	−0.654478	−	0.756081i	$-0.727112\pi$
$859$	−38.3638	−1.30896	−0.654478	+	0.756081i	$0.727112\pi$
$860$	−29.8074	−1.01642
$861$	1.88533	0.0642520
$862$	1.00000	0.0340601
$863$	−4.51115	−0.153561	−0.0767807	−	0.997048i	$-0.524464\pi$
$863$	−4.51115	−0.153561	−0.0767807	+	0.997048i	$0.524464\pi$
$864$	−3.65231	−0.124254
$865$	10.3011	0.350248
$866$	−35.6836	−1.21258
$867$	−0.929712	−0.0315747
$868$	−8.67327	−0.294390
$869$	2.20391	0.0747627
$870$	−6.18020	−0.209529
$871$	6.66730	0.225913
$872$	15.5115	0.525287
$873$	−1.61717	−0.0547329
$874$	31.4100	1.06246
$875$	−9.24220	−0.312443
$876$	0.585731	0.0197900
$877$	27.3721	0.924290	0.462145	−	0.886804i	$-0.347080\pi$
$877$	27.3721	0.924290	0.462145	+	0.886804i	$0.347080\pi$
$878$	13.5828	0.458397
$879$	−5.62817	−0.189833
$880$	−1.90901	−0.0643528
$881$	−58.5842	−1.97375	−0.986876	−	0.161480i	$-0.948373\pi$
$881$	−58.5842	−1.97375	−0.986876	+	0.161480i	$0.948373\pi$
$882$	2.57005	0.0865382
$883$	45.0868	1.51729	0.758646	−	0.651503i	$-0.225861\pi$
$883$	45.0868	1.51729	0.758646	+	0.651503i	$0.225861\pi$
$884$	7.38363	0.248338
$885$	−7.89145	−0.265268
$886$	16.6069	0.557919
$887$	54.6042	1.83343	0.916715	−	0.399541i	$-0.130830\pi$
$887$	54.6042	1.83343	0.916715	+	0.399541i	$0.130830\pi$
$888$	2.36222	0.0792708
$889$	−15.4038	−0.516626
$890$	−15.4100	−0.516543
$891$	4.03462	0.135165
$892$	−18.0990	−0.605999
$893$	51.8884	1.73638
$894$	−0.353915	−0.0118367
$895$	34.2921	1.14626
$896$	1.00000	0.0334077
$897$	7.53694	0.251651
$898$	3.85810	0.128746
$899$	32.5044	1.08408
$900$	−3.40569	−0.113523
$901$	−42.8417	−1.42726
$902$	−2.18250	−0.0726692
$903$	7.77135	0.258614
$904$	10.0968	0.335816
$905$	−5.77391	−0.191931
$906$	13.6357	0.453017
$907$	48.2602	1.60245	0.801227	−	0.598361i	$-0.204181\pi$
$907$	48.2602	1.60245	0.801227	+	0.598361i	$0.204181\pi$
$908$	9.16802	0.304251
$909$	41.7091	1.38341
$910$	4.32698	0.143438
$911$	−46.1453	−1.52886	−0.764431	−	0.644706i	$-0.776980\pi$
$911$	−46.1453	−1.52886	−0.764431	+	0.644706i	$0.776980\pi$
$912$	3.08275	0.102080
$913$	−1.12948	−0.0373804
$914$	−24.0805	−0.796512
$915$	−6.63235	−0.219259
$916$	−3.16196	−0.104474
$917$	−19.7518	−0.652263
$918$	15.6743	0.517328
$919$	−10.7182	−0.353562	−0.176781	−	0.984250i	$-0.556568\pi$
$919$	−10.7182	−0.353562	−0.176781	+	0.984250i	$0.556568\pi$
$920$	16.8024	0.553960
$921$	2.40858	0.0793653
$922$	32.0748	1.05633
$923$	−22.5166	−0.741144
$924$	0.497716	0.0163736
$925$	4.77392	0.156966
$926$	10.4014	0.341812
$927$	−0.0871406	−0.00286207
$928$	−3.74766	−0.123023
$929$	18.0458	0.592062	0.296031	−	0.955178i	$-0.404337\pi$
$929$	18.0458	0.592062	0.296031	+	0.955178i	$0.404337\pi$
$930$	−14.3030	−0.469013
$931$	−4.70144	−0.154083
$932$	−14.6050	−0.478402
$933$	7.88621	0.258183
$934$	−7.71150	−0.252328
$935$	8.19273	0.267931
$936$	−4.42173	−0.144529
$937$	22.0013	0.718752	0.359376	−	0.933193i	$-0.382990\pi$
$937$	22.0013	0.718752	0.359376	+	0.933193i	$0.382990\pi$
$938$	−3.87525	−0.126532
$939$	8.01862	0.261678
$940$	27.7572	0.905339
$941$	−29.1442	−0.950073	−0.475036	−	0.879966i	$-0.657565\pi$
$941$	−29.1442	−0.950073	−0.475036	+	0.879966i	$0.657565\pi$
$942$	15.5052	0.505185
$943$	19.2096	0.625549
$944$	−4.78535	−0.155750
$945$	9.18549	0.298804
$946$	−8.99626	−0.292494
$947$	29.0608	0.944350	0.472175	−	0.881505i	$-0.343469\pi$
$947$	29.0608	0.944350	0.472175	+	0.881505i	$0.343469\pi$
$948$	−1.90383	−0.0618337
$949$	1.53688	0.0498892
$950$	6.23008	0.202131
$951$	9.56480	0.310160
$952$	−4.29161	−0.139092
$953$	12.5512	0.406575	0.203287	−	0.979119i	$-0.434837\pi$
$953$	12.5512	0.406575	0.203287	+	0.979119i	$0.434837\pi$
$954$	25.6560	0.830644
$955$	−10.1795	−0.329400
$956$	−23.1227	−0.747843
$957$	−1.86527	−0.0602955
$958$	9.56556	0.309049
$959$	16.0199	0.517310
$960$	1.64909	0.0532240
$961$	44.2256	1.42663
$962$	6.19815	0.199836
$963$	27.2703	0.878774
$964$	−31.0035	−0.998554
$965$	−42.2844	−1.36118
$966$	−4.38071	−0.140947
$967$	−4.01625	−0.129154	−0.0645770	−	0.997913i	$-0.520570\pi$
$967$	−4.01625	−0.129154	−0.0645770	+	0.997913i	$0.520570\pi$
$968$	10.4238	0.335035
$969$	−13.2300	−0.425007
$970$	1.58252	0.0508116
$971$	−4.79115	−0.153755	−0.0768777	−	0.997041i	$-0.524495\pi$
$971$	−4.79115	−0.153755	−0.0768777	+	0.997041i	$0.524495\pi$
$972$	−14.4422	−0.463234
$973$	3.68155	0.118025
$974$	−32.0631	−1.02737
$975$	1.49493	0.0478761
$976$	−4.02184	−0.128736
$977$	−10.9897	−0.351592	−0.175796	−	0.984427i	$-0.556250\pi$
$977$	−10.9897	−0.351592	−0.175796	+	0.984427i	$0.556250\pi$
$978$	14.5119	0.464038
$979$	−4.65093	−0.148644
$980$	−2.51498	−0.0803382
$981$	39.8654	1.27281
$982$	37.8419	1.20758
$983$	2.88261	0.0919409	0.0459704	−	0.998943i	$-0.485362\pi$
$983$	2.88261	0.0919409	0.0459704	+	0.998943i	$0.485362\pi$
$984$	1.88533	0.0601023
$985$	64.7585	2.06338
$986$	16.0835	0.512202
$987$	−7.23682	−0.230351
$988$	8.08873	0.257337
$989$	79.1819	2.51784
$990$	−4.90626	−0.155931
$991$	−41.6740	−1.32382	−0.661909	−	0.749584i	$-0.730254\pi$
$991$	−41.6740	−1.32382	−0.661909	+	0.749584i	$0.730254\pi$
$992$	−8.67327	−0.275377
$993$	19.5957	0.621850
$994$	13.0874	0.415107
$995$	40.8825	1.29606
$996$	0.975695	0.0309161
$997$	40.9883	1.29811	0.649056	−	0.760740i	$-0.275164\pi$
$997$	40.9883	1.29811	0.649056	+	0.760740i	$0.275164\pi$
$998$	31.0246	0.982068
$999$	13.1577	0.416290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.11	✓	25	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.655704 q^{3} +1.00000 q^{4} -2.51498 q^{5} +0.655704 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.57005 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.655704 q^{3} +1.00000 q^{4} -2.51498 q^{5} +0.655704 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.57005 q^{9} +2.51498 q^{10} +0.759055 q^{11} -0.655704 q^{12} -1.72048 q^{13} +1.00000 q^{14} +1.64909 q^{15} +1.00000 q^{16} -4.29161 q^{17} +2.57005 q^{18} -4.70144 q^{19} -2.51498 q^{20} +0.655704 q^{21} -0.759055 q^{22} +6.68093 q^{23} +0.655704 q^{24} +1.32515 q^{25} +1.72048 q^{26} +3.65231 q^{27} -1.00000 q^{28} +3.74766 q^{29} -1.64909 q^{30} +8.67327 q^{31} -1.00000 q^{32} -0.497716 q^{33} +4.29161 q^{34} +2.51498 q^{35} -2.57005 q^{36} +3.60257 q^{37} +4.70144 q^{38} +1.12813 q^{39} +2.51498 q^{40} +2.87528 q^{41} -0.655704 q^{42} +11.8519 q^{43} +0.759055 q^{44} +6.46364 q^{45} -6.68093 q^{46} -11.0367 q^{47} -0.655704 q^{48} +1.00000 q^{49} -1.32515 q^{50} +2.81402 q^{51} -1.72048 q^{52} +9.98268 q^{53} -3.65231 q^{54} -1.90901 q^{55} +1.00000 q^{56} +3.08275 q^{57} -3.74766 q^{58} -4.78535 q^{59} +1.64909 q^{60} -4.02184 q^{61} -8.67327 q^{62} +2.57005 q^{63} +1.00000 q^{64} +4.32698 q^{65} +0.497716 q^{66} -3.87525 q^{67} -4.29161 q^{68} -4.38071 q^{69} -2.51498 q^{70} +13.0874 q^{71} +2.57005 q^{72} -0.893285 q^{73} -3.60257 q^{74} -0.868903 q^{75} -4.70144 q^{76} -0.759055 q^{77} -1.12813 q^{78} +2.90350 q^{79} -2.51498 q^{80} +5.31532 q^{81} -2.87528 q^{82} -1.48801 q^{83} +0.655704 q^{84} +10.7933 q^{85} -11.8519 q^{86} -2.45735 q^{87} -0.759055 q^{88} -6.12726 q^{89} -6.46364 q^{90} +1.72048 q^{91} +6.68093 q^{92} -5.68710 q^{93} +11.0367 q^{94} +11.8240 q^{95} +0.655704 q^{96} +0.629236 q^{97} -1.00000 q^{98} -1.95081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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