LMFDB - Embedded newform 4022.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.92131 q^{3} +1.00000 q^{4} -0.749362 q^{5} +1.92131 q^{6} -4.27002 q^{7} -1.00000 q^{8} +0.691416 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.92131 q^{3} +1.00000 q^{4} -0.749362 q^{5} +1.92131 q^{6} -4.27002 q^{7} -1.00000 q^{8} +0.691416 q^{9} +0.749362 q^{10} +1.34581 q^{11} -1.92131 q^{12} +6.84965 q^{13} +4.27002 q^{14} +1.43975 q^{15} +1.00000 q^{16} -5.15765 q^{17} -0.691416 q^{18} -2.23802 q^{19} -0.749362 q^{20} +8.20401 q^{21} -1.34581 q^{22} +2.73754 q^{23} +1.92131 q^{24} -4.43846 q^{25} -6.84965 q^{26} +4.43550 q^{27} -4.27002 q^{28} -4.65208 q^{29} -1.43975 q^{30} +1.81434 q^{31} -1.00000 q^{32} -2.58571 q^{33} +5.15765 q^{34} +3.19979 q^{35} +0.691416 q^{36} -3.65955 q^{37} +2.23802 q^{38} -13.1603 q^{39} +0.749362 q^{40} -4.18883 q^{41} -8.20401 q^{42} -2.14797 q^{43} +1.34581 q^{44} -0.518121 q^{45} -2.73754 q^{46} +10.3772 q^{47} -1.92131 q^{48} +11.2331 q^{49} +4.43846 q^{50} +9.90942 q^{51} +6.84965 q^{52} +11.0202 q^{53} -4.43550 q^{54} -1.00850 q^{55} +4.27002 q^{56} +4.29993 q^{57} +4.65208 q^{58} +6.96928 q^{59} +1.43975 q^{60} +13.7783 q^{61} -1.81434 q^{62} -2.95236 q^{63} +1.00000 q^{64} -5.13286 q^{65} +2.58571 q^{66} -0.0238480 q^{67} -5.15765 q^{68} -5.25965 q^{69} -3.19979 q^{70} +13.6179 q^{71} -0.691416 q^{72} -10.2812 q^{73} +3.65955 q^{74} +8.52763 q^{75} -2.23802 q^{76} -5.74663 q^{77} +13.1603 q^{78} +8.32895 q^{79} -0.749362 q^{80} -10.5962 q^{81} +4.18883 q^{82} +2.56948 q^{83} +8.20401 q^{84} +3.86495 q^{85} +2.14797 q^{86} +8.93808 q^{87} -1.34581 q^{88} +4.14049 q^{89} +0.518121 q^{90} -29.2481 q^{91} +2.73754 q^{92} -3.48590 q^{93} -10.3772 q^{94} +1.67709 q^{95} +1.92131 q^{96} -11.4952 q^{97} -11.2331 q^{98} +0.930515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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
$3$	−1.92131	−1.10927	−0.554633	−	0.832095i	$-0.687141\pi$
$3$	−1.92131	−1.10927	−0.554633	+	0.832095i	$0.687141\pi$
$4$	1.00000	0.500000
$5$	−0.749362	−0.335125	−0.167562	−	0.985861i	$-0.553590\pi$
$5$	−0.749362	−0.335125	−0.167562	+	0.985861i	$0.553590\pi$
$6$	1.92131	0.784370
$7$	−4.27002	−1.61392	−0.806958	−	0.590609i	$-0.798887\pi$
$7$	−4.27002	−1.61392	−0.806958	+	0.590609i	$0.798887\pi$
$8$	−1.00000	−0.353553
$9$	0.691416	0.230472
$10$	0.749362	0.236969
$11$	1.34581	0.405777	0.202888	−	0.979202i	$-0.434967\pi$
$11$	1.34581	0.405777	0.202888	+	0.979202i	$0.434967\pi$
$12$	−1.92131	−0.554633
$13$	6.84965	1.89975	0.949875	−	0.312629i	$-0.101210\pi$
$13$	6.84965	1.89975	0.949875	+	0.312629i	$0.101210\pi$
$14$	4.27002	1.14121
$15$	1.43975	0.371743
$16$	1.00000	0.250000
$17$	−5.15765	−1.25091	−0.625457	−	0.780259i	$-0.715087\pi$
$17$	−5.15765	−1.25091	−0.625457	+	0.780259i	$0.715087\pi$
$18$	−0.691416	−0.162968
$19$	−2.23802	−0.513438	−0.256719	−	0.966486i	$-0.582641\pi$
$19$	−2.23802	−0.513438	−0.256719	+	0.966486i	$0.582641\pi$
$20$	−0.749362	−0.167562
$21$	8.20401	1.79026
$22$	−1.34581	−0.286928
$23$	2.73754	0.570816	0.285408	−	0.958406i	$-0.407871\pi$
$23$	2.73754	0.570816	0.285408	+	0.958406i	$0.407871\pi$
$24$	1.92131	0.392185
$25$	−4.43846	−0.887691
$26$	−6.84965	−1.34333
$27$	4.43550	0.853611
$28$	−4.27002	−0.806958
$29$	−4.65208	−0.863870	−0.431935	−	0.901905i	$-0.642169\pi$
$29$	−4.65208	−0.863870	−0.431935	+	0.901905i	$0.642169\pi$
$30$	−1.43975	−0.262862
$31$	1.81434	0.325865	0.162932	−	0.986637i	$-0.447905\pi$
$31$	1.81434	0.325865	0.162932	+	0.986637i	$0.447905\pi$
$32$	−1.00000	−0.176777
$33$	−2.58571	−0.450115
$34$	5.15765	0.884530
$35$	3.19979	0.540863
$36$	0.691416	0.115236
$37$	−3.65955	−0.601627	−0.300813	−	0.953683i	$-0.597258\pi$
$37$	−3.65955	−0.601627	−0.300813	+	0.953683i	$0.597258\pi$
$38$	2.23802	0.363055
$39$	−13.1603	−2.10733
$40$	0.749362	0.118484
$41$	−4.18883	−0.654185	−0.327093	−	0.944992i	$-0.606069\pi$
$41$	−4.18883	−0.654185	−0.327093	+	0.944992i	$0.606069\pi$
$42$	−8.20401	−1.26591
$43$	−2.14797	−0.327563	−0.163781	−	0.986497i	$-0.552369\pi$
$43$	−2.14797	−0.327563	−0.163781	+	0.986497i	$0.552369\pi$
$44$	1.34581	0.202888
$45$	−0.518121	−0.0772369
$46$	−2.73754	−0.403628
$47$	10.3772	1.51367	0.756836	−	0.653604i	$-0.226744\pi$
$47$	10.3772	1.51367	0.756836	+	0.653604i	$0.226744\pi$
$48$	−1.92131	−0.277317
$49$	11.2331	1.60472
$50$	4.43846	0.627693
$51$	9.90942	1.38760
$52$	6.84965	0.949875
$53$	11.0202	1.51374	0.756868	−	0.653568i	$-0.226729\pi$
$53$	11.0202	1.51374	0.756868	+	0.653568i	$0.226729\pi$
$54$	−4.43550	−0.603594
$55$	−1.00850	−0.135986
$56$	4.27002	0.570605
$57$	4.29993	0.569539
$58$	4.65208	0.610849
$59$	6.96928	0.907323	0.453661	−	0.891174i	$-0.350118\pi$
$59$	6.96928	0.907323	0.453661	+	0.891174i	$0.350118\pi$
$60$	1.43975	0.185871
$61$	13.7783	1.76413	0.882064	−	0.471130i	$-0.156154\pi$
$61$	13.7783	1.76413	0.882064	+	0.471130i	$0.156154\pi$
$62$	−1.81434	−0.230421
$63$	−2.95236	−0.371962
$64$	1.00000	0.125000
$65$	−5.13286	−0.636653
$66$	2.58571	0.318279
$67$	−0.0238480	−0.00291349	−0.00145675	−	0.999999i	$-0.500464\pi$
$67$	−0.0238480	−0.00291349	−0.00145675	+	0.999999i	$0.500464\pi$
$68$	−5.15765	−0.625457
$69$	−5.25965	−0.633187
$70$	−3.19979	−0.382448
$71$	13.6179	1.61615	0.808076	−	0.589078i	$-0.200509\pi$
$71$	13.6179	1.61615	0.808076	+	0.589078i	$0.200509\pi$
$72$	−0.691416	−0.0814842
$73$	−10.2812	−1.20333	−0.601663	−	0.798750i	$-0.705495\pi$
$73$	−10.2812	−1.20333	−0.601663	+	0.798750i	$0.705495\pi$
$74$	3.65955	0.425415
$75$	8.52763	0.984686
$76$	−2.23802	−0.256719
$77$	−5.74663	−0.654890
$78$	13.1603	1.49011
$79$	8.32895	0.937080	0.468540	−	0.883442i	$-0.344780\pi$
$79$	8.32895	0.937080	0.468540	+	0.883442i	$0.344780\pi$
$80$	−0.749362	−0.0837812
$81$	−10.5962	−1.17735
$82$	4.18883	0.462579
$83$	2.56948	0.282037	0.141019	−	0.990007i	$-0.454962\pi$
$83$	2.56948	0.282037	0.141019	+	0.990007i	$0.454962\pi$
$84$	8.20401	0.895131
$85$	3.86495	0.419212
$86$	2.14797	0.231622
$87$	8.93808	0.958262
$88$	−1.34581	−0.143464
$89$	4.14049	0.438892	0.219446	−	0.975625i	$-0.429575\pi$
$89$	4.14049	0.438892	0.219446	+	0.975625i	$0.429575\pi$
$90$	0.518121	0.0546147
$91$	−29.2481	−3.06604
$92$	2.73754	0.285408
$93$	−3.48590	−0.361471
$94$	−10.3772	−1.07033
$95$	1.67709	0.172066
$96$	1.92131	0.196092
$97$	−11.4952	−1.16717	−0.583583	−	0.812054i	$-0.698350\pi$
$97$	−11.4952	−1.16717	−0.583583	+	0.812054i	$0.698350\pi$
$98$	−11.2331	−1.13471
$99$	0.930515	0.0935203
$100$	−4.43846	−0.443846
$101$	−2.16048	−0.214976	−0.107488	−	0.994206i	$-0.534281\pi$
$101$	−2.16048	−0.214976	−0.107488	+	0.994206i	$0.534281\pi$
$102$	−9.90942	−0.981179
$103$	−10.6788	−1.05222	−0.526108	−	0.850418i	$-0.676349\pi$
$103$	−10.6788	−1.05222	−0.526108	+	0.850418i	$0.676349\pi$
$104$	−6.84965	−0.671663
$105$	−6.14777	−0.599961
$106$	−11.0202	−1.07037
$107$	9.74906	0.942477	0.471238	−	0.882006i	$-0.343807\pi$
$107$	9.74906	0.942477	0.471238	+	0.882006i	$0.343807\pi$
$108$	4.43550	0.426806
$109$	12.5982	1.20669	0.603344	−	0.797481i	$-0.293835\pi$
$109$	12.5982	1.20669	0.603344	+	0.797481i	$0.293835\pi$
$110$	1.00850	0.0961565
$111$	7.03112	0.667365
$112$	−4.27002	−0.403479
$113$	−19.4452	−1.82925	−0.914627	−	0.404299i	$-0.867515\pi$
$113$	−19.4452	−1.82925	−0.914627	+	0.404299i	$0.867515\pi$
$114$	−4.29993	−0.402725
$115$	−2.05141	−0.191295
$116$	−4.65208	−0.431935
$117$	4.73596	0.437840
$118$	−6.96928	−0.641574
$119$	22.0233	2.01887
$120$	−1.43975	−0.131431
$121$	−9.18880	−0.835345
$122$	−13.7783	−1.24743
$123$	8.04802	0.725666
$124$	1.81434	0.162932
$125$	7.07282	0.632612
$126$	2.95236	0.263017
$127$	−3.64747	−0.323661	−0.161830	−	0.986819i	$-0.551740\pi$
$127$	−3.64747	−0.323661	−0.161830	+	0.986819i	$0.551740\pi$
$128$	−1.00000	−0.0883883
$129$	4.12691	0.363354
$130$	5.13286	0.450182
$131$	0.569514	0.0497587	0.0248793	−	0.999690i	$-0.492080\pi$
$131$	0.569514	0.0497587	0.0248793	+	0.999690i	$0.492080\pi$
$132$	−2.58571	−0.225057
$133$	9.55640	0.828645
$134$	0.0238480	0.00206015
$135$	−3.32379	−0.286066
$136$	5.15765	0.442265
$137$	−19.7852	−1.69037	−0.845183	−	0.534478i	$-0.820508\pi$
$137$	−19.7852	−1.69037	−0.845183	+	0.534478i	$0.820508\pi$
$138$	5.25965	0.447731
$139$	4.86443	0.412595	0.206298	−	0.978489i	$-0.433859\pi$
$139$	4.86443	0.412595	0.206298	+	0.978489i	$0.433859\pi$
$140$	3.19979	0.270431
$141$	−19.9378	−1.67907
$142$	−13.6179	−1.14279
$143$	9.21832	0.770875
$144$	0.691416	0.0576180
$145$	3.48609	0.289504
$146$	10.2812	0.850880
$147$	−21.5821	−1.78006
$148$	−3.65955	−0.300813
$149$	−8.56540	−0.701705	−0.350853	−	0.936431i	$-0.614108\pi$
$149$	−8.56540	−0.701705	−0.350853	+	0.936431i	$0.614108\pi$
$150$	−8.52763	−0.696278
$151$	3.99192	0.324858	0.162429	−	0.986720i	$-0.448067\pi$
$151$	3.99192	0.324858	0.162429	+	0.986720i	$0.448067\pi$
$152$	2.23802	0.181528
$153$	−3.56608	−0.288301
$154$	5.74663	0.463077
$155$	−1.35959	−0.109205
$156$	−13.1603	−1.05366
$157$	8.09120	0.645748	0.322874	−	0.946442i	$-0.395351\pi$
$157$	8.09120	0.645748	0.322874	+	0.946442i	$0.395351\pi$
$158$	−8.32895	−0.662616
$159$	−21.1731	−1.67914
$160$	0.749362	0.0592422
$161$	−11.6893	−0.921249
$162$	10.5962	0.832516
$163$	1.57824	0.123617	0.0618085	−	0.998088i	$-0.480313\pi$
$163$	1.57824	0.123617	0.0618085	+	0.998088i	$0.480313\pi$
$164$	−4.18883	−0.327093
$165$	1.93763	0.150845
$166$	−2.56948	−0.199430
$167$	2.73785	0.211862	0.105931	−	0.994374i	$-0.466218\pi$
$167$	2.73785	0.211862	0.105931	+	0.994374i	$0.466218\pi$
$168$	−8.20401	−0.632953
$169$	33.9177	2.60905
$170$	−3.86495	−0.296428
$171$	−1.54741	−0.118333
$172$	−2.14797	−0.163781
$173$	24.0284	1.82685	0.913424	−	0.407010i	$-0.133429\pi$
$173$	24.0284	1.82685	0.913424	+	0.407010i	$0.133429\pi$
$174$	−8.93808	−0.677594
$175$	18.9523	1.43266
$176$	1.34581	0.101444
$177$	−13.3901	−1.00646
$178$	−4.14049	−0.310343
$179$	16.8671	1.26071	0.630354	−	0.776308i	$-0.282910\pi$
$179$	16.8671	1.26071	0.630354	+	0.776308i	$0.282910\pi$
$180$	−0.518121	−0.0386185
$181$	−8.99191	−0.668363	−0.334182	−	0.942509i	$-0.608460\pi$
$181$	−8.99191	−0.668363	−0.334182	+	0.942509i	$0.608460\pi$
$182$	29.2481	2.16802
$183$	−26.4723	−1.95689
$184$	−2.73754	−0.201814
$185$	2.74233	0.201620
$186$	3.48590	0.255598
$187$	−6.94122	−0.507592
$188$	10.3772	0.756836
$189$	−18.9396	−1.37766
$190$	−1.67709	−0.121669
$191$	−24.5115	−1.77359	−0.886796	−	0.462160i	$-0.847075\pi$
$191$	−24.5115	−1.77359	−0.886796	+	0.462160i	$0.847075\pi$
$192$	−1.92131	−0.138658
$193$	−18.6295	−1.34098	−0.670489	−	0.741920i	$-0.733915\pi$
$193$	−18.6295	−1.34098	−0.670489	+	0.741920i	$0.733915\pi$
$194$	11.4952	0.825311
$195$	9.86180	0.706218
$196$	11.2331	0.802361
$197$	−16.1873	−1.15330	−0.576650	−	0.816992i	$-0.695640\pi$
$197$	−16.1873	−1.15330	−0.576650	+	0.816992i	$0.695640\pi$
$198$	−0.930515	−0.0661288
$199$	−12.2000	−0.864832	−0.432416	−	0.901674i	$-0.642339\pi$
$199$	−12.2000	−0.864832	−0.432416	+	0.901674i	$0.642339\pi$
$200$	4.43846	0.313846
$201$	0.0458193	0.00323184
$202$	2.16048	0.152011
$203$	19.8645	1.39421
$204$	9.90942	0.693799
$205$	3.13895	0.219234
$206$	10.6788	0.744029
$207$	1.89278	0.131557
$208$	6.84965	0.474938
$209$	−3.01195	−0.208341
$210$	6.14777	0.424237
$211$	−1.69403	−0.116621	−0.0583107	−	0.998298i	$-0.518571\pi$
$211$	−1.69403	−0.116621	−0.0583107	+	0.998298i	$0.518571\pi$
$212$	11.0202	0.756868
$213$	−26.1642	−1.79274
$214$	−9.74906	−0.666432
$215$	1.60961	0.109774
$216$	−4.43550	−0.301797
$217$	−7.74725	−0.525918
$218$	−12.5982	−0.853258
$219$	19.7534	1.33481
$220$	−1.00850	−0.0679929
$221$	−35.3281	−2.37642
$222$	−7.03112	−0.471898
$223$	−22.2532	−1.49019	−0.745093	−	0.666960i	$-0.767595\pi$
$223$	−22.2532	−1.49019	−0.745093	+	0.666960i	$0.767595\pi$
$224$	4.27002	0.285303
$225$	−3.06882	−0.204588
$226$	19.4452	1.29348
$227$	−28.1341	−1.86733	−0.933664	−	0.358149i	$-0.883408\pi$
$227$	−28.1341	−1.86733	−0.933664	+	0.358149i	$0.883408\pi$
$228$	4.29993	0.284770
$229$	17.9872	1.18863	0.594314	−	0.804233i	$-0.297424\pi$
$229$	17.9872	1.18863	0.594314	+	0.804233i	$0.297424\pi$
$230$	2.05141	0.135266
$231$	11.0410	0.726447
$232$	4.65208	0.305424
$233$	−4.12034	−0.269932	−0.134966	−	0.990850i	$-0.543093\pi$
$233$	−4.12034	−0.269932	−0.134966	+	0.990850i	$0.543093\pi$
$234$	−4.73596	−0.309599
$235$	−7.77629	−0.507269
$236$	6.96928	0.453661
$237$	−16.0025	−1.03947
$238$	−22.0233	−1.42756
$239$	−25.5323	−1.65155	−0.825773	−	0.564002i	$-0.809261\pi$
$239$	−25.5323	−1.65155	−0.825773	+	0.564002i	$0.809261\pi$
$240$	1.43975	0.0929357
$241$	−22.1028	−1.42377	−0.711884	−	0.702297i	$-0.752158\pi$
$241$	−22.1028	−1.42377	−0.711884	+	0.702297i	$0.752158\pi$
$242$	9.18880	0.590678
$243$	7.05204	0.452389
$244$	13.7783	0.882064
$245$	−8.41762	−0.537782
$246$	−8.04802	−0.513123
$247$	−15.3297	−0.975404
$248$	−1.81434	−0.115211
$249$	−4.93676	−0.312854
$250$	−7.07282	−0.447324
$251$	13.8490	0.874143	0.437072	−	0.899427i	$-0.356016\pi$
$251$	13.8490	0.874143	0.437072	+	0.899427i	$0.356016\pi$
$252$	−2.95236	−0.185981
$253$	3.68421	0.231624
$254$	3.64747	0.228863
$255$	−7.42574	−0.465018
$256$	1.00000	0.0625000
$257$	−17.8319	−1.11232	−0.556161	−	0.831074i	$-0.687726\pi$
$257$	−17.8319	−1.11232	−0.556161	+	0.831074i	$0.687726\pi$
$258$	−4.12691	−0.256930
$259$	15.6264	0.970975
$260$	−5.13286	−0.318327
$261$	−3.21653	−0.199098
$262$	−0.569514	−0.0351847
$263$	31.2782	1.92869	0.964347	−	0.264640i	$-0.0852531\pi$
$263$	31.2782	1.92869	0.964347	+	0.264640i	$0.0852531\pi$
$264$	2.58571	0.159140
$265$	−8.25809	−0.507290
$266$	−9.55640	−0.585941
$267$	−7.95516	−0.486848
$268$	−0.0238480	−0.00145675
$269$	−18.2408	−1.11216	−0.556081	−	0.831128i	$-0.687696\pi$
$269$	−18.2408	−1.11216	−0.556081	+	0.831128i	$0.687696\pi$
$270$	3.32379	0.202279
$271$	31.2712	1.89959	0.949794	−	0.312876i	$-0.101293\pi$
$271$	31.2712	1.89959	0.949794	+	0.312876i	$0.101293\pi$
$272$	−5.15765	−0.312729
$273$	56.1946	3.40105
$274$	19.7852	1.19527
$275$	−5.97332	−0.360205
$276$	−5.25965	−0.316594
$277$	−5.02468	−0.301904	−0.150952	−	0.988541i	$-0.548234\pi$
$277$	−5.02468	−0.301904	−0.150952	+	0.988541i	$0.548234\pi$
$278$	−4.86443	−0.291749
$279$	1.25446	0.0751027
$280$	−3.19979	−0.191224
$281$	7.28144	0.434375	0.217187	−	0.976130i	$-0.430312\pi$
$281$	7.28144	0.434375	0.217187	+	0.976130i	$0.430312\pi$
$282$	19.9378	1.18728
$283$	0.922772	0.0548531	0.0274265	−	0.999624i	$-0.491269\pi$
$283$	0.922772	0.0548531	0.0274265	+	0.999624i	$0.491269\pi$
$284$	13.6179	0.808076
$285$	−3.22220	−0.190867
$286$	−9.21832	−0.545091
$287$	17.8864	1.05580
$288$	−0.691416	−0.0407421
$289$	9.60136	0.564786
$290$	−3.48609	−0.204710
$291$	22.0859	1.29470
$292$	−10.2812	−0.601663
$293$	4.32064	0.252415	0.126207	−	0.992004i	$-0.459720\pi$
$293$	4.32064	0.252415	0.126207	+	0.992004i	$0.459720\pi$
$294$	21.5821	1.25870
$295$	−5.22251	−0.304066
$296$	3.65955	0.212707
$297$	5.96933	0.346376
$298$	8.56540	0.496181
$299$	18.7512	1.08441
$300$	8.52763	0.492343
$301$	9.17188	0.528659
$302$	−3.99192	−0.229709
$303$	4.15094	0.238465
$304$	−2.23802	−0.128359
$305$	−10.3249	−0.591203
$306$	3.56608	0.203859
$307$	−12.4801	−0.712277	−0.356138	−	0.934433i	$-0.615907\pi$
$307$	−12.4801	−0.712277	−0.356138	+	0.934433i	$0.615907\pi$
$308$	−5.74663	−0.327445
$309$	20.5173	1.16719
$310$	1.35959	0.0772198
$311$	−13.6102	−0.771766	−0.385883	−	0.922548i	$-0.626103\pi$
$311$	−13.6102	−0.771766	−0.385883	+	0.922548i	$0.626103\pi$
$312$	13.1603	0.745054
$313$	−12.0556	−0.681424	−0.340712	−	0.940168i	$-0.610668\pi$
$313$	−12.0556	−0.681424	−0.340712	+	0.940168i	$0.610668\pi$
$314$	−8.09120	−0.456613
$315$	2.21239	0.124654
$316$	8.32895	0.468540
$317$	32.8224	1.84349	0.921744	−	0.387799i	$-0.126764\pi$
$317$	32.8224	1.84349	0.921744	+	0.387799i	$0.126764\pi$
$318$	21.1731	1.18733
$319$	−6.26082	−0.350539
$320$	−0.749362	−0.0418906
$321$	−18.7309	−1.04546
$322$	11.6893	0.651421
$323$	11.5429	0.642267
$324$	−10.5962	−0.588677
$325$	−30.4019	−1.68639
$326$	−1.57824	−0.0874105
$327$	−24.2050	−1.33854
$328$	4.18883	0.231289
$329$	−44.3109	−2.44294
$330$	−1.93763	−0.106663
$331$	7.25452	0.398744	0.199372	−	0.979924i	$-0.436110\pi$
$331$	7.25452	0.398744	0.199372	+	0.979924i	$0.436110\pi$
$332$	2.56948	0.141019
$333$	−2.53028	−0.138658
$334$	−2.73785	−0.149809
$335$	0.0178708	0.000976384 0
$336$	8.20401	0.447566
$337$	−35.6021	−1.93937	−0.969685	−	0.244357i	$-0.921423\pi$
$337$	−35.6021	−1.93937	−0.969685	+	0.244357i	$0.921423\pi$
$338$	−33.9177	−1.84488
$339$	37.3602	2.02913
$340$	3.86495	0.209606
$341$	2.44175	0.132228
$342$	1.54741	0.0836741
$343$	−18.0752	−0.975971
$344$	2.14797	0.115811
$345$	3.94138	0.212197
$346$	−24.0284	−1.29178
$347$	11.8121	0.634108	0.317054	−	0.948407i	$-0.397306\pi$
$347$	11.8121	0.634108	0.317054	+	0.948407i	$0.397306\pi$
$348$	8.93808	0.479131
$349$	−9.20734	−0.492857	−0.246429	−	0.969161i	$-0.579257\pi$
$349$	−9.20734	−0.492857	−0.246429	+	0.969161i	$0.579257\pi$
$350$	−18.9523	−1.01304
$351$	30.3816	1.62165
$352$	−1.34581	−0.0717319
$353$	−12.0249	−0.640020	−0.320010	−	0.947414i	$-0.603686\pi$
$353$	−12.0249	−0.640020	−0.320010	+	0.947414i	$0.603686\pi$
$354$	13.3901	0.711677
$355$	−10.2048	−0.541613
$356$	4.14049	0.219446
$357$	−42.3134	−2.23946
$358$	−16.8671	−0.891455
$359$	13.0781	0.690238	0.345119	−	0.938559i	$-0.387839\pi$
$359$	13.0781	0.690238	0.345119	+	0.938559i	$0.387839\pi$
$360$	0.518121	0.0273074
$361$	−13.9913	−0.736382
$362$	8.99191	0.472604
$363$	17.6545	0.926620
$364$	−29.2481	−1.53302
$365$	7.70435	0.403264
$366$	26.4723	1.38373
$367$	−34.6480	−1.80861	−0.904305	−	0.426887i	$-0.859610\pi$
$367$	−34.6480	−1.80861	−0.904305	+	0.426887i	$0.859610\pi$
$368$	2.73754	0.142704
$369$	−2.89622	−0.150771
$370$	−2.74233	−0.142567
$371$	−47.0563	−2.44304
$372$	−3.48590	−0.180735
$373$	−4.59005	−0.237664	−0.118832	−	0.992914i	$-0.537915\pi$
$373$	−4.59005	−0.237664	−0.118832	+	0.992914i	$0.537915\pi$
$374$	6.94122	0.358922
$375$	−13.5890	−0.701735
$376$	−10.3772	−0.535164
$377$	−31.8651	−1.64114
$378$	18.9396	0.974150
$379$	−9.65705	−0.496049	−0.248025	−	0.968754i	$-0.579781\pi$
$379$	−9.65705	−0.496049	−0.248025	+	0.968754i	$0.579781\pi$
$380$	1.67709	0.0860329
$381$	7.00791	0.359026
$382$	24.5115	1.25412
$383$	4.41983	0.225843	0.112921	−	0.993604i	$-0.463979\pi$
$383$	4.41983	0.225843	0.112921	+	0.993604i	$0.463979\pi$
$384$	1.92131	0.0980462
$385$	4.30631	0.219470
$386$	18.6295	0.948214
$387$	−1.48514	−0.0754941
$388$	−11.4952	−0.583583
$389$	19.8100	1.00440	0.502202	−	0.864750i	$-0.332523\pi$
$389$	19.8100	1.00440	0.502202	+	0.864750i	$0.332523\pi$
$390$	−9.86180	−0.499372
$391$	−14.1193	−0.714042
$392$	−11.2331	−0.567355
$393$	−1.09421	−0.0551956
$394$	16.1873	0.815506
$395$	−6.24140	−0.314039
$396$	0.930515	0.0467601
$397$	−27.4536	−1.37786	−0.688929	−	0.724829i	$-0.741919\pi$
$397$	−27.4536	−1.37786	−0.688929	+	0.724829i	$0.741919\pi$
$398$	12.2000	0.611528
$399$	−18.3608	−0.919188
$400$	−4.43846	−0.221923
$401$	−2.81990	−0.140819	−0.0704096	−	0.997518i	$-0.522431\pi$
$401$	−2.81990	−0.140819	−0.0704096	+	0.997518i	$0.522431\pi$
$402$	−0.0458193	−0.00228526
$403$	12.4276	0.619062
$404$	−2.16048	−0.107488
$405$	7.94038	0.394561
$406$	−19.8645	−0.985858
$407$	−4.92506	−0.244126
$408$	−9.90942	−0.490590
$409$	38.1736	1.88756	0.943782	−	0.330570i	$-0.107241\pi$
$409$	38.1736	1.88756	0.943782	+	0.330570i	$0.107241\pi$
$410$	−3.13895	−0.155022
$411$	38.0135	1.87507
$412$	−10.6788	−0.526108
$413$	−29.7590	−1.46434
$414$	−1.89278	−0.0930250
$415$	−1.92547	−0.0945177
$416$	−6.84965	−0.335832
$417$	−9.34605	−0.457678
$418$	3.01195	0.147319
$419$	−17.2140	−0.840958	−0.420479	−	0.907302i	$-0.638138\pi$
$419$	−17.2140	−0.840958	−0.420479	+	0.907302i	$0.638138\pi$
$420$	−6.14777	−0.299981
$421$	−27.4796	−1.33927	−0.669637	−	0.742689i	$-0.733550\pi$
$421$	−27.4796	−1.33927	−0.669637	+	0.742689i	$0.733550\pi$
$422$	1.69403	0.0824638
$423$	7.17498	0.348859
$424$	−11.0202	−0.535186
$425$	22.8920	1.11043
$426$	26.1642	1.26766
$427$	−58.8335	−2.84715
$428$	9.74906	0.471238
$429$	−17.7112	−0.855106
$430$	−1.60961	−0.0776222
$431$	16.2167	0.781130	0.390565	−	0.920575i	$-0.372280\pi$
$431$	16.2167	0.781130	0.390565	+	0.920575i	$0.372280\pi$
$432$	4.43550	0.213403
$433$	25.8960	1.24448	0.622241	−	0.782826i	$-0.286222\pi$
$433$	25.8960	1.24448	0.622241	+	0.782826i	$0.286222\pi$
$434$	7.74725	0.371880
$435$	−6.69785	−0.321137
$436$	12.5982	0.603344
$437$	−6.12667	−0.293079
$438$	−19.7534	−0.943852
$439$	12.2998	0.587037	0.293518	−	0.955953i	$-0.405174\pi$
$439$	12.2998	0.587037	0.293518	+	0.955953i	$0.405174\pi$
$440$	1.00850	0.0480783
$441$	7.76672	0.369844
$442$	35.3281	1.68039
$443$	−11.8647	−0.563708	−0.281854	−	0.959457i	$-0.590949\pi$
$443$	−11.8647	−0.563708	−0.281854	+	0.959457i	$0.590949\pi$
$444$	7.03112	0.333682
$445$	−3.10273	−0.147083
$446$	22.2532	1.05372
$447$	16.4568	0.778378
$448$	−4.27002	−0.201739
$449$	17.0884	0.806452	0.403226	−	0.915101i	$-0.367889\pi$
$449$	17.0884	0.806452	0.403226	+	0.915101i	$0.367889\pi$
$450$	3.06882	0.144666
$451$	−5.63737	−0.265453
$452$	−19.4452	−0.914627
$453$	−7.66970	−0.360354
$454$	28.1341	1.32040
$455$	21.9174	1.02750
$456$	−4.29993	−0.201363
$457$	−8.85122	−0.414043	−0.207021	−	0.978336i	$-0.566377\pi$
$457$	−8.85122	−0.414043	−0.207021	+	0.978336i	$0.566377\pi$
$458$	−17.9872	−0.840487
$459$	−22.8767	−1.06779
$460$	−2.05141	−0.0956473
$461$	23.5079	1.09487	0.547435	−	0.836848i	$-0.315604\pi$
$461$	23.5079	1.09487	0.547435	+	0.836848i	$0.315604\pi$
$462$	−11.0410	−0.513676
$463$	−34.2301	−1.59081	−0.795405	−	0.606079i	$-0.792742\pi$
$463$	−34.2301	−1.59081	−0.795405	+	0.606079i	$0.792742\pi$
$464$	−4.65208	−0.215968
$465$	2.61220	0.121138
$466$	4.12034	0.190871
$467$	12.8200	0.593239	0.296619	−	0.954996i	$-0.404141\pi$
$467$	12.8200	0.593239	0.296619	+	0.954996i	$0.404141\pi$
$468$	4.73596	0.218920
$469$	0.101831	0.00470213
$470$	7.77629	0.358693
$471$	−15.5457	−0.716307
$472$	−6.96928	−0.320787
$473$	−2.89076	−0.132917
$474$	16.0025	0.735018
$475$	9.93337	0.455774
$476$	22.0233	1.00943
$477$	7.61952	0.348874
$478$	25.5323	1.16782
$479$	−18.6596	−0.852577	−0.426289	−	0.904587i	$-0.640179\pi$
$479$	−18.6596	−0.852577	−0.426289	+	0.904587i	$0.640179\pi$
$480$	−1.43975	−0.0657154
$481$	−25.0667	−1.14294
$482$	22.1028	1.00676
$483$	22.4588	1.02191
$484$	−9.18880	−0.417673
$485$	8.61410	0.391146
$486$	−7.05204	−0.319887
$487$	0.499629	0.0226404	0.0113202	−	0.999936i	$-0.496397\pi$
$487$	0.499629	0.0226404	0.0113202	+	0.999936i	$0.496397\pi$
$488$	−13.7783	−0.623713
$489$	−3.03228	−0.137124
$490$	8.41762	0.380269
$491$	−37.7003	−1.70139	−0.850695	−	0.525659i	$-0.823819\pi$
$491$	−37.7003	−1.70139	−0.850695	+	0.525659i	$0.823819\pi$
$492$	8.04802	0.362833
$493$	23.9938	1.08063
$494$	15.3297	0.689715
$495$	−0.697292	−0.0313410
$496$	1.81434	0.0814662
$497$	−58.1489	−2.60833
$498$	4.93676	0.221222
$499$	−8.34798	−0.373707	−0.186854	−	0.982388i	$-0.559829\pi$
$499$	−8.34798	−0.373707	−0.186854	+	0.982388i	$0.559829\pi$
$500$	7.07282	0.316306
$501$	−5.26026	−0.235011
$502$	−13.8490	−0.618113
$503$	23.8116	1.06170	0.530852	−	0.847464i	$-0.321872\pi$
$503$	23.8116	1.06170	0.530852	+	0.847464i	$0.321872\pi$
$504$	2.95236	0.131509
$505$	1.61898	0.0720436
$506$	−3.68421	−0.163783
$507$	−65.1662	−2.89413
$508$	−3.64747	−0.161830
$509$	−23.5985	−1.04598	−0.522992	−	0.852338i	$-0.675184\pi$
$509$	−23.5985	−1.04598	−0.522992	+	0.852338i	$0.675184\pi$
$510$	7.42574	0.328817
$511$	43.9010	1.94207
$512$	−1.00000	−0.0441942
$513$	−9.92674	−0.438276
$514$	17.8319	0.786531
$515$	8.00230	0.352624
$516$	4.12691	0.181677
$517$	13.9658	0.614214
$518$	−15.6264	−0.686583
$519$	−46.1659	−2.02646
$520$	5.13286	0.225091
$521$	−10.9118	−0.478054	−0.239027	−	0.971013i	$-0.576828\pi$
$521$	−10.9118	−0.478054	−0.239027	+	0.971013i	$0.576828\pi$
$522$	3.21653	0.140784
$523$	1.18394	0.0517699	0.0258850	−	0.999665i	$-0.491760\pi$
$523$	1.18394	0.0517699	0.0258850	+	0.999665i	$0.491760\pi$
$524$	0.569514	0.0248793
$525$	−36.4132	−1.58920
$526$	−31.2782	−1.36379
$527$	−9.35772	−0.407629
$528$	−2.58571	−0.112529
$529$	−15.5059	−0.674169
$530$	8.25809	0.358708
$531$	4.81867	0.209113
$532$	9.55640	0.414323
$533$	−28.6920	−1.24279
$534$	7.95516	0.344253
$535$	−7.30557	−0.315847
$536$	0.0238480	0.00103008
$537$	−32.4069	−1.39846
$538$	18.2408	0.786417
$539$	15.1176	0.651159
$540$	−3.32379	−0.143033
$541$	30.4759	1.31026	0.655131	−	0.755515i	$-0.272613\pi$
$541$	30.4759	1.31026	0.655131	+	0.755515i	$0.272613\pi$
$542$	−31.2712	−1.34321
$543$	17.2762	0.741393
$544$	5.15765	0.221132
$545$	−9.44061	−0.404391
$546$	−56.1946	−2.40491
$547$	−18.5735	−0.794145	−0.397073	−	0.917787i	$-0.629974\pi$
$547$	−18.5735	−0.794145	−0.397073	+	0.917787i	$0.629974\pi$
$548$	−19.7852	−0.845183
$549$	9.52653	0.406582
$550$	5.97332	0.254703
$551$	10.4115	0.443544
$552$	5.25965	0.223865
$553$	−35.5648	−1.51237
$554$	5.02468	0.213478
$555$	−5.26885	−0.223650
$556$	4.86443	0.206298
$557$	38.0377	1.61171	0.805855	−	0.592112i	$-0.201706\pi$
$557$	38.0377	1.61171	0.805855	+	0.592112i	$0.201706\pi$
$558$	−1.25446	−0.0531056
$559$	−14.7129	−0.622288
$560$	3.19979	0.135216
$561$	13.3362	0.563055
$562$	−7.28144	−0.307149
$563$	−27.0602	−1.14045	−0.570226	−	0.821488i	$-0.693144\pi$
$563$	−27.0602	−1.14045	−0.570226	+	0.821488i	$0.693144\pi$
$564$	−19.9378	−0.839533
$565$	14.5715	0.613028
$566$	−0.922772	−0.0387870
$567$	45.2459	1.90015
$568$	−13.6179	−0.571396
$569$	31.1535	1.30602	0.653012	−	0.757347i	$-0.273505\pi$
$569$	31.1535	1.30602	0.653012	+	0.757347i	$0.273505\pi$
$570$	3.22220	0.134963
$571$	26.1349	1.09371	0.546855	−	0.837227i	$-0.315825\pi$
$571$	26.1349	1.09371	0.546855	+	0.837227i	$0.315825\pi$
$572$	9.21832	0.385437
$573$	47.0942	1.96739
$574$	−17.8864	−0.746563
$575$	−12.1504	−0.506709
$576$	0.691416	0.0288090
$577$	4.92437	0.205004	0.102502	−	0.994733i	$-0.467315\pi$
$577$	4.92437	0.205004	0.102502	+	0.994733i	$0.467315\pi$
$578$	−9.60136	−0.399364
$579$	35.7929	1.48750
$580$	3.48609	0.144752
$581$	−10.9717	−0.455184
$582$	−22.0859	−0.915489
$583$	14.8310	0.614239
$584$	10.2812	0.425440
$585$	−3.54895	−0.146731
$586$	−4.32064	−0.178484
$587$	−26.5540	−1.09600	−0.548000	−	0.836479i	$-0.684610\pi$
$587$	−26.5540	−1.09600	−0.548000	+	0.836479i	$0.684610\pi$
$588$	−21.5821	−0.890032
$589$	−4.06053	−0.167311
$590$	5.22251	0.215007
$591$	31.1008	1.27932
$592$	−3.65955	−0.150407
$593$	44.4415	1.82499	0.912496	−	0.409085i	$-0.134152\pi$
$593$	44.4415	1.82499	0.912496	+	0.409085i	$0.134152\pi$
$594$	−5.96933	−0.244925
$595$	−16.5034	−0.676573
$596$	−8.56540	−0.350853
$597$	23.4398	0.959329
$598$	−18.7512	−0.766792
$599$	4.24396	0.173403	0.0867017	−	0.996234i	$-0.472367\pi$
$599$	4.24396	0.173403	0.0867017	+	0.996234i	$0.472367\pi$
$600$	−8.52763	−0.348139
$601$	1.34659	0.0549288	0.0274644	−	0.999623i	$-0.491257\pi$
$601$	1.34659	0.0549288	0.0274644	+	0.999623i	$0.491257\pi$
$602$	−9.17188	−0.373818
$603$	−0.0164889	−0.000671479 0
$604$	3.99192	0.162429
$605$	6.88573	0.279945
$606$	−4.15094	−0.168620
$607$	−9.70947	−0.394095	−0.197048	−	0.980394i	$-0.563135\pi$
$607$	−9.70947	−0.394095	−0.197048	+	0.980394i	$0.563135\pi$
$608$	2.23802	0.0907638
$609$	−38.1658	−1.54655
$610$	10.3249	0.418044
$611$	71.0803	2.87560
$612$	−3.56608	−0.144150
$613$	−11.1838	−0.451711	−0.225855	−	0.974161i	$-0.572518\pi$
$613$	−11.1838	−0.451711	−0.225855	+	0.974161i	$0.572518\pi$
$614$	12.4801	0.503656
$615$	−6.03088	−0.243188
$616$	5.74663	0.231538
$617$	−27.9113	−1.12367	−0.561833	−	0.827251i	$-0.689904\pi$
$617$	−27.9113	−1.12367	−0.561833	+	0.827251i	$0.689904\pi$
$618$	−20.5173	−0.825326
$619$	43.8027	1.76058	0.880289	−	0.474439i	$-0.157349\pi$
$619$	43.8027	1.76058	0.880289	+	0.474439i	$0.157349\pi$
$620$	−1.35959	−0.0546026
$621$	12.1423	0.487255
$622$	13.6102	0.545721
$623$	−17.6800	−0.708334
$624$	−13.1603	−0.526832
$625$	16.8922	0.675687
$626$	12.0556	0.481840
$627$	5.78689	0.231106
$628$	8.09120	0.322874
$629$	18.8747	0.752584
$630$	−2.21239	−0.0881436
$631$	−13.3841	−0.532811	−0.266406	−	0.963861i	$-0.585836\pi$
$631$	−13.3841	−0.532811	−0.266406	+	0.963861i	$0.585836\pi$
$632$	−8.32895	−0.331308
$633$	3.25474	0.129364
$634$	−32.8224	−1.30354
$635$	2.73328	0.108467
$636$	−21.1731	−0.839568
$637$	76.9425	3.04857
$638$	6.26082	0.247868
$639$	9.41567	0.372478
$640$	0.749362	0.0296211
$641$	−23.6350	−0.933525	−0.466763	−	0.884383i	$-0.654580\pi$
$641$	−23.6350	−0.933525	−0.466763	+	0.884383i	$0.654580\pi$
$642$	18.7309	0.739250
$643$	−40.9368	−1.61439	−0.807195	−	0.590284i	$-0.799016\pi$
$643$	−40.9368	−1.61439	−0.807195	+	0.590284i	$0.799016\pi$
$644$	−11.6893	−0.460624
$645$	−3.09255	−0.121769
$646$	−11.5429	−0.454151
$647$	−34.1455	−1.34240	−0.671200	−	0.741277i	$-0.734221\pi$
$647$	−34.1455	−1.34240	−0.671200	+	0.741277i	$0.734221\pi$
$648$	10.5962	0.416258
$649$	9.37933	0.368171
$650$	30.4019	1.19246
$651$	14.8848	0.583383
$652$	1.57824	0.0618085
$653$	2.44489	0.0956761	0.0478380	−	0.998855i	$-0.484767\pi$
$653$	2.44489	0.0956761	0.0478380	+	0.998855i	$0.484767\pi$
$654$	24.2050	0.946490
$655$	−0.426772	−0.0166754
$656$	−4.18883	−0.163546
$657$	−7.10860	−0.277333
$658$	44.3109	1.72742
$659$	5.53585	0.215646	0.107823	−	0.994170i	$-0.465612\pi$
$659$	5.53585	0.215646	0.107823	+	0.994170i	$0.465612\pi$
$660$	1.93763	0.0754223
$661$	−45.1186	−1.75491	−0.877454	−	0.479660i	$-0.840760\pi$
$661$	−45.1186	−1.75491	−0.877454	+	0.479660i	$0.840760\pi$
$662$	−7.25452	−0.281955
$663$	67.8761	2.63609
$664$	−2.56948	−0.0997152
$665$	−7.16120	−0.277699
$666$	2.53028	0.0980462
$667$	−12.7353	−0.493111
$668$	2.73785	0.105931
$669$	42.7553	1.65301
$670$	−0.0178708	−0.000690408 0
$671$	18.5429	0.715842
$672$	−8.20401	−0.316477
$673$	−48.1658	−1.85666	−0.928328	−	0.371763i	$-0.878753\pi$
$673$	−48.1658	−1.85666	−0.928328	+	0.371763i	$0.878753\pi$
$674$	35.6021	1.37134
$675$	−19.6868	−0.757744
$676$	33.9177	1.30453
$677$	34.6096	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$677$	34.6096	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$678$	−37.3602	−1.43481
$679$	49.0849	1.88371
$680$	−3.86495	−0.148214
$681$	54.0543	2.07137
$682$	−2.44175	−0.0934996
$683$	−27.9510	−1.06952	−0.534758	−	0.845005i	$-0.679597\pi$
$683$	−27.9510	−1.06952	−0.534758	+	0.845005i	$0.679597\pi$
$684$	−1.54741	−0.0591666
$685$	14.8263	0.566483
$686$	18.0752	0.690115
$687$	−34.5589	−1.31851
$688$	−2.14797	−0.0818907
$689$	75.4842	2.87572
$690$	−3.94138	−0.150046
$691$	−31.1358	−1.18446	−0.592231	−	0.805768i	$-0.701753\pi$
$691$	−31.1358	−1.18446	−0.592231	+	0.805768i	$0.701753\pi$
$692$	24.0284	0.913424
$693$	−3.97332	−0.150934
$694$	−11.8121	−0.448382
$695$	−3.64521	−0.138271
$696$	−8.93808	−0.338797
$697$	21.6045	0.818329
$698$	9.20734	0.348503
$699$	7.91642	0.299427
$700$	18.9523	0.716329
$701$	22.3419	0.843841	0.421920	−	0.906633i	$-0.361356\pi$
$701$	22.3419	0.843841	0.421920	+	0.906633i	$0.361356\pi$
$702$	−30.3816	−1.14668
$703$	8.19017	0.308898
$704$	1.34581	0.0507221
$705$	14.9406	0.562697
$706$	12.0249	0.452563
$707$	9.22528	0.346952
$708$	−13.3901	−0.503231
$709$	−0.848309	−0.0318589	−0.0159295	−	0.999873i	$-0.505071\pi$
$709$	−0.848309	−0.0318589	−0.0159295	+	0.999873i	$0.505071\pi$
$710$	10.2048	0.382978
$711$	5.75878	0.215971
$712$	−4.14049	−0.155172
$713$	4.96682	0.186009
$714$	42.3134	1.58354
$715$	−6.90786	−0.258339
$716$	16.8671	0.630354
$717$	49.0554	1.83201
$718$	−13.0781	−0.488072
$719$	10.9085	0.406820	0.203410	−	0.979094i	$-0.434798\pi$
$719$	10.9085	0.406820	0.203410	+	0.979094i	$0.434798\pi$
$720$	−0.518121	−0.0193092
$721$	45.5988	1.69819
$722$	13.9913	0.520700
$723$	42.4663	1.57934
$724$	−8.99191	−0.334182
$725$	20.6481	0.766850
$726$	−17.6545	−0.655219
$727$	8.99717	0.333687	0.166843	−	0.985983i	$-0.446643\pi$
$727$	8.99717	0.333687	0.166843	+	0.985983i	$0.446643\pi$
$728$	29.2481	1.08401
$729$	18.2394	0.675535
$730$	−7.70435	−0.285151
$731$	11.0785	0.409753
$732$	−26.4723	−0.978444
$733$	18.1900	0.671863	0.335932	−	0.941886i	$-0.390949\pi$
$733$	18.1900	0.671863	0.335932	+	0.941886i	$0.390949\pi$
$734$	34.6480	1.27888
$735$	16.1728	0.596544
$736$	−2.73754	−0.100907
$737$	−0.0320948	−0.00118223
$738$	2.89622	0.106612
$739$	14.6694	0.539623	0.269811	−	0.962913i	$-0.413039\pi$
$739$	14.6694	0.539623	0.269811	+	0.962913i	$0.413039\pi$
$740$	2.74233	0.100810
$741$	29.4530	1.08198
$742$	47.0563	1.72749
$743$	36.1035	1.32451	0.662255	−	0.749279i	$-0.269600\pi$
$743$	36.1035	1.32451	0.662255	+	0.749279i	$0.269600\pi$
$744$	3.48590	0.127799
$745$	6.41859	0.235159
$746$	4.59005	0.168054
$747$	1.77658	0.0650017
$748$	−6.94122	−0.253796
$749$	−41.6286	−1.52108
$750$	13.5890	0.496202
$751$	−11.3729	−0.415003	−0.207502	−	0.978235i	$-0.566533\pi$
$751$	−11.3729	−0.415003	−0.207502	+	0.978235i	$0.566533\pi$
$752$	10.3772	0.378418
$753$	−26.6082	−0.969658
$754$	31.8651	1.16046
$755$	−2.99139	−0.108868
$756$	−18.9396	−0.688828
$757$	−35.9289	−1.30586	−0.652929	−	0.757419i	$-0.726460\pi$
$757$	−35.9289	−1.30586	−0.652929	+	0.757419i	$0.726460\pi$
$758$	9.65705	0.350760
$759$	−7.07849	−0.256933
$760$	−1.67709	−0.0608344
$761$	30.3579	1.10047	0.550237	−	0.835008i	$-0.314537\pi$
$761$	30.3579	1.10047	0.550237	+	0.835008i	$0.314537\pi$
$762$	−7.00791	−0.253870
$763$	−53.7945	−1.94749
$764$	−24.5115	−0.886796
$765$	2.67229	0.0966167
$766$	−4.41983	−0.159695
$767$	47.7371	1.72369
$768$	−1.92131	−0.0693292
$769$	−40.2606	−1.45184	−0.725918	−	0.687781i	$-0.758585\pi$
$769$	−40.2606	−1.45184	−0.725918	+	0.687781i	$0.758585\pi$
$770$	−4.30631	−0.155188
$771$	34.2605	1.23386
$772$	−18.6295	−0.670489
$773$	25.5248	0.918065	0.459032	−	0.888420i	$-0.348196\pi$
$773$	25.5248	0.918065	0.459032	+	0.888420i	$0.348196\pi$
$774$	1.48514	0.0533824
$775$	−8.05286	−0.289267
$776$	11.4952	0.412655
$777$	−30.0230	−1.07707
$778$	−19.8100	−0.710221
$779$	9.37470	0.335883
$780$	9.86180	0.353109
$781$	18.3272	0.655797
$782$	14.1193	0.504904
$783$	−20.6343	−0.737410
$784$	11.2331	0.401181
$785$	−6.06323	−0.216406
$786$	1.09421	0.0390292
$787$	−11.5146	−0.410451	−0.205225	−	0.978715i	$-0.565793\pi$
$787$	−11.5146	−0.410451	−0.205225	+	0.978715i	$0.565793\pi$
$788$	−16.1873	−0.576650
$789$	−60.0949	−2.13944
$790$	6.24140	0.222059
$791$	83.0315	2.95226
$792$	−0.930515	−0.0330644
$793$	94.3764	3.35140
$794$	27.4536	0.974293
$795$	15.8663	0.562720
$796$	−12.2000	−0.432416
$797$	9.32710	0.330383	0.165191	−	0.986262i	$-0.447176\pi$
$797$	9.32710	0.330383	0.165191	+	0.986262i	$0.447176\pi$
$798$	18.3608	0.649964
$799$	−53.5221	−1.89347
$800$	4.43846	0.156923
$801$	2.86281	0.101152
$802$	2.81990	0.0995741
$803$	−13.8366	−0.488282
$804$	0.0458193	0.00161592
$805$	8.75954	0.308733
$806$	−12.4276	−0.437743
$807$	35.0462	1.23368
$808$	2.16048	0.0760053
$809$	32.5883	1.14575	0.572873	−	0.819644i	$-0.305829\pi$
$809$	32.5883	1.14575	0.572873	+	0.819644i	$0.305829\pi$
$810$	−7.94038	−0.278997
$811$	−42.1967	−1.48173	−0.740863	−	0.671656i	$-0.765583\pi$
$811$	−42.1967	−1.48173	−0.740863	+	0.671656i	$0.765583\pi$
$812$	19.8645	0.697107
$813$	−60.0815	−2.10715
$814$	4.92506	0.172623
$815$	−1.18267	−0.0414271
$816$	9.90942	0.346899
$817$	4.80721	0.168183
$818$	−38.1736	−1.33471
$819$	−20.2226	−0.706636
$820$	3.13895	0.109617
$821$	−20.3503	−0.710229	−0.355115	−	0.934823i	$-0.615558\pi$
$821$	−20.3503	−0.710229	−0.355115	+	0.934823i	$0.615558\pi$
$822$	−38.0135	−1.32587
$823$	29.0397	1.01226	0.506131	−	0.862457i	$-0.331075\pi$
$823$	29.0397	1.01226	0.506131	+	0.862457i	$0.331075\pi$
$824$	10.6788	0.372015
$825$	11.4766	0.399563
$826$	29.7590	1.03545
$827$	31.8655	1.10807	0.554037	−	0.832492i	$-0.313087\pi$
$827$	31.8655	1.10807	0.554037	+	0.832492i	$0.313087\pi$
$828$	1.89278	0.0657786
$829$	−24.6707	−0.856850	−0.428425	−	0.903577i	$-0.640931\pi$
$829$	−24.6707	−0.856850	−0.428425	+	0.903577i	$0.640931\pi$
$830$	1.92547	0.0668341
$831$	9.65394	0.334892
$832$	6.84965	0.237469
$833$	−57.9362	−2.00737
$834$	9.34605	0.323627
$835$	−2.05164	−0.0710000
$836$	−3.01195	−0.104171
$837$	8.04749	0.278162
$838$	17.2140	0.594647
$839$	4.26641	0.147293	0.0736464	−	0.997284i	$-0.476536\pi$
$839$	4.26641	0.147293	0.0736464	+	0.997284i	$0.476536\pi$
$840$	6.14777	0.212118
$841$	−7.35811	−0.253728
$842$	27.4796	0.947009
$843$	−13.9899	−0.481837
$844$	−1.69403	−0.0583107
$845$	−25.4166	−0.874358
$846$	−7.17498	−0.246681
$847$	39.2363	1.34818
$848$	11.0202	0.378434
$849$	−1.77293	−0.0608467
$850$	−22.8920	−0.785190
$851$	−10.0182	−0.343418
$852$	−26.1642	−0.896372
$853$	−6.69358	−0.229184	−0.114592	−	0.993413i	$-0.536556\pi$
$853$	−6.69358	−0.229184	−0.114592	+	0.993413i	$0.536556\pi$
$854$	58.8335	2.01324
$855$	1.15957	0.0396564
$856$	−9.74906	−0.333216
$857$	16.5562	0.565549	0.282775	−	0.959186i	$-0.408745\pi$
$857$	16.5562	0.565549	0.282775	+	0.959186i	$0.408745\pi$
$858$	17.7112	0.604651
$859$	55.5281	1.89459	0.947297	−	0.320356i	$-0.103803\pi$
$859$	55.5281	1.89459	0.947297	+	0.320356i	$0.103803\pi$
$860$	1.60961	0.0548872
$861$	−34.3652	−1.17116
$862$	−16.2167	−0.552342
$863$	−46.0233	−1.56665	−0.783326	−	0.621611i	$-0.786479\pi$
$863$	−46.0233	−1.56665	−0.783326	+	0.621611i	$0.786479\pi$
$864$	−4.43550	−0.150899
$865$	−18.0060	−0.612222
$866$	−25.8960	−0.879982
$867$	−18.4472	−0.626498
$868$	−7.74725	−0.262959
$869$	11.2092	0.380246
$870$	6.69785	0.227078
$871$	−0.163350	−0.00553491
$872$	−12.5982	−0.426629
$873$	−7.94800	−0.268999
$874$	6.12667	0.207238
$875$	−30.2011	−1.02098
$876$	19.7534	0.667404
$877$	−40.9775	−1.38371	−0.691855	−	0.722036i	$-0.743206\pi$
$877$	−40.9775	−1.38371	−0.691855	+	0.722036i	$0.743206\pi$
$878$	−12.2998	−0.415098
$879$	−8.30128	−0.279995
$880$	−1.00850	−0.0339965
$881$	−38.2595	−1.28900	−0.644498	−	0.764606i	$-0.722933\pi$
$881$	−38.2595	−1.28900	−0.644498	+	0.764606i	$0.722933\pi$
$882$	−7.76672	−0.261519
$883$	−15.5834	−0.524422	−0.262211	−	0.965011i	$-0.584452\pi$
$883$	−15.5834	−0.524422	−0.262211	+	0.965011i	$0.584452\pi$
$884$	−35.3281	−1.18821
$885$	10.0340	0.337291
$886$	11.8647	0.398602
$887$	−40.2547	−1.35162	−0.675811	−	0.737075i	$-0.736206\pi$
$887$	−40.2547	−1.35162	−0.675811	+	0.737075i	$0.736206\pi$
$888$	−7.03112	−0.235949
$889$	15.5748	0.522361
$890$	3.10273	0.104004
$891$	−14.2605	−0.477743
$892$	−22.2532	−0.745093
$893$	−23.2245	−0.777177
$894$	−16.4568	−0.550396
$895$	−12.6396	−0.422494
$896$	4.27002	0.142651
$897$	−36.0267	−1.20290
$898$	−17.0884	−0.570247
$899$	−8.44045	−0.281505
$900$	−3.06882	−0.102294
$901$	−56.8382	−1.89355
$902$	5.63737	0.187704
$903$	−17.6220	−0.586423
$904$	19.4452	0.646739
$905$	6.73819	0.223985
$906$	7.66970	0.254809
$907$	52.2411	1.73464	0.867318	−	0.497754i	$-0.165842\pi$
$907$	52.2411	1.73464	0.867318	+	0.497754i	$0.165842\pi$
$908$	−28.1341	−0.933664
$909$	−1.49379	−0.0495459
$910$	−21.9174	−0.726555
$911$	36.9918	1.22559	0.612797	−	0.790241i	$-0.290044\pi$
$911$	36.9918	1.22559	0.612797	+	0.790241i	$0.290044\pi$
$912$	4.29993	0.142385
$913$	3.45803	0.114444
$914$	8.85122	0.292772
$915$	19.8373	0.655801
$916$	17.9872	0.594314
$917$	−2.43184	−0.0803063
$918$	22.8767	0.755045
$919$	13.1076	0.432380	0.216190	−	0.976351i	$-0.430637\pi$
$919$	13.1076	0.432380	0.216190	+	0.976351i	$0.430637\pi$
$920$	2.05141	0.0676328
$921$	23.9781	0.790105
$922$	−23.5079	−0.774191
$923$	93.2781	3.07029
$924$	11.0410	0.363224
$925$	16.2428	0.534059
$926$	34.2301	1.12487
$927$	−7.38352	−0.242506
$928$	4.65208	0.152712
$929$	27.3986	0.898920	0.449460	−	0.893300i	$-0.351616\pi$
$929$	27.3986	0.898920	0.449460	+	0.893300i	$0.351616\pi$
$930$	−2.61220	−0.0856573
$931$	−25.1398	−0.823925
$932$	−4.12034	−0.134966
$933$	26.1494	0.856094
$934$	−12.8200	−0.419483
$935$	5.20148	0.170107
$936$	−4.73596	−0.154800
$937$	43.9266	1.43502	0.717510	−	0.696548i	$-0.245282\pi$
$937$	43.9266	1.43502	0.717510	+	0.696548i	$0.245282\pi$
$938$	−0.101831	−0.00332491
$939$	23.1626	0.755881
$940$	−7.77629	−0.253635
$941$	−33.4424	−1.09019	−0.545096	−	0.838374i	$-0.683507\pi$
$941$	−33.4424	−1.09019	−0.545096	+	0.838374i	$0.683507\pi$
$942$	15.5457	0.506505
$943$	−11.4671	−0.373419
$944$	6.96928	0.226831
$945$	14.1926	0.461687
$946$	2.89076	0.0939868
$947$	−18.2159	−0.591936	−0.295968	−	0.955198i	$-0.595642\pi$
$947$	−18.2159	−0.591936	−0.295968	+	0.955198i	$0.595642\pi$
$948$	−16.0025	−0.519736
$949$	−70.4227	−2.28602
$950$	−9.93337	−0.322281
$951$	−63.0618	−2.04492
$952$	−22.0233	−0.713778
$953$	38.5444	1.24858	0.624289	−	0.781194i	$-0.285389\pi$
$953$	38.5444	1.24858	0.624289	+	0.781194i	$0.285389\pi$
$954$	−7.61952	−0.246691
$955$	18.3680	0.594375
$956$	−25.5323	−0.825773
$957$	12.0290	0.388841
$958$	18.6596	0.602863
$959$	84.4832	2.72811
$960$	1.43975	0.0464678
$961$	−27.7082	−0.893812
$962$	25.0667	0.808181
$963$	6.74066	0.217215
$964$	−22.1028	−0.711884
$965$	13.9602	0.449395
$966$	−22.4588	−0.722600
$967$	−12.8719	−0.413933	−0.206966	−	0.978348i	$-0.566359\pi$
$967$	−12.8719	−0.413933	−0.206966	+	0.978348i	$0.566359\pi$
$968$	9.18880	0.295339
$969$	−22.1775	−0.712445
$970$	−8.61410	−0.276582
$971$	16.8622	0.541135	0.270567	−	0.962701i	$-0.412789\pi$
$971$	16.8622	0.541135	0.270567	+	0.962701i	$0.412789\pi$
$972$	7.05204	0.226194
$973$	−20.7712	−0.665894
$974$	−0.499629	−0.0160092
$975$	58.4113	1.87066
$976$	13.7783	0.441032
$977$	33.9529	1.08625	0.543126	−	0.839651i	$-0.317241\pi$
$977$	33.9529	1.08625	0.543126	+	0.839651i	$0.317241\pi$
$978$	3.03228	0.0969615
$979$	5.57232	0.178092
$980$	−8.41762	−0.268891
$981$	8.71060	0.278108
$982$	37.7003	1.20306
$983$	−3.08672	−0.0984511	−0.0492256	−	0.998788i	$-0.515675\pi$
$983$	−3.08672	−0.0984511	−0.0492256	+	0.998788i	$0.515675\pi$
$984$	−8.04802	−0.256562
$985$	12.1302	0.386499
$986$	−23.9938	−0.764119
$987$	85.1348	2.70987
$988$	−15.3297	−0.487702
$989$	−5.88016	−0.186978
$990$	0.697292	0.0221614
$991$	30.9101	0.981892	0.490946	−	0.871190i	$-0.336651\pi$
$991$	30.9101	0.981892	0.490946	+	0.871190i	$0.336651\pi$
$992$	−1.81434	−0.0576053
$993$	−13.9382	−0.442314
$994$	58.1489	1.84437
$995$	9.14217	0.289826
$996$	−4.93676	−0.156427
$997$	−8.48660	−0.268773	−0.134387	−	0.990929i	$-0.542906\pi$
$997$	−8.48660	−0.268773	−0.134387	+	0.990929i	$0.542906\pi$
$998$	8.34798	0.264251
$999$	−16.2319	−0.513556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.10	✓	37	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.92131 q^{3} +1.00000 q^{4} -0.749362 q^{5} +1.92131 q^{6} -4.27002 q^{7} -1.00000 q^{8} +0.691416 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.92131 q^{3} +1.00000 q^{4} -0.749362 q^{5} +1.92131 q^{6} -4.27002 q^{7} -1.00000 q^{8} +0.691416 q^{9} +0.749362 q^{10} +1.34581 q^{11} -1.92131 q^{12} +6.84965 q^{13} +4.27002 q^{14} +1.43975 q^{15} +1.00000 q^{16} -5.15765 q^{17} -0.691416 q^{18} -2.23802 q^{19} -0.749362 q^{20} +8.20401 q^{21} -1.34581 q^{22} +2.73754 q^{23} +1.92131 q^{24} -4.43846 q^{25} -6.84965 q^{26} +4.43550 q^{27} -4.27002 q^{28} -4.65208 q^{29} -1.43975 q^{30} +1.81434 q^{31} -1.00000 q^{32} -2.58571 q^{33} +5.15765 q^{34} +3.19979 q^{35} +0.691416 q^{36} -3.65955 q^{37} +2.23802 q^{38} -13.1603 q^{39} +0.749362 q^{40} -4.18883 q^{41} -8.20401 q^{42} -2.14797 q^{43} +1.34581 q^{44} -0.518121 q^{45} -2.73754 q^{46} +10.3772 q^{47} -1.92131 q^{48} +11.2331 q^{49} +4.43846 q^{50} +9.90942 q^{51} +6.84965 q^{52} +11.0202 q^{53} -4.43550 q^{54} -1.00850 q^{55} +4.27002 q^{56} +4.29993 q^{57} +4.65208 q^{58} +6.96928 q^{59} +1.43975 q^{60} +13.7783 q^{61} -1.81434 q^{62} -2.95236 q^{63} +1.00000 q^{64} -5.13286 q^{65} +2.58571 q^{66} -0.0238480 q^{67} -5.15765 q^{68} -5.25965 q^{69} -3.19979 q^{70} +13.6179 q^{71} -0.691416 q^{72} -10.2812 q^{73} +3.65955 q^{74} +8.52763 q^{75} -2.23802 q^{76} -5.74663 q^{77} +13.1603 q^{78} +8.32895 q^{79} -0.749362 q^{80} -10.5962 q^{81} +4.18883 q^{82} +2.56948 q^{83} +8.20401 q^{84} +3.86495 q^{85} +2.14797 q^{86} +8.93808 q^{87} -1.34581 q^{88} +4.14049 q^{89} +0.518121 q^{90} -29.2481 q^{91} +2.73754 q^{92} -3.48590 q^{93} -10.3772 q^{94} +1.67709 q^{95} +1.92131 q^{96} -11.4952 q^{97} -11.2331 q^{98} +0.930515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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