LMFDB - Embedded newform 6035.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04946 q^{2} -2.65729 q^{3} +2.20029 q^{4} +1.00000 q^{5} +5.44602 q^{6} -0.551924 q^{7} -0.410497 q^{8} +4.06121 q^{9} +O(q^{10})$	\(q-2.04946 q^{2} -2.65729 q^{3} +2.20029 q^{4} +1.00000 q^{5} +5.44602 q^{6} -0.551924 q^{7} -0.410497 q^{8} +4.06121 q^{9} -2.04946 q^{10} -2.27257 q^{11} -5.84683 q^{12} +3.17452 q^{13} +1.13115 q^{14} -2.65729 q^{15} -3.55929 q^{16} +1.00000 q^{17} -8.32329 q^{18} +3.96256 q^{19} +2.20029 q^{20} +1.46662 q^{21} +4.65754 q^{22} +0.158967 q^{23} +1.09081 q^{24} +1.00000 q^{25} -6.50606 q^{26} -2.81994 q^{27} -1.21440 q^{28} -3.30606 q^{29} +5.44602 q^{30} -1.54948 q^{31} +8.11563 q^{32} +6.03887 q^{33} -2.04946 q^{34} -0.551924 q^{35} +8.93585 q^{36} +0.442239 q^{37} -8.12113 q^{38} -8.43563 q^{39} -0.410497 q^{40} -6.61145 q^{41} -3.00579 q^{42} +0.716223 q^{43} -5.00032 q^{44} +4.06121 q^{45} -0.325797 q^{46} +8.62993 q^{47} +9.45808 q^{48} -6.69538 q^{49} -2.04946 q^{50} -2.65729 q^{51} +6.98488 q^{52} +0.784664 q^{53} +5.77935 q^{54} -2.27257 q^{55} +0.226563 q^{56} -10.5297 q^{57} +6.77564 q^{58} +11.6229 q^{59} -5.84683 q^{60} -9.42978 q^{61} +3.17561 q^{62} -2.24148 q^{63} -9.51409 q^{64} +3.17452 q^{65} -12.3764 q^{66} -6.70202 q^{67} +2.20029 q^{68} -0.422421 q^{69} +1.13115 q^{70} -1.00000 q^{71} -1.66711 q^{72} -6.31194 q^{73} -0.906353 q^{74} -2.65729 q^{75} +8.71881 q^{76} +1.25428 q^{77} +17.2885 q^{78} -11.0345 q^{79} -3.55929 q^{80} -4.69022 q^{81} +13.5499 q^{82} +9.59267 q^{83} +3.22700 q^{84} +1.00000 q^{85} -1.46787 q^{86} +8.78516 q^{87} +0.932881 q^{88} -4.93816 q^{89} -8.32329 q^{90} -1.75209 q^{91} +0.349774 q^{92} +4.11744 q^{93} -17.6867 q^{94} +3.96256 q^{95} -21.5656 q^{96} -17.2989 q^{97} +13.7219 q^{98} -9.22936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * 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 $

$2$	−2.04946	−1.44919	−0.724594	−	0.689176i	$-0.757973\pi$
$2$	−2.04946	−1.44919	−0.724594	+	0.689176i	$0.757973\pi$
$3$	−2.65729	−1.53419	−0.767094	−	0.641534i	$-0.778298\pi$
$3$	−2.65729	−1.53419	−0.767094	+	0.641534i	$0.778298\pi$
$4$	2.20029	1.10015
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.44602	2.22333
$7$	−0.551924	−0.208608	−0.104304	−	0.994545i	$-0.533261\pi$
$7$	−0.551924	−0.208608	−0.104304	+	0.994545i	$0.533261\pi$
$8$	−0.410497	−0.145132
$9$	4.06121	1.35374
$10$	−2.04946	−0.648097
$11$	−2.27257	−0.685204	−0.342602	−	0.939481i	$-0.611308\pi$
$11$	−2.27257	−0.685204	−0.342602	+	0.939481i	$0.611308\pi$
$12$	−5.84683	−1.68783
$13$	3.17452	0.880453	0.440227	−	0.897887i	$-0.354898\pi$
$13$	3.17452	0.880453	0.440227	+	0.897887i	$0.354898\pi$
$14$	1.13115	0.302312
$15$	−2.65729	−0.686110
$16$	−3.55929	−0.889823
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−8.32329	−1.96182
$19$	3.96256	0.909075	0.454537	−	0.890728i	$-0.349805\pi$
$19$	3.96256	0.909075	0.454537	+	0.890728i	$0.349805\pi$
$20$	2.20029	0.492001
$21$	1.46662	0.320044
$22$	4.65754	0.992990
$23$	0.158967	0.0331469	0.0165734	−	0.999863i	$-0.494724\pi$
$23$	0.158967	0.0331469	0.0165734	+	0.999863i	$0.494724\pi$
$24$	1.09081	0.222661
$25$	1.00000	0.200000
$26$	−6.50606	−1.27594
$27$	−2.81994	−0.542697
$28$	−1.21440	−0.229499
$29$	−3.30606	−0.613919	−0.306960	−	0.951723i	$-0.599312\pi$
$29$	−3.30606	−0.613919	−0.306960	+	0.951723i	$0.599312\pi$
$30$	5.44602	0.994303
$31$	−1.54948	−0.278296	−0.139148	−	0.990272i	$-0.544436\pi$
$31$	−1.54948	−0.278296	−0.139148	+	0.990272i	$0.544436\pi$
$32$	8.11563	1.43465
$33$	6.03887	1.05123
$34$	−2.04946	−0.351480
$35$	−0.551924	−0.0932922
$36$	8.93585	1.48931
$37$	0.442239	0.0727037	0.0363519	−	0.999339i	$-0.488426\pi$
$37$	0.442239	0.0727037	0.0363519	+	0.999339i	$0.488426\pi$
$38$	−8.12113	−1.31742
$39$	−8.43563	−1.35078
$40$	−0.410497	−0.0649052
$41$	−6.61145	−1.03253	−0.516267	−	0.856428i	$-0.672679\pi$
$41$	−6.61145	−1.03253	−0.516267	+	0.856428i	$0.672679\pi$
$42$	−3.00579	−0.463803
$43$	0.716223	0.109223	0.0546115	−	0.998508i	$-0.482608\pi$
$43$	0.716223	0.109223	0.0546115	+	0.998508i	$0.482608\pi$
$44$	−5.00032	−0.753826
$45$	4.06121	0.605409
$46$	−0.325797	−0.0480361
$47$	8.62993	1.25880	0.629402	−	0.777080i	$-0.283300\pi$
$47$	8.62993	1.25880	0.629402	+	0.777080i	$0.283300\pi$
$48$	9.45808	1.36516
$49$	−6.69538	−0.956483
$50$	−2.04946	−0.289838
$51$	−2.65729	−0.372095
$52$	6.98488	0.968628
$53$	0.784664	0.107782	0.0538910	−	0.998547i	$-0.482838\pi$
$53$	0.784664	0.107782	0.0538910	+	0.998547i	$0.482838\pi$
$54$	5.77935	0.786470
$55$	−2.27257	−0.306433
$56$	0.226563	0.0302758
$57$	−10.5297	−1.39469
$58$	6.77564	0.889685
$59$	11.6229	1.51318	0.756588	−	0.653892i	$-0.226865\pi$
$59$	11.6229	1.51318	0.756588	+	0.653892i	$0.226865\pi$
$60$	−5.84683	−0.754822
$61$	−9.42978	−1.20736	−0.603680	−	0.797227i	$-0.706299\pi$
$61$	−9.42978	−1.20736	−0.603680	+	0.797227i	$0.706299\pi$
$62$	3.17561	0.403303
$63$	−2.24148	−0.282400
$64$	−9.51409	−1.18926
$65$	3.17452	0.393751
$66$	−12.3764	−1.52343
$67$	−6.70202	−0.818782	−0.409391	−	0.912359i	$-0.634259\pi$
$67$	−6.70202	−0.818782	−0.409391	+	0.912359i	$0.634259\pi$
$68$	2.20029	0.266825
$69$	−0.422421	−0.0508536
$70$	1.13115	0.135198
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−1.66711	−0.196471
$73$	−6.31194	−0.738757	−0.369378	−	0.929279i	$-0.620429\pi$
$73$	−6.31194	−0.738757	−0.369378	+	0.929279i	$0.620429\pi$
$74$	−0.906353	−0.105361
$75$	−2.65729	−0.306838
$76$	8.71881	1.00012
$77$	1.25428	0.142939
$78$	17.2885	1.95754
$79$	−11.0345	−1.24148	−0.620741	−	0.784015i	$-0.713168\pi$
$79$	−11.0345	−1.24148	−0.620741	+	0.784015i	$0.713168\pi$
$80$	−3.55929	−0.397941
$81$	−4.69022	−0.521136
$82$	13.5499	1.49634
$83$	9.59267	1.05293	0.526466	−	0.850196i	$-0.323517\pi$
$83$	9.59267	1.05293	0.526466	+	0.850196i	$0.323517\pi$
$84$	3.22700	0.352095
$85$	1.00000	0.108465
$86$	−1.46787	−0.158285
$87$	8.78516	0.941868
$88$	0.932881	0.0994454
$89$	−4.93816	−0.523443	−0.261722	−	0.965143i	$-0.584290\pi$
$89$	−4.93816	−0.523443	−0.261722	+	0.965143i	$0.584290\pi$
$90$	−8.32329	−0.877352
$91$	−1.75209	−0.183669
$92$	0.349774	0.0364665
$93$	4.11744	0.426958
$94$	−17.6867	−1.82424
$95$	3.96256	0.406551
$96$	−21.5656	−2.20103
$97$	−17.2989	−1.75643	−0.878216	−	0.478263i	$-0.841266\pi$
$97$	−17.2989	−1.75643	−0.878216	+	0.478263i	$0.841266\pi$
$98$	13.7219	1.38612
$99$	−9.22936	−0.927586
$100$	2.20029	0.220029
$101$	−5.69177	−0.566352	−0.283176	−	0.959068i	$-0.591388\pi$
$101$	−5.69177	−0.566352	−0.283176	+	0.959068i	$0.591388\pi$
$102$	5.44602	0.539236
$103$	17.6043	1.73461	0.867303	−	0.497780i	$-0.165851\pi$
$103$	17.6043	1.73461	0.867303	+	0.497780i	$0.165851\pi$
$104$	−1.30313	−0.127782
$105$	1.46662	0.143128
$106$	−1.60814	−0.156196
$107$	0.0190068	0.00183746	0.000918729	−	1.00000i	$-0.499708\pi$
$107$	0.0190068	0.00183746	0.000918729		1.00000i	$0.499708\pi$
$108$	−6.20469	−0.597047
$109$	9.59875	0.919393	0.459697	−	0.888076i	$-0.347958\pi$
$109$	9.59875	0.919393	0.459697	+	0.888076i	$0.347958\pi$
$110$	4.65754	0.444079
$111$	−1.17516	−0.111541
$112$	1.96446	0.185624
$113$	−17.2245	−1.62035	−0.810175	−	0.586189i	$-0.800628\pi$
$113$	−17.2245	−1.62035	−0.810175	+	0.586189i	$0.800628\pi$
$114$	21.5802	2.02117
$115$	0.158967	0.0148237
$116$	−7.27430	−0.675402
$117$	12.8924	1.19190
$118$	−23.8207	−2.19288
$119$	−0.551924	−0.0505948
$120$	1.09081	0.0995769
$121$	−5.83544	−0.530495
$122$	19.3260	1.74969
$123$	17.5685	1.58410
$124$	−3.40932	−0.306166
$125$	1.00000	0.0894427
$126$	4.59382	0.409250
$127$	2.64109	0.234359	0.117180	−	0.993111i	$-0.462615\pi$
$127$	2.64109	0.234359	0.117180	+	0.993111i	$0.462615\pi$
$128$	3.26750	0.288809
$129$	−1.90321	−0.167569
$130$	−6.50606	−0.570619
$131$	−8.58109	−0.749733	−0.374867	−	0.927079i	$-0.622312\pi$
$131$	−8.58109	−0.749733	−0.374867	+	0.927079i	$0.622312\pi$
$132$	13.2873	1.15651
$133$	−2.18703	−0.189640
$134$	13.7355	1.18657
$135$	−2.81994	−0.242701
$136$	−0.410497	−0.0351998
$137$	4.06146	0.346994	0.173497	−	0.984834i	$-0.444493\pi$
$137$	4.06146	0.346994	0.173497	+	0.984834i	$0.444493\pi$
$138$	0.865737	0.0736964
$139$	−9.41172	−0.798292	−0.399146	−	0.916887i	$-0.630693\pi$
$139$	−9.41172	−0.798292	−0.399146	+	0.916887i	$0.630693\pi$
$140$	−1.21440	−0.102635
$141$	−22.9322	−1.93124
$142$	2.04946	0.171987
$143$	−7.21431	−0.603291
$144$	−14.4550	−1.20459
$145$	−3.30606	−0.274553
$146$	12.9361	1.07060
$147$	17.7916	1.46743
$148$	0.973057	0.0799848
$149$	4.56644	0.374097	0.187048	−	0.982351i	$-0.440108\pi$
$149$	4.56644	0.374097	0.187048	+	0.982351i	$0.440108\pi$
$150$	5.44602	0.444666
$151$	22.1216	1.80023	0.900114	−	0.435655i	$-0.143483\pi$
$151$	22.1216	1.80023	0.900114	+	0.435655i	$0.143483\pi$
$152$	−1.62662	−0.131936
$153$	4.06121	0.328329
$154$	−2.57061	−0.207145
$155$	−1.54948	−0.124458
$156$	−18.5609	−1.48606
$157$	15.2760	1.21916	0.609579	−	0.792725i	$-0.291339\pi$
$157$	15.2760	1.21916	0.609579	+	0.792725i	$0.291339\pi$
$158$	22.6149	1.79914
$159$	−2.08508	−0.165358
$160$	8.11563	0.641597
$161$	−0.0877376	−0.00691469
$162$	9.61243	0.755224
$163$	−5.59290	−0.438070	−0.219035	−	0.975717i	$-0.570291\pi$
$163$	−5.59290	−0.438070	−0.219035	+	0.975717i	$0.570291\pi$
$164$	−14.5471	−1.13594
$165$	6.03887	0.470126
$166$	−19.6598	−1.52590
$167$	−6.31267	−0.488489	−0.244244	−	0.969714i	$-0.578540\pi$
$167$	−6.31267	−0.488489	−0.244244	+	0.969714i	$0.578540\pi$
$168$	−0.602044	−0.0464487
$169$	−2.92243	−0.224802
$170$	−2.04946	−0.157187
$171$	16.0928	1.23065
$172$	1.57590	0.120161
$173$	11.4639	0.871584	0.435792	−	0.900047i	$-0.356468\pi$
$173$	11.4639	0.871584	0.435792	+	0.900047i	$0.356468\pi$
$174$	−18.0049	−1.36494
$175$	−0.551924	−0.0417215
$176$	8.08873	0.609711
$177$	−30.8855	−2.32150
$178$	10.1206	0.758568
$179$	−12.6784	−0.947629	−0.473815	−	0.880625i	$-0.657123\pi$
$179$	−12.6784	−0.947629	−0.473815	+	0.880625i	$0.657123\pi$
$180$	8.93585	0.666039
$181$	16.1158	1.19788	0.598938	−	0.800796i	$-0.295590\pi$
$181$	16.1158	1.19788	0.598938	+	0.800796i	$0.295590\pi$
$182$	3.59085	0.266171
$183$	25.0577	1.85232
$184$	−0.0652554	−0.00481069
$185$	0.442239	0.0325141
$186$	−8.43853	−0.618743
$187$	−2.27257	−0.166186
$188$	18.9884	1.38487
$189$	1.55639	0.113211
$190$	−8.12113	−0.589168
$191$	7.12472	0.515527	0.257763	−	0.966208i	$-0.417014\pi$
$191$	7.12472	0.515527	0.257763	+	0.966208i	$0.417014\pi$
$192$	25.2817	1.82455
$193$	2.17562	0.156605	0.0783024	−	0.996930i	$-0.475050\pi$
$193$	2.17562	0.156605	0.0783024	+	0.996930i	$0.475050\pi$
$194$	35.4534	2.54540
$195$	−8.43563	−0.604088
$196$	−14.7318	−1.05227
$197$	21.2115	1.51126	0.755629	−	0.655000i	$-0.227331\pi$
$197$	21.2115	1.51126	0.755629	+	0.655000i	$0.227331\pi$
$198$	18.9152	1.34425
$199$	14.7729	1.04722	0.523612	−	0.851957i	$-0.324584\pi$
$199$	14.7729	1.04722	0.523612	+	0.851957i	$0.324584\pi$
$200$	−0.410497	−0.0290265
$201$	17.8092	1.25617
$202$	11.6651	0.820751
$203$	1.82469	0.128068
$204$	−5.84683	−0.409360
$205$	−6.61145	−0.461763
$206$	−36.0794	−2.51377
$207$	0.645597	0.0448721
$208$	−11.2990	−0.783448
$209$	−9.00519	−0.622902
$210$	−3.00579	−0.207419
$211$	0.238719	0.0164341	0.00821705	−	0.999966i	$-0.497384\pi$
$211$	0.238719	0.0164341	0.00821705	+	0.999966i	$0.497384\pi$
$212$	1.72649	0.118576
$213$	2.65729	0.182075
$214$	−0.0389537	−0.00266282
$215$	0.716223	0.0488460
$216$	1.15757	0.0787630
$217$	0.855198	0.0580546
$218$	−19.6723	−1.33237
$219$	16.7727	1.13339
$220$	−5.00032	−0.337121
$221$	3.17452	0.213541
$222$	2.40844	0.161644
$223$	−13.7601	−0.921441	−0.460721	−	0.887545i	$-0.652409\pi$
$223$	−13.7601	−0.921441	−0.460721	+	0.887545i	$0.652409\pi$
$224$	−4.47921	−0.299280
$225$	4.06121	0.270747
$226$	35.3011	2.34819
$227$	29.4973	1.95781	0.978903	−	0.204327i	$-0.0655007\pi$
$227$	29.4973	1.95781	0.978903	+	0.204327i	$0.0655007\pi$
$228$	−23.1684	−1.53437
$229$	−5.69112	−0.376080	−0.188040	−	0.982161i	$-0.560213\pi$
$229$	−5.69112	−0.376080	−0.188040	+	0.982161i	$0.560213\pi$
$230$	−0.325797	−0.0214824
$231$	−3.33300	−0.219295
$232$	1.35713	0.0890996
$233$	−7.28482	−0.477245	−0.238622	−	0.971112i	$-0.576696\pi$
$233$	−7.28482	−0.477245	−0.238622	+	0.971112i	$0.576696\pi$
$234$	−26.4224	−1.72729
$235$	8.62993	0.562954
$236$	25.5738	1.66472
$237$	29.3220	1.90467
$238$	1.13115	0.0733214
$239$	11.5377	0.746309	0.373154	−	0.927769i	$-0.378276\pi$
$239$	11.5377	0.746309	0.373154	+	0.927769i	$0.378276\pi$
$240$	9.45808	0.610517
$241$	−30.3892	−1.95754	−0.978769	−	0.204965i	$-0.934292\pi$
$241$	−30.3892	−1.95754	−0.978769	+	0.204965i	$0.934292\pi$
$242$	11.9595	0.768787
$243$	20.9231	1.34222
$244$	−20.7483	−1.32827
$245$	−6.69538	−0.427752
$246$	−36.0061	−2.29566
$247$	12.5792	0.800398
$248$	0.636058	0.0403897
$249$	−25.4905	−1.61540
$250$	−2.04946	−0.129619
$251$	4.20804	0.265609	0.132804	−	0.991142i	$-0.457602\pi$
$251$	4.20804	0.265609	0.132804	+	0.991142i	$0.457602\pi$
$252$	−4.93191	−0.310681
$253$	−0.361263	−0.0227124
$254$	−5.41282	−0.339631
$255$	−2.65729	−0.166406
$256$	12.3315	0.770722
$257$	3.09654	0.193157	0.0965785	−	0.995325i	$-0.469210\pi$
$257$	3.09654	0.193157	0.0965785	+	0.995325i	$0.469210\pi$
$258$	3.90057	0.242839
$259$	−0.244083	−0.0151666
$260$	6.98488	0.433184
$261$	−13.4266	−0.831084
$262$	17.5866	1.08651
$263$	2.82000	0.173889	0.0869443	−	0.996213i	$-0.472290\pi$
$263$	2.82000	0.173889	0.0869443	+	0.996213i	$0.472290\pi$
$264$	−2.47894	−0.152568
$265$	0.784664	0.0482015
$266$	4.48224	0.274824
$267$	13.1221	0.803061
$268$	−14.7464	−0.900781
$269$	25.5272	1.55642	0.778212	−	0.628002i	$-0.216127\pi$
$269$	25.5272	1.55642	0.778212	+	0.628002i	$0.216127\pi$
$270$	5.77935	0.351720
$271$	32.2714	1.96035	0.980173	−	0.198142i	$-0.0634909\pi$
$271$	32.2714	1.96035	0.980173	+	0.198142i	$0.0634909\pi$
$272$	−3.55929	−0.215814
$273$	4.65583	0.281783
$274$	−8.32382	−0.502860
$275$	−2.27257	−0.137041
$276$	−0.929452	−0.0559464
$277$	−0.530774	−0.0318911	−0.0159456	−	0.999873i	$-0.505076\pi$
$277$	−0.530774	−0.0318911	−0.0159456	+	0.999873i	$0.505076\pi$
$278$	19.2890	1.15688
$279$	−6.29278	−0.376739
$280$	0.226563	0.0135397
$281$	−6.88188	−0.410539	−0.205269	−	0.978706i	$-0.565807\pi$
$281$	−6.88188	−0.410539	−0.205269	+	0.978706i	$0.565807\pi$
$282$	46.9988	2.79874
$283$	5.30648	0.315437	0.157719	−	0.987484i	$-0.449586\pi$
$283$	5.30648	0.315437	0.157719	+	0.987484i	$0.449586\pi$
$284$	−2.20029	−0.130563
$285$	−10.5297	−0.623725
$286$	14.7854	0.874282
$287$	3.64902	0.215395
$288$	32.9592	1.94214
$289$	1.00000	0.0588235
$290$	6.77564	0.397879
$291$	45.9681	2.69470
$292$	−13.8881	−0.812741
$293$	−24.4414	−1.42788	−0.713940	−	0.700207i	$-0.753091\pi$
$293$	−24.4414	−1.42788	−0.713940	+	0.700207i	$0.753091\pi$
$294$	−36.4632	−2.12658
$295$	11.6229	0.676712
$296$	−0.181538	−0.0105517
$297$	6.40849	0.371858
$298$	−9.35874	−0.542137
$299$	0.504643	0.0291843
$300$	−5.84683	−0.337567
$301$	−0.395301	−0.0227848
$302$	−45.3373	−2.60887
$303$	15.1247	0.868891
$304$	−14.1039	−0.808916
$305$	−9.42978	−0.539948
$306$	−8.32329	−0.475811
$307$	−10.0341	−0.572675	−0.286338	−	0.958129i	$-0.592438\pi$
$307$	−10.0341	−0.572675	−0.286338	+	0.958129i	$0.592438\pi$
$308$	2.75979	0.157254
$309$	−46.7799	−2.66121
$310$	3.17561	0.180363
$311$	20.0249	1.13551	0.567753	−	0.823199i	$-0.307813\pi$
$311$	20.0249	1.13551	0.567753	+	0.823199i	$0.307813\pi$
$312$	3.46280	0.196042
$313$	5.37569	0.303852	0.151926	−	0.988392i	$-0.451452\pi$
$313$	5.37569	0.303852	0.151926	+	0.988392i	$0.451452\pi$
$314$	−31.3076	−1.76679
$315$	−2.24148	−0.126293
$316$	−24.2792	−1.36581
$317$	−13.4983	−0.758141	−0.379070	−	0.925368i	$-0.623756\pi$
$317$	−13.4983	−0.758141	−0.379070	+	0.925368i	$0.623756\pi$
$318$	4.27330	0.239635
$319$	7.51323	0.420660
$320$	−9.51409	−0.531854
$321$	−0.0505067	−0.00281901
$322$	0.179815	0.0100207
$323$	3.96256	0.220483
$324$	−10.3199	−0.573326
$325$	3.17452	0.176091
$326$	11.4624	0.634846
$327$	−25.5067	−1.41052
$328$	2.71398	0.149854
$329$	−4.76306	−0.262596
$330$	−12.3764	−0.681301
$331$	−30.5546	−1.67943	−0.839717	−	0.543024i	$-0.817279\pi$
$331$	−30.5546	−1.67943	−0.839717	+	0.543024i	$0.817279\pi$
$332$	21.1067	1.15838
$333$	1.79603	0.0984216
$334$	12.9376	0.707912
$335$	−6.70202	−0.366171
$336$	−5.22014	−0.284782
$337$	10.9744	0.597812	0.298906	−	0.954283i	$-0.403378\pi$
$337$	10.9744	0.597812	0.298906	+	0.954283i	$0.403378\pi$
$338$	5.98940	0.325781
$339$	45.7707	2.48592
$340$	2.20029	0.119328
$341$	3.52131	0.190689
$342$	−32.9816	−1.78344
$343$	7.55881	0.408137
$344$	−0.294007	−0.0158518
$345$	−0.422421	−0.0227424
$346$	−23.4948	−1.26309
$347$	−2.32535	−0.124831	−0.0624156	−	0.998050i	$-0.519880\pi$
$347$	−2.32535	−0.124831	−0.0624156	+	0.998050i	$0.519880\pi$
$348$	19.3299	1.03619
$349$	−33.4093	−1.78836	−0.894179	−	0.447710i	$-0.852240\pi$
$349$	−33.4093	−1.78836	−0.894179	+	0.447710i	$0.852240\pi$
$350$	1.13115	0.0604624
$351$	−8.95194	−0.477819
$352$	−18.4433	−0.983031
$353$	13.7311	0.730834	0.365417	−	0.930844i	$-0.380926\pi$
$353$	13.7311	0.730834	0.365417	+	0.930844i	$0.380926\pi$
$354$	63.2987	3.36429
$355$	−1.00000	−0.0530745
$356$	−10.8654	−0.575865
$357$	1.46662	0.0776220
$358$	25.9839	1.37329
$359$	−15.3800	−0.811725	−0.405862	−	0.913934i	$-0.633029\pi$
$359$	−15.3800	−0.811725	−0.405862	+	0.913934i	$0.633029\pi$
$360$	−1.66711	−0.0878645
$361$	−3.29808	−0.173583
$362$	−33.0287	−1.73595
$363$	15.5065	0.813879
$364$	−3.85512	−0.202063
$365$	−6.31194	−0.330382
$366$	−51.3548	−2.68436
$367$	−0.701464	−0.0366161	−0.0183081	−	0.999832i	$-0.505828\pi$
$367$	−0.701464	−0.0366161	−0.0183081	+	0.999832i	$0.505828\pi$
$368$	−0.565809	−0.0294949
$369$	−26.8504	−1.39778
$370$	−0.906353	−0.0471190
$371$	−0.433075	−0.0224841
$372$	9.05957	0.469717
$373$	4.36337	0.225927	0.112963	−	0.993599i	$-0.463966\pi$
$373$	4.36337	0.225927	0.112963	+	0.993599i	$0.463966\pi$
$374$	4.65754	0.240836
$375$	−2.65729	−0.137222
$376$	−3.54256	−0.182693
$377$	−10.4951	−0.540527
$378$	−3.18976	−0.164064
$379$	−25.4582	−1.30770	−0.653851	−	0.756623i	$-0.726848\pi$
$379$	−25.4582	−1.30770	−0.653851	+	0.756623i	$0.726848\pi$
$380$	8.71881	0.447266
$381$	−7.01816	−0.359551
$382$	−14.6018	−0.747096
$383$	−9.38923	−0.479767	−0.239884	−	0.970802i	$-0.577109\pi$
$383$	−9.38923	−0.479767	−0.239884	+	0.970802i	$0.577109\pi$
$384$	−8.68272	−0.443088
$385$	1.25428	0.0639242
$386$	−4.45886	−0.226950
$387$	2.90873	0.147859
$388$	−38.0626	−1.93234
$389$	−36.5682	−1.85408	−0.927042	−	0.374958i	$-0.877657\pi$
$389$	−36.5682	−1.85408	−0.927042	+	0.374958i	$0.877657\pi$
$390$	17.2885	0.875437
$391$	0.158967	0.00803930
$392$	2.74843	0.138817
$393$	22.8025	1.15023
$394$	−43.4722	−2.19010
$395$	−11.0345	−0.555208
$396$	−20.3073	−1.02048
$397$	−31.8481	−1.59841	−0.799205	−	0.601059i	$-0.794746\pi$
$397$	−31.8481	−1.59841	−0.799205	+	0.601059i	$0.794746\pi$
$398$	−30.2765	−1.51762
$399$	5.81159	0.290944
$400$	−3.55929	−0.177965
$401$	−19.9722	−0.997366	−0.498683	−	0.866784i	$-0.666183\pi$
$401$	−19.9722	−0.997366	−0.498683	+	0.866784i	$0.666183\pi$
$402$	−36.4993	−1.82042
$403$	−4.91887	−0.245026
$404$	−12.5236	−0.623071
$405$	−4.69022	−0.233059
$406$	−3.73964	−0.185595
$407$	−1.00502	−0.0498169
$408$	1.09081	0.0540031
$409$	24.4118	1.20709	0.603543	−	0.797331i	$-0.293755\pi$
$409$	24.4118	1.20709	0.603543	+	0.797331i	$0.293755\pi$
$410$	13.5499	0.669182
$411$	−10.7925	−0.532355
$412$	38.7347	1.90832
$413$	−6.41497	−0.315660
$414$	−1.32313	−0.0650281
$415$	9.59267	0.470886
$416$	25.7632	1.26315
$417$	25.0097	1.22473
$418$	18.4558	0.902703
$419$	−16.1910	−0.790981	−0.395490	−	0.918470i	$-0.629425\pi$
$419$	−16.1910	−0.790981	−0.395490	+	0.918470i	$0.629425\pi$
$420$	3.22700	0.157462
$421$	8.48222	0.413398	0.206699	−	0.978405i	$-0.433728\pi$
$421$	8.48222	0.413398	0.206699	+	0.978405i	$0.433728\pi$
$422$	−0.489246	−0.0238161
$423$	35.0479	1.70409
$424$	−0.322102	−0.0156427
$425$	1.00000	0.0485071
$426$	−5.44602	−0.263861
$427$	5.20452	0.251865
$428$	0.0418206	0.00202147
$429$	19.1705	0.925562
$430$	−1.46787	−0.0707871
$431$	−12.1853	−0.586947	−0.293473	−	0.955967i	$-0.594811\pi$
$431$	−12.1853	−0.586947	−0.293473	+	0.955967i	$0.594811\pi$
$432$	10.0370	0.482904
$433$	−13.7375	−0.660180	−0.330090	−	0.943950i	$-0.607079\pi$
$433$	−13.7375	−0.660180	−0.330090	+	0.943950i	$0.607079\pi$
$434$	−1.75270	−0.0841321
$435$	8.78516	0.421216
$436$	21.1201	1.01147
$437$	0.629916	0.0301330
$438$	−34.3750	−1.64250
$439$	29.6319	1.41425	0.707127	−	0.707087i	$-0.249991\pi$
$439$	29.6319	1.41425	0.707127	+	0.707087i	$0.249991\pi$
$440$	0.932881	0.0444733
$441$	−27.1913	−1.29482
$442$	−6.50606	−0.309462
$443$	27.7615	1.31899	0.659495	−	0.751709i	$-0.270770\pi$
$443$	27.7615	1.31899	0.659495	+	0.751709i	$0.270770\pi$
$444$	−2.58570	−0.122712
$445$	−4.93816	−0.234091
$446$	28.2007	1.33534
$447$	−12.1344	−0.573935
$448$	5.25105	0.248089
$449$	17.8956	0.844544	0.422272	−	0.906469i	$-0.361233\pi$
$449$	17.8956	0.844544	0.422272	+	0.906469i	$0.361233\pi$
$450$	−8.32329	−0.392364
$451$	15.0249	0.707497
$452$	−37.8991	−1.78262
$453$	−58.7835	−2.76189
$454$	−60.4536	−2.83723
$455$	−1.75209	−0.0821394
$456$	4.32241	0.202415
$457$	−24.0766	−1.12625	−0.563127	−	0.826370i	$-0.690402\pi$
$457$	−24.0766	−1.12625	−0.563127	+	0.826370i	$0.690402\pi$
$458$	11.6637	0.545011
$459$	−2.81994	−0.131623
$460$	0.349774	0.0163083
$461$	34.1364	1.58989	0.794945	−	0.606682i	$-0.207500\pi$
$461$	34.1364	1.58989	0.794945	+	0.606682i	$0.207500\pi$
$462$	6.83086	0.317800
$463$	9.27737	0.431156	0.215578	−	0.976487i	$-0.430836\pi$
$463$	9.27737	0.431156	0.215578	+	0.976487i	$0.430836\pi$
$464$	11.7672	0.546280
$465$	4.11744	0.190941
$466$	14.9300	0.691618
$467$	−34.8045	−1.61056	−0.805281	−	0.592893i	$-0.797986\pi$
$467$	−34.8045	−1.61056	−0.805281	+	0.592893i	$0.797986\pi$
$468$	28.3670	1.31127
$469$	3.69901	0.170804
$470$	−17.6867	−0.815827
$471$	−40.5928	−1.87042
$472$	−4.77117	−0.219611
$473$	−1.62766	−0.0748401
$474$	−60.0944	−2.76023
$475$	3.96256	0.181815
$476$	−1.21440	−0.0556617
$477$	3.18668	0.145908
$478$	−23.6460	−1.08154
$479$	−0.573652	−0.0262108	−0.0131054	−	0.999914i	$-0.504172\pi$
$479$	−0.573652	−0.0262108	−0.0131054	+	0.999914i	$0.504172\pi$
$480$	−21.5656	−0.984331
$481$	1.40390	0.0640122
$482$	62.2815	2.83684
$483$	0.233145	0.0106084
$484$	−12.8397	−0.583623
$485$	−17.2989	−0.785501
$486$	−42.8811	−1.94513
$487$	−2.88641	−0.130796	−0.0653979	−	0.997859i	$-0.520832\pi$
$487$	−2.88641	−0.130796	−0.0653979	+	0.997859i	$0.520832\pi$
$488$	3.87089	0.175227
$489$	14.8620	0.672082
$490$	13.7219	0.619893
$491$	14.4974	0.654260	0.327130	−	0.944979i	$-0.393918\pi$
$491$	14.4974	0.654260	0.327130	+	0.944979i	$0.393918\pi$
$492$	38.6560	1.74275
$493$	−3.30606	−0.148897
$494$	−25.7807	−1.15993
$495$	−9.22936	−0.414829
$496$	5.51507	0.247634
$497$	0.551924	0.0247572
$498$	52.2419	2.34101
$499$	−22.9686	−1.02822	−0.514109	−	0.857725i	$-0.671877\pi$
$499$	−22.9686	−1.02822	−0.514109	+	0.857725i	$0.671877\pi$
$500$	2.20029	0.0984002
$501$	16.7746	0.749434
$502$	−8.62421	−0.384917
$503$	10.1919	0.454432	0.227216	−	0.973844i	$-0.427038\pi$
$503$	10.1919	0.454432	0.227216	+	0.973844i	$0.427038\pi$
$504$	0.920119	0.0409854
$505$	−5.69177	−0.253280
$506$	0.740394	0.0329145
$507$	7.76574	0.344889
$508$	5.81119	0.257830
$509$	−30.1304	−1.33551	−0.667754	−	0.744382i	$-0.732744\pi$
$509$	−30.1304	−1.33551	−0.667754	+	0.744382i	$0.732744\pi$
$510$	5.44602	0.241154
$511$	3.48371	0.154110
$512$	−31.8080	−1.40573
$513$	−11.1742	−0.493352
$514$	−6.34624	−0.279921
$515$	17.6043	0.775740
$516$	−4.18763	−0.184350
$517$	−19.6121	−0.862538
$518$	0.500238	0.0219792
$519$	−30.4629	−1.33717
$520$	−1.30313	−0.0571460
$521$	29.9980	1.31424	0.657118	−	0.753787i	$-0.271775\pi$
$521$	29.9980	1.31424	0.657118	+	0.753787i	$0.271775\pi$
$522$	27.5173	1.20440
$523$	−44.5473	−1.94792	−0.973958	−	0.226729i	$-0.927197\pi$
$523$	−44.5473	−1.94792	−0.973958	+	0.226729i	$0.927197\pi$
$524$	−18.8809	−0.824817
$525$	1.46662	0.0640087
$526$	−5.77948	−0.251997
$527$	−1.54948	−0.0674966
$528$	−21.4941	−0.935411
$529$	−22.9747	−0.998901
$530$	−1.60814	−0.0698531
$531$	47.2031	2.04844
$532$	−4.81212	−0.208632
$533$	−20.9882	−0.909098
$534$	−26.8933	−1.16379
$535$	0.0190068	0.000821736 0
$536$	2.75116	0.118832
$537$	33.6903	1.45384
$538$	−52.3171	−2.25555
$539$	15.2157	0.655386
$540$	−6.20469	−0.267007
$541$	20.4424	0.878888	0.439444	−	0.898270i	$-0.355175\pi$
$541$	20.4424	0.878888	0.439444	+	0.898270i	$0.355175\pi$
$542$	−66.1390	−2.84091
$543$	−42.8243	−1.83777
$544$	8.11563	0.347955
$545$	9.59875	0.411165
$546$	−9.54194	−0.408357
$547$	−37.7304	−1.61324	−0.806618	−	0.591073i	$-0.798705\pi$
$547$	−37.7304	−1.61324	−0.806618	+	0.591073i	$0.798705\pi$
$548$	8.93642	0.381745
$549$	−38.2963	−1.63445
$550$	4.65754	0.198598
$551$	−13.1005	−0.558099
$552$	0.173403	0.00738051
$553$	6.09023	0.258983
$554$	1.08780	0.0462162
$555$	−1.17516	−0.0498827
$556$	−20.7086	−0.878239
$557$	−46.2801	−1.96095	−0.980475	−	0.196644i	$-0.936996\pi$
$557$	−46.2801	−1.96095	−0.980475	+	0.196644i	$0.936996\pi$
$558$	12.8968	0.545965
$559$	2.27366	0.0961658
$560$	1.96446	0.0830135
$561$	6.03887	0.254961
$562$	14.1042	0.594948
$563$	−17.6292	−0.742981	−0.371490	−	0.928437i	$-0.621153\pi$
$563$	−17.6292	−0.742981	−0.371490	+	0.928437i	$0.621153\pi$
$564$	−50.4577	−2.12465
$565$	−17.2245	−0.724642
$566$	−10.8754	−0.457128
$567$	2.58865	0.108713
$568$	0.410497	0.0172241
$569$	−36.0867	−1.51283	−0.756416	−	0.654091i	$-0.773051\pi$
$569$	−36.0867	−1.51283	−0.756416	+	0.654091i	$0.773051\pi$
$570$	21.5802	0.903896
$571$	−17.1173	−0.716335	−0.358168	−	0.933657i	$-0.616598\pi$
$571$	−17.1173	−0.716335	−0.358168	+	0.933657i	$0.616598\pi$
$572$	−15.8736	−0.663708
$573$	−18.9325	−0.790916
$574$	−7.47852	−0.312147
$575$	0.158967	0.00662938
$576$	−38.6387	−1.60994
$577$	4.31769	0.179748	0.0898739	−	0.995953i	$-0.471354\pi$
$577$	4.31769	0.179748	0.0898739	+	0.995953i	$0.471354\pi$
$578$	−2.04946	−0.0852464
$579$	−5.78127	−0.240261
$580$	−7.27430	−0.302049
$581$	−5.29443	−0.219650
$582$	−94.2100	−3.90513
$583$	−1.78320	−0.0738527
$584$	2.59103	0.107218
$585$	12.8924	0.533034
$586$	50.0916	2.06927
$587$	−17.6392	−0.728047	−0.364024	−	0.931390i	$-0.618597\pi$
$587$	−17.6392	−0.728047	−0.364024	+	0.931390i	$0.618597\pi$
$588$	39.1467	1.61438
$589$	−6.13993	−0.252992
$590$	−23.8207	−0.980684
$591$	−56.3652	−2.31855
$592$	−1.57406	−0.0646934
$593$	39.7798	1.63356	0.816781	−	0.576948i	$-0.195757\pi$
$593$	39.7798	1.63356	0.816781	+	0.576948i	$0.195757\pi$
$594$	−13.1340	−0.538893
$595$	−0.551924	−0.0226267
$596$	10.0475	0.411562
$597$	−39.2559	−1.60664
$598$	−1.03425	−0.0422935
$599$	42.2681	1.72703	0.863513	−	0.504326i	$-0.168259\pi$
$599$	42.2681	1.72703	0.863513	+	0.504326i	$0.168259\pi$
$600$	1.09081	0.0445321
$601$	−16.4988	−0.673001	−0.336501	−	0.941683i	$-0.609243\pi$
$601$	−16.4988	−0.673001	−0.336501	+	0.941683i	$0.609243\pi$
$602$	0.810154	0.0330194
$603$	−27.2183	−1.10841
$604$	48.6740	1.98052
$605$	−5.83544	−0.237245
$606$	−30.9975	−1.25919
$607$	23.1949	0.941451	0.470725	−	0.882280i	$-0.343992\pi$
$607$	23.1949	0.941451	0.470725	+	0.882280i	$0.343992\pi$
$608$	32.1587	1.30421
$609$	−4.84874	−0.196481
$610$	19.3260	0.782486
$611$	27.3959	1.10832
$612$	8.93585	0.361210
$613$	−40.0104	−1.61601	−0.808003	−	0.589178i	$-0.799452\pi$
$613$	−40.0104	−1.61601	−0.808003	+	0.589178i	$0.799452\pi$
$614$	20.5645	0.829914
$615$	17.5685	0.708432
$616$	−0.514879	−0.0207451
$617$	26.3027	1.05891	0.529454	−	0.848338i	$-0.322397\pi$
$617$	26.3027	1.05891	0.529454	+	0.848338i	$0.322397\pi$
$618$	95.8736	3.85660
$619$	−34.4151	−1.38326	−0.691631	−	0.722251i	$-0.743107\pi$
$619$	−34.4151	−1.38326	−0.691631	+	0.722251i	$0.743107\pi$
$620$	−3.40932	−0.136922
$621$	−0.448276	−0.0179887
$622$	−41.0402	−1.64556
$623$	2.72549	0.109194
$624$	30.0249	1.20196
$625$	1.00000	0.0400000
$626$	−11.0173	−0.440339
$627$	23.9294	0.955649
$628$	33.6117	1.34125
$629$	0.442239	0.0176332
$630$	4.59382	0.183022
$631$	−24.7838	−0.986628	−0.493314	−	0.869851i	$-0.664215\pi$
$631$	−24.7838	−0.986628	−0.493314	+	0.869851i	$0.664215\pi$
$632$	4.52964	0.180180
$633$	−0.634347	−0.0252130
$634$	27.6643	1.09869
$635$	2.64109	0.104809
$636$	−4.58780	−0.181918
$637$	−21.2546	−0.842138
$638$	−15.3981	−0.609616
$639$	−4.06121	−0.160659
$640$	3.26750	0.129159
$641$	−15.5907	−0.615797	−0.307898	−	0.951419i	$-0.599626\pi$
$641$	−15.5907	−0.615797	−0.307898	+	0.951419i	$0.599626\pi$
$642$	0.103511	0.00408527
$643$	23.2427	0.916601	0.458300	−	0.888797i	$-0.348458\pi$
$643$	23.2427	0.916601	0.458300	+	0.888797i	$0.348458\pi$
$644$	−0.193049	−0.00760718
$645$	−1.90321	−0.0749390
$646$	−8.12113	−0.319521
$647$	37.8722	1.48891	0.744455	−	0.667673i	$-0.232709\pi$
$647$	37.8722	1.48891	0.744455	+	0.667673i	$0.232709\pi$
$648$	1.92532	0.0756337
$649$	−26.4139	−1.03683
$650$	−6.50606	−0.255189
$651$	−2.27251	−0.0890668
$652$	−12.3060	−0.481941
$653$	27.0289	1.05772	0.528861	−	0.848708i	$-0.322619\pi$
$653$	27.0289	1.05772	0.528861	+	0.848708i	$0.322619\pi$
$654$	52.2750	2.04411
$655$	−8.58109	−0.335291
$656$	23.5321	0.918773
$657$	−25.6341	−1.00008
$658$	9.76172	0.380551
$659$	−16.9532	−0.660404	−0.330202	−	0.943910i	$-0.607117\pi$
$659$	−16.9532	−0.660404	−0.330202	+	0.943910i	$0.607117\pi$
$660$	13.2873	0.517208
$661$	33.7798	1.31388	0.656941	−	0.753942i	$-0.271850\pi$
$661$	33.7798	1.31388	0.656941	+	0.753942i	$0.271850\pi$
$662$	62.6205	2.43382
$663$	−8.43563	−0.327613
$664$	−3.93776	−0.152815
$665$	−2.18703	−0.0848096
$666$	−3.68089	−0.142631
$667$	−0.525553	−0.0203495
$668$	−13.8897	−0.537410
$669$	36.5645	1.41366
$670$	13.7355	0.530650
$671$	21.4298	0.827288
$672$	11.9026	0.459152
$673$	33.6056	1.29540	0.647701	−	0.761895i	$-0.275731\pi$
$673$	33.6056	1.29540	0.647701	+	0.761895i	$0.275731\pi$
$674$	−22.4915	−0.866342
$675$	−2.81994	−0.108539
$676$	−6.43020	−0.247315
$677$	15.7887	0.606808	0.303404	−	0.952862i	$-0.401877\pi$
$677$	15.7887	0.606808	0.303404	+	0.952862i	$0.401877\pi$
$678$	−93.8053	−3.60257
$679$	9.54766	0.366405
$680$	−0.410497	−0.0157418
$681$	−78.3830	−3.00364
$682$	−7.21679	−0.276345
$683$	−1.01826	−0.0389627	−0.0194813	−	0.999810i	$-0.506201\pi$
$683$	−1.01826	−0.0389627	−0.0194813	+	0.999810i	$0.506201\pi$
$684$	35.4089	1.35389
$685$	4.06146	0.155181
$686$	−15.4915	−0.591468
$687$	15.1230	0.576977
$688$	−2.54925	−0.0971892
$689$	2.49093	0.0948969
$690$	0.865737	0.0329580
$691$	−1.12770	−0.0428996	−0.0214498	−	0.999770i	$-0.506828\pi$
$691$	−1.12770	−0.0428996	−0.0214498	+	0.999770i	$0.506828\pi$
$692$	25.2239	0.958871
$693$	5.09391	0.193501
$694$	4.76571	0.180904
$695$	−9.41172	−0.357007
$696$	−3.60628	−0.136696
$697$	−6.61145	−0.250426
$698$	68.4710	2.59167
$699$	19.3579	0.732184
$700$	−1.21440	−0.0458998
$701$	25.6795	0.969901	0.484951	−	0.874542i	$-0.338838\pi$
$701$	25.6795	0.969901	0.484951	+	0.874542i	$0.338838\pi$
$702$	18.3467	0.692450
$703$	1.75240	0.0660931
$704$	21.6214	0.814887
$705$	−22.9322	−0.863678
$706$	−28.1414	−1.05912
$707$	3.14142	0.118145
$708$	−67.9572	−2.55399
$709$	−22.3618	−0.839816	−0.419908	−	0.907567i	$-0.637938\pi$
$709$	−22.3618	−0.839816	−0.419908	+	0.907567i	$0.637938\pi$
$710$	2.04946	0.0769149
$711$	−44.8136	−1.68064
$712$	2.02710	0.0759687
$713$	−0.246317	−0.00922463
$714$	−3.00579	−0.112489
$715$	−7.21431	−0.269800
$716$	−27.8963	−1.04253
$717$	−30.6589	−1.14498
$718$	31.5207	1.17634
$719$	−29.3493	−1.09455	−0.547273	−	0.836954i	$-0.684334\pi$
$719$	−29.3493	−1.09455	−0.547273	+	0.836954i	$0.684334\pi$
$720$	−14.4550	−0.538707
$721$	−9.71626	−0.361852
$722$	6.75929	0.251555
$723$	80.7529	3.00323
$724$	35.4594	1.31784
$725$	−3.30606	−0.122784
$726$	−31.7799	−1.17946
$727$	1.58027	0.0586089	0.0293044	−	0.999571i	$-0.490671\pi$
$727$	1.58027	0.0586089	0.0293044	+	0.999571i	$0.490671\pi$
$728$	0.719229	0.0266564
$729$	−41.5282	−1.53808
$730$	12.9361	0.478786
$731$	0.716223	0.0264905
$732$	55.1343	2.03782
$733$	−22.0357	−0.813905	−0.406953	−	0.913449i	$-0.633409\pi$
$733$	−22.0357	−0.813905	−0.406953	+	0.913449i	$0.633409\pi$
$734$	1.43762	0.0530636
$735$	17.7916	0.656253
$736$	1.29012	0.0475543
$737$	15.2308	0.561033
$738$	55.0290	2.02564
$739$	−27.4740	−1.01065	−0.505324	−	0.862930i	$-0.668627\pi$
$739$	−27.4740	−1.01065	−0.505324	+	0.862930i	$0.668627\pi$
$740$	0.973057	0.0357703
$741$	−33.4267	−1.22796
$742$	0.887571	0.0325838
$743$	−49.0199	−1.79837	−0.899183	−	0.437572i	$-0.855839\pi$
$743$	−49.0199	−1.79837	−0.899183	+	0.437572i	$0.855839\pi$
$744$	−1.69019	−0.0619655
$745$	4.56644	0.167301
$746$	−8.94256	−0.327410
$747$	38.9578	1.42539
$748$	−5.00032	−0.182830
$749$	−0.0104903	−0.000383308 0
$750$	5.44602	0.198861
$751$	−27.1706	−0.991469	−0.495734	−	0.868474i	$-0.665101\pi$
$751$	−27.1706	−0.991469	−0.495734	+	0.868474i	$0.665101\pi$
$752$	−30.7164	−1.12011
$753$	−11.1820	−0.407494
$754$	21.5094	0.783326
$755$	22.1216	0.805086
$756$	3.42452	0.124549
$757$	−30.0725	−1.09300	−0.546501	−	0.837458i	$-0.684041\pi$
$757$	−30.0725	−1.09300	−0.546501	+	0.837458i	$0.684041\pi$
$758$	52.1757	1.89511
$759$	0.959981	0.0348451
$760$	−1.62662	−0.0590037
$761$	11.7677	0.426580	0.213290	−	0.976989i	$-0.431582\pi$
$761$	11.7677	0.426580	0.213290	+	0.976989i	$0.431582\pi$
$762$	14.3835	0.521058
$763$	−5.29778	−0.191792
$764$	15.6765	0.567156
$765$	4.06121	0.146833
$766$	19.2429	0.695273
$767$	36.8972	1.33228
$768$	−32.7685	−1.18243
$769$	−29.1226	−1.05019	−0.525093	−	0.851045i	$-0.675969\pi$
$769$	−29.1226	−1.05019	−0.525093	+	0.851045i	$0.675969\pi$
$770$	−2.57061	−0.0926383
$771$	−8.22842	−0.296339
$772$	4.78702	0.172288
$773$	45.0081	1.61883	0.809414	−	0.587239i	$-0.199785\pi$
$773$	45.0081	1.61883	0.809414	+	0.587239i	$0.199785\pi$
$774$	−5.96133	−0.214276
$775$	−1.54948	−0.0556591
$776$	7.10112	0.254915
$777$	0.648599	0.0232684
$778$	74.9452	2.68692
$779$	−26.1983	−0.938651
$780$	−18.5609	−0.664586
$781$	2.27257	0.0813188
$782$	−0.325797	−0.0116505
$783$	9.32287	0.333172
$784$	23.8308	0.851101
$785$	15.2760	0.545224
$786$	−46.7328	−1.66690
$787$	−32.2111	−1.14820	−0.574100	−	0.818785i	$-0.694648\pi$
$787$	−32.2111	−1.14820	−0.574100	+	0.818785i	$0.694648\pi$
$788$	46.6716	1.66261
$789$	−7.49357	−0.266778
$790$	22.6149	0.804601
$791$	9.50664	0.338017
$792$	3.78862	0.134623
$793$	−29.9350	−1.06302
$794$	65.2714	2.31640
$795$	−2.08508	−0.0739503
$796$	32.5047	1.15210
$797$	7.66955	0.271669	0.135835	−	0.990732i	$-0.456628\pi$
$797$	7.66955	0.271669	0.135835	+	0.990732i	$0.456628\pi$
$798$	−11.9106	−0.421632
$799$	8.62993	0.305305
$800$	8.11563	0.286931
$801$	−20.0549	−0.708604
$802$	40.9324	1.44537
$803$	14.3443	0.506199
$804$	39.1856	1.38197
$805$	−0.0877376	−0.00309234
$806$	10.0810	0.355089
$807$	−67.8334	−2.38785
$808$	2.33645	0.0821961
$809$	−13.9473	−0.490361	−0.245180	−	0.969477i	$-0.578847\pi$
$809$	−13.9473	−0.490361	−0.245180	+	0.969477i	$0.578847\pi$
$810$	9.61243	0.337746
$811$	2.02281	0.0710306	0.0355153	−	0.999369i	$-0.488693\pi$
$811$	2.02281	0.0710306	0.0355153	+	0.999369i	$0.488693\pi$
$812$	4.01486	0.140894
$813$	−85.7545	−3.00754
$814$	2.05975	0.0721941
$815$	−5.59290	−0.195911
$816$	9.45808	0.331099
$817$	2.83808	0.0992919
$818$	−50.0310	−1.74929
$819$	−7.11561	−0.248640
$820$	−14.5471	−0.508008
$821$	31.1429	1.08689	0.543447	−	0.839443i	$-0.317119\pi$
$821$	31.1429	1.08689	0.543447	+	0.839443i	$0.317119\pi$
$822$	22.1188	0.771483
$823$	−29.2483	−1.01953	−0.509766	−	0.860313i	$-0.670268\pi$
$823$	−29.2483	−1.01953	−0.509766	+	0.860313i	$0.670268\pi$
$824$	−7.22652	−0.251748
$825$	6.03887	0.210247
$826$	13.1472	0.457451
$827$	12.1737	0.423321	0.211661	−	0.977343i	$-0.432113\pi$
$827$	12.1737	0.423321	0.211661	+	0.977343i	$0.432113\pi$
$828$	1.42050	0.0493659
$829$	−13.7500	−0.477558	−0.238779	−	0.971074i	$-0.576747\pi$
$829$	−13.7500	−0.477558	−0.238779	+	0.971074i	$0.576747\pi$
$830$	−19.6598	−0.682402
$831$	1.41042	0.0489270
$832$	−30.2027	−1.04709
$833$	−6.69538	−0.231981
$834$	−51.2565	−1.77487
$835$	−6.31267	−0.218459
$836$	−19.8141	−0.685284
$837$	4.36945	0.151030
$838$	33.1828	1.14628
$839$	−40.4792	−1.39750	−0.698749	−	0.715367i	$-0.746260\pi$
$839$	−40.4792	−1.39750	−0.698749	+	0.715367i	$0.746260\pi$
$840$	−0.602044	−0.0207725
$841$	−18.0700	−0.623103
$842$	−17.3840	−0.599092
$843$	18.2872	0.629844
$844$	0.525253	0.0180799
$845$	−2.92243	−0.100535
$846$	−71.8294	−2.46954
$847$	3.22072	0.110665
$848$	−2.79285	−0.0959068
$849$	−14.1009	−0.483941
$850$	−2.04946	−0.0702960
$851$	0.0703014	0.00240990
$852$	5.84683	0.200309
$853$	−52.8238	−1.80865	−0.904327	−	0.426841i	$-0.859626\pi$
$853$	−52.8238	−1.80865	−0.904327	+	0.426841i	$0.859626\pi$
$854$	−10.6665	−0.364999
$855$	16.0928	0.550362
$856$	−0.00780223	−0.000266675 0
$857$	39.3976	1.34580	0.672899	−	0.739735i	$-0.265049\pi$
$857$	39.3976	1.34580	0.672899	+	0.739735i	$0.265049\pi$
$858$	−39.2893	−1.34131
$859$	2.53769	0.0865849	0.0432925	−	0.999062i	$-0.486215\pi$
$859$	2.53769	0.0865849	0.0432925	+	0.999062i	$0.486215\pi$
$860$	1.57590	0.0537378
$861$	−9.69650	−0.330456
$862$	24.9734	0.850596
$863$	−0.836957	−0.0284904	−0.0142452	−	0.999899i	$-0.504535\pi$
$863$	−0.836957	−0.0284904	−0.0142452	+	0.999899i	$0.504535\pi$
$864$	−22.8856	−0.778582
$865$	11.4639	0.389784
$866$	28.1544	0.956725
$867$	−2.65729	−0.0902464
$868$	1.88169	0.0638686
$869$	25.0767	0.850670
$870$	−18.0049	−0.610422
$871$	−21.2757	−0.720899
$872$	−3.94025	−0.133434
$873$	−70.2542	−2.37775
$874$	−1.29099	−0.0436684
$875$	−0.551924	−0.0186584
$876$	36.9048	1.24690
$877$	3.79927	0.128292	0.0641462	−	0.997941i	$-0.479568\pi$
$877$	3.79927	0.128292	0.0641462	+	0.997941i	$0.479568\pi$
$878$	−60.7295	−2.04952
$879$	64.9479	2.19064
$880$	8.08873	0.272671
$881$	16.1798	0.545111	0.272555	−	0.962140i	$-0.412131\pi$
$881$	16.1798	0.545111	0.272555	+	0.962140i	$0.412131\pi$
$882$	55.7276	1.87645
$883$	8.26903	0.278275	0.139138	−	0.990273i	$-0.455567\pi$
$883$	8.26903	0.278275	0.139138	+	0.990273i	$0.455567\pi$
$884$	6.98488	0.234927
$885$	−30.8855	−1.03820
$886$	−56.8962	−1.91146
$887$	2.82999	0.0950219	0.0475109	−	0.998871i	$-0.484871\pi$
$887$	2.82999	0.0950219	0.0475109	+	0.998871i	$0.484871\pi$
$888$	0.482399	0.0161883
$889$	−1.45768	−0.0488891
$890$	10.1206	0.339242
$891$	10.6588	0.357085
$892$	−30.2762	−1.01372
$893$	34.1966	1.14435
$894$	24.8689	0.831741
$895$	−12.6784	−0.423793
$896$	−1.80341	−0.0602479
$897$	−1.34099	−0.0447742
$898$	−36.6763	−1.22390
$899$	5.12269	0.170851
$900$	8.93585	0.297862
$901$	0.784664	0.0261410
$902$	−30.7931	−1.02530
$903$	1.05043	0.0349561
$904$	7.07062	0.235165
$905$	16.1158	0.535706
$906$	120.475	4.00250
$907$	16.0216	0.531987	0.265993	−	0.963975i	$-0.414300\pi$
$907$	16.0216	0.531987	0.265993	+	0.963975i	$0.414300\pi$
$908$	64.9028	2.15387
$909$	−23.1154	−0.766691
$910$	3.59085	0.119035
$911$	21.1220	0.699803	0.349901	−	0.936787i	$-0.386215\pi$
$911$	21.1220	0.699803	0.349901	+	0.936787i	$0.386215\pi$
$912$	37.4783	1.24103
$913$	−21.8000	−0.721474
$914$	49.3440	1.63216
$915$	25.0577	0.828382
$916$	−12.5221	−0.413743
$917$	4.73611	0.156400
$918$	5.77935	0.190747
$919$	0.349094	0.0115155	0.00575777	−	0.999983i	$-0.498167\pi$
$919$	0.349094	0.0115155	0.00575777	+	0.999983i	$0.498167\pi$
$920$	−0.0652554	−0.00215141
$921$	26.6635	0.878592
$922$	−69.9612	−2.30405
$923$	−3.17452	−0.104491
$924$	−7.33358	−0.241257
$925$	0.442239	0.0145407
$926$	−19.0136	−0.624826
$927$	71.4948	2.34820
$928$	−26.8307	−0.880762
$929$	5.80172	0.190348	0.0951742	−	0.995461i	$-0.469659\pi$
$929$	5.80172	0.190348	0.0951742	+	0.995461i	$0.469659\pi$
$930$	−8.43853	−0.276710
$931$	−26.5309	−0.869514
$932$	−16.0288	−0.525040
$933$	−53.2120	−1.74208
$934$	71.3306	2.33401
$935$	−2.27257	−0.0743209
$936$	−5.29228	−0.172984
$937$	−7.22364	−0.235986	−0.117993	−	0.993014i	$-0.537646\pi$
$937$	−7.22364	−0.235986	−0.117993	+	0.993014i	$0.537646\pi$
$938$	−7.58097	−0.247528
$939$	−14.2848	−0.466167
$940$	18.9884	0.619333
$941$	45.8724	1.49540	0.747700	−	0.664037i	$-0.231158\pi$
$941$	45.8724	1.49540	0.747700	+	0.664037i	$0.231158\pi$
$942$	83.1934	2.71059
$943$	−1.05100	−0.0342253
$944$	−41.3694	−1.34646
$945$	1.55639	0.0506294
$946$	3.33584	0.108457
$947$	9.97314	0.324084	0.162042	−	0.986784i	$-0.448192\pi$
$947$	9.97314	0.324084	0.162042	+	0.986784i	$0.448192\pi$
$948$	64.5171	2.09542
$949$	−20.0374	−0.650441
$950$	−8.12113	−0.263484
$951$	35.8690	1.16313
$952$	0.226563	0.00734295
$953$	0.553048	0.0179150	0.00895749	−	0.999960i	$-0.497149\pi$
$953$	0.553048	0.0179150	0.00895749	+	0.999960i	$0.497149\pi$
$954$	−6.53099	−0.211449
$955$	7.12472	0.230551
$956$	25.3862	0.821050
$957$	−19.9649	−0.645372
$958$	1.17568	0.0379845
$959$	−2.24162	−0.0723857
$960$	25.2817	0.815964
$961$	−28.5991	−0.922551
$962$	−2.87723	−0.0927658
$963$	0.0771906	0.00248743
$964$	−66.8651	−2.15358
$965$	2.17562	0.0700358
$966$	−0.477821	−0.0153736
$967$	−51.9763	−1.67145	−0.835723	−	0.549151i	$-0.814951\pi$
$967$	−51.9763	−1.67145	−0.835723	+	0.549151i	$0.814951\pi$
$968$	2.39543	0.0769920
$969$	−10.5297	−0.338263
$970$	35.4534	1.13834
$971$	−23.8663	−0.765905	−0.382952	−	0.923768i	$-0.625093\pi$
$971$	−23.8663	−0.765905	−0.382952	+	0.923768i	$0.625093\pi$
$972$	46.0370	1.47664
$973$	5.19456	0.166530
$974$	5.91559	0.189548
$975$	−8.43563	−0.270156
$976$	33.5633	1.07434
$977$	10.5605	0.337859	0.168930	−	0.985628i	$-0.445969\pi$
$977$	10.5605	0.337859	0.168930	+	0.985628i	$0.445969\pi$
$978$	−30.4591	−0.973973
$979$	11.2223	0.358666
$980$	−14.7318	−0.470590
$981$	38.9825	1.24462
$982$	−29.7119	−0.948146
$983$	1.11010	0.0354066	0.0177033	−	0.999843i	$-0.494365\pi$
$983$	1.11010	0.0354066	0.0177033	+	0.999843i	$0.494365\pi$
$984$	−7.21183	−0.229905
$985$	21.2115	0.675855
$986$	6.77564	0.215780
$987$	12.6569	0.402872
$988$	27.6780	0.880556
$989$	0.113856	0.00362040
$990$	18.9152	0.601165
$991$	−3.15911	−0.100352	−0.0501762	−	0.998740i	$-0.515978\pi$
$991$	−3.15911	−0.100352	−0.0501762	+	0.998740i	$0.515978\pi$
$992$	−12.5750	−0.399258
$993$	81.1926	2.57657
$994$	−1.13115	−0.0358778
$995$	14.7729	0.468332
$996$	−56.0867	−1.77717
$997$	29.5339	0.935347	0.467673	−	0.883901i	$-0.345092\pi$
$997$	29.5339	0.935347	0.467673	+	0.883901i	$0.345092\pi$
$998$	47.0733	1.49008
$999$	−1.24709	−0.0394561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.7	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.04946 q^{2} -2.65729 q^{3} +2.20029 q^{4} +1.00000 q^{5} +5.44602 q^{6} -0.551924 q^{7} -0.410497 q^{8} +4.06121 q^{9} +O(q^{10})\)	\(q-2.04946 q^{2} -2.65729 q^{3} +2.20029 q^{4} +1.00000 q^{5} +5.44602 q^{6} -0.551924 q^{7} -0.410497 q^{8} +4.06121 q^{9} -2.04946 q^{10} -2.27257 q^{11} -5.84683 q^{12} +3.17452 q^{13} +1.13115 q^{14} -2.65729 q^{15} -3.55929 q^{16} +1.00000 q^{17} -8.32329 q^{18} +3.96256 q^{19} +2.20029 q^{20} +1.46662 q^{21} +4.65754 q^{22} +0.158967 q^{23} +1.09081 q^{24} +1.00000 q^{25} -6.50606 q^{26} -2.81994 q^{27} -1.21440 q^{28} -3.30606 q^{29} +5.44602 q^{30} -1.54948 q^{31} +8.11563 q^{32} +6.03887 q^{33} -2.04946 q^{34} -0.551924 q^{35} +8.93585 q^{36} +0.442239 q^{37} -8.12113 q^{38} -8.43563 q^{39} -0.410497 q^{40} -6.61145 q^{41} -3.00579 q^{42} +0.716223 q^{43} -5.00032 q^{44} +4.06121 q^{45} -0.325797 q^{46} +8.62993 q^{47} +9.45808 q^{48} -6.69538 q^{49} -2.04946 q^{50} -2.65729 q^{51} +6.98488 q^{52} +0.784664 q^{53} +5.77935 q^{54} -2.27257 q^{55} +0.226563 q^{56} -10.5297 q^{57} +6.77564 q^{58} +11.6229 q^{59} -5.84683 q^{60} -9.42978 q^{61} +3.17561 q^{62} -2.24148 q^{63} -9.51409 q^{64} +3.17452 q^{65} -12.3764 q^{66} -6.70202 q^{67} +2.20029 q^{68} -0.422421 q^{69} +1.13115 q^{70} -1.00000 q^{71} -1.66711 q^{72} -6.31194 q^{73} -0.906353 q^{74} -2.65729 q^{75} +8.71881 q^{76} +1.25428 q^{77} +17.2885 q^{78} -11.0345 q^{79} -3.55929 q^{80} -4.69022 q^{81} +13.5499 q^{82} +9.59267 q^{83} +3.22700 q^{84} +1.00000 q^{85} -1.46787 q^{86} +8.78516 q^{87} +0.932881 q^{88} -4.93816 q^{89} -8.32329 q^{90} -1.75209 q^{91} +0.349774 q^{92} +4.11744 q^{93} -17.6867 q^{94} +3.96256 q^{95} -21.5656 q^{96} -17.2989 q^{97} +13.7219 q^{98} -9.22936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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