LMFDB - Embedded newform 211.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,2,Mod(1,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, 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("211.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	211.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:	$1.68484348265$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.11491$ of defining polynomial
Character	$\chi$	$=$	211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11491 q^{2} +1.11491 q^{3} +2.47283 q^{4} -1.35793 q^{5} -2.35793 q^{6} -3.11491 q^{7} -1.00000 q^{8} -1.75698 q^{9} +O(q^{10})$	\(q-2.11491 q^{2} +1.11491 q^{3} +2.47283 q^{4} -1.35793 q^{5} -2.35793 q^{6} -3.11491 q^{7} -1.00000 q^{8} -1.75698 q^{9} +2.87189 q^{10} -3.00000 q^{11} +2.75698 q^{12} +3.94567 q^{13} +6.58774 q^{14} -1.51396 q^{15} -2.83076 q^{16} -7.47283 q^{17} +3.71585 q^{18} +2.47283 q^{19} -3.35793 q^{20} -3.47283 q^{21} +6.34472 q^{22} +1.41226 q^{23} -1.11491 q^{24} -3.15604 q^{25} -8.34472 q^{26} -5.30359 q^{27} -7.70265 q^{28} -10.5877 q^{29} +3.20189 q^{30} -4.41850 q^{31} +7.98680 q^{32} -3.34472 q^{33} +15.8044 q^{34} +4.22982 q^{35} -4.34472 q^{36} +5.58774 q^{37} -5.22982 q^{38} +4.39905 q^{39} +1.35793 q^{40} +8.10170 q^{41} +7.34472 q^{42} +9.45963 q^{43} -7.41850 q^{44} +2.38585 q^{45} -2.98680 q^{46} -3.75698 q^{47} -3.15604 q^{48} +2.70265 q^{49} +6.67472 q^{50} -8.33152 q^{51} +9.75698 q^{52} +1.47283 q^{53} +11.2166 q^{54} +4.07378 q^{55} +3.11491 q^{56} +2.75698 q^{57} +22.3921 q^{58} +3.53341 q^{59} -3.74378 q^{60} +0.926221 q^{61} +9.34472 q^{62} +5.47283 q^{63} -11.2298 q^{64} -5.35793 q^{65} +7.07378 q^{66} -18.4791 q^{68} +1.57454 q^{69} -8.94567 q^{70} -5.21037 q^{71} +1.75698 q^{72} +3.11491 q^{73} -11.8176 q^{74} -3.51869 q^{75} +6.11491 q^{76} +9.34472 q^{77} -9.30359 q^{78} -7.96511 q^{79} +3.84396 q^{80} -0.642074 q^{81} -17.1344 q^{82} +17.1755 q^{83} -8.58774 q^{84} +10.1476 q^{85} -20.0062 q^{86} -11.8044 q^{87} +3.00000 q^{88} -5.91302 q^{89} -5.04585 q^{90} -12.2904 q^{91} +3.49228 q^{92} -4.92622 q^{93} +7.94567 q^{94} -3.35793 q^{95} +8.90454 q^{96} +1.45339 q^{97} -5.71585 q^{98} +5.27094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} + q^{12} + q^{13} + 8 q^{14} + 10 q^{15} - 4 q^{16} - 17 q^{17} + 13 q^{18} + 2 q^{19} - 11 q^{20} - 5 q^{21} + 16 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 5 q^{28} - 20 q^{29} + 26 q^{30} + 3 q^{31} + 4 q^{32} + 9 q^{33} + 3 q^{34} + 6 q^{36} + 5 q^{37} - 3 q^{38} + 5 q^{39} + 5 q^{40} - 2 q^{41} + 3 q^{42} + 3 q^{43} - 6 q^{44} - 21 q^{45} + 11 q^{46} - 4 q^{47} + 6 q^{48} - 10 q^{49} + 31 q^{50} + 14 q^{51} + 22 q^{52} - q^{53} + q^{54} + 15 q^{55} + 3 q^{56} + q^{57} + 11 q^{58} - 12 q^{59} + 16 q^{60} + 9 q^{62} + 11 q^{63} - 21 q^{64} - 17 q^{65} + 24 q^{66} - 22 q^{68} - 27 q^{69} - 16 q^{70} - 11 q^{71} - 2 q^{72} + 3 q^{73} - 11 q^{74} - 37 q^{75} + 12 q^{76} + 9 q^{77} - 18 q^{78} - 5 q^{79} + 27 q^{80} - q^{81} - 37 q^{82} + 28 q^{83} - 14 q^{84} + 36 q^{85} - 32 q^{86} + 9 q^{87} + 9 q^{88} + 5 q^{89} - 47 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 13 q^{94} - 11 q^{95} + 25 q^{96} + 7 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 + q^12 + q^13 + 8 * q^14 + 10 * q^15 - 4 * q^16 - 17 * q^17 + 13 * q^18 + 2 * q^19 - 11 * q^20 - 5 * q^21 + 16 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 5 * q^28 - 20 * q^29 + 26 * q^30 + 3 * q^31 + 4 * q^32 + 9 * q^33 + 3 * q^34 + 6 * q^36 + 5 * q^37 - 3 * q^38 + 5 * q^39 + 5 * q^40 - 2 * q^41 + 3 * q^42 + 3 * q^43 - 6 * q^44 - 21 * q^45 + 11 * q^46 - 4 * q^47 + 6 * q^48 - 10 * q^49 + 31 * q^50 + 14 * q^51 + 22 * q^52 - q^53 + q^54 + 15 * q^55 + 3 * q^56 + q^57 + 11 * q^58 - 12 * q^59 + 16 * q^60 + 9 * q^62 + 11 * q^63 - 21 * q^64 - 17 * q^65 + 24 * q^66 - 22 * q^68 - 27 * q^69 - 16 * q^70 - 11 * q^71 - 2 * q^72 + 3 * q^73 - 11 * q^74 - 37 * q^75 + 12 * q^76 + 9 * q^77 - 18 * q^78 - 5 * q^79 + 27 * q^80 - q^81 - 37 * q^82 + 28 * q^83 - 14 * q^84 + 36 * q^85 - 32 * q^86 + 9 * q^87 + 9 * q^88 + 5 * q^89 - 47 * q^90 - 7 * q^91 - 3 * q^92 - 12 * q^93 + 13 * q^94 - 11 * q^95 + 25 * q^96 + 7 * q^97 - 19 * q^98 - 6 * 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 $

$2$	−2.11491	−1.49547	−0.747733	−	0.664000i	$-0.768858\pi$
$2$	−2.11491	−1.49547	−0.747733	+	0.664000i	$0.768858\pi$
$3$	1.11491	0.643692	0.321846	−	0.946792i	$-0.395697\pi$
$3$	1.11491	0.643692	0.321846	+	0.946792i	$0.395697\pi$
$4$	2.47283	1.23642
$5$	−1.35793	−0.607283	−0.303642	−	0.952786i	$-0.598203\pi$
$5$	−1.35793	−0.607283	−0.303642	+	0.952786i	$0.598203\pi$
$6$	−2.35793	−0.962619
$7$	−3.11491	−1.17732	−0.588662	−	0.808379i	$-0.700345\pi$
$7$	−3.11491	−1.17732	−0.588662	+	0.808379i	$0.700345\pi$
$8$	−1.00000	−0.353553
$9$	−1.75698	−0.585660
$10$	2.87189	0.908171
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	2.75698	0.795872
$13$	3.94567	1.09433	0.547166	−	0.837024i	$-0.315707\pi$
$13$	3.94567	1.09433	0.547166	+	0.837024i	$0.315707\pi$
$14$	6.58774	1.76065
$15$	−1.51396	−0.390903
$16$	−2.83076	−0.707690
$17$	−7.47283	−1.81243	−0.906214	−	0.422819i	$-0.861041\pi$
$17$	−7.47283	−1.81243	−0.906214	+	0.422819i	$0.861041\pi$
$18$	3.71585	0.875835
$19$	2.47283	0.567307	0.283654	−	0.958927i	$-0.408453\pi$
$19$	2.47283	0.567307	0.283654	+	0.958927i	$0.408453\pi$
$20$	−3.35793	−0.750855
$21$	−3.47283	−0.757834
$22$	6.34472	1.35270
$23$	1.41226	0.294476	0.147238	−	0.989101i	$-0.452962\pi$
$23$	1.41226	0.294476	0.147238	+	0.989101i	$0.452962\pi$
$24$	−1.11491	−0.227580
$25$	−3.15604	−0.631207
$26$	−8.34472	−1.63653
$27$	−5.30359	−1.02068
$28$	−7.70265	−1.45566
$29$	−10.5877	−1.96609	−0.983047	−	0.183353i	$-0.941305\pi$
$29$	−10.5877	−1.96609	−0.983047	+	0.183353i	$0.941305\pi$
$30$	3.20189	0.584583
$31$	−4.41850	−0.793586	−0.396793	−	0.917908i	$-0.629877\pi$
$31$	−4.41850	−0.793586	−0.396793	+	0.917908i	$0.629877\pi$
$32$	7.98680	1.41188
$33$	−3.34472	−0.582241
$34$	15.8044	2.71042
$35$	4.22982	0.714969
$36$	−4.34472	−0.724120
$37$	5.58774	0.918619	0.459310	−	0.888276i	$-0.348097\pi$
$37$	5.58774	0.918619	0.459310	+	0.888276i	$0.348097\pi$
$38$	−5.22982	−0.848388
$39$	4.39905	0.704413
$40$	1.35793	0.214707
$41$	8.10170	1.26527	0.632637	−	0.774449i	$-0.281973\pi$
$41$	8.10170	1.26527	0.632637	+	0.774449i	$0.281973\pi$
$42$	7.34472	1.13332
$43$	9.45963	1.44258	0.721290	−	0.692633i	$-0.243549\pi$
$43$	9.45963	1.44258	0.721290	+	0.692633i	$0.243549\pi$
$44$	−7.41850	−1.11838
$45$	2.38585	0.355662
$46$	−2.98680	−0.440379
$47$	−3.75698	−0.548012	−0.274006	−	0.961728i	$-0.588349\pi$
$47$	−3.75698	−0.548012	−0.274006	+	0.961728i	$0.588349\pi$
$48$	−3.15604	−0.455535
$49$	2.70265	0.386093
$50$	6.67472	0.943949
$51$	−8.33152	−1.16665
$52$	9.75698	1.35305
$53$	1.47283	0.202309	0.101155	−	0.994871i	$-0.467746\pi$
$53$	1.47283	0.202309	0.101155	+	0.994871i	$0.467746\pi$
$54$	11.2166	1.52639
$55$	4.07378	0.549308
$56$	3.11491	0.416247
$57$	2.75698	0.365171
$58$	22.3921	2.94023
$59$	3.53341	0.460011	0.230005	−	0.973189i	$-0.426126\pi$
$59$	3.53341	0.460011	0.230005	+	0.973189i	$0.426126\pi$
$60$	−3.74378	−0.483320
$61$	0.926221	0.118590	0.0592952	−	0.998240i	$-0.481115\pi$
$61$	0.926221	0.118590	0.0592952	+	0.998240i	$0.481115\pi$
$62$	9.34472	1.18678
$63$	5.47283	0.689512
$64$	−11.2298	−1.40373
$65$	−5.35793	−0.664569
$66$	7.07378	0.870722
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−18.4791	−2.24092
$69$	1.57454	0.189552
$70$	−8.94567	−1.06921
$71$	−5.21037	−0.618357	−0.309178	−	0.951004i	$-0.600054\pi$
$71$	−5.21037	−0.618357	−0.309178	+	0.951004i	$0.600054\pi$
$72$	1.75698	0.207062
$73$	3.11491	0.364572	0.182286	−	0.983246i	$-0.441650\pi$
$73$	3.11491	0.364572	0.182286	+	0.983246i	$0.441650\pi$
$74$	−11.8176	−1.37376
$75$	−3.51869	−0.406303
$76$	6.11491	0.701428
$77$	9.34472	1.06493
$78$	−9.30359	−1.05342
$79$	−7.96511	−0.896145	−0.448073	−	0.893997i	$-0.647889\pi$
$79$	−7.96511	−0.896145	−0.448073	+	0.893997i	$0.647889\pi$
$80$	3.84396	0.429768
$81$	−0.642074	−0.0713415
$82$	−17.1344	−1.89217
$83$	17.1755	1.88525	0.942627	−	0.333848i	$-0.108347\pi$
$83$	17.1755	1.88525	0.942627	+	0.333848i	$0.108347\pi$
$84$	−8.58774	−0.936999
$85$	10.1476	1.10066
$86$	−20.0062	−2.15733
$87$	−11.8044	−1.26556
$88$	3.00000	0.319801
$89$	−5.91302	−0.626779	−0.313389	−	0.949625i	$-0.601464\pi$
$89$	−5.91302	−0.626779	−0.313389	+	0.949625i	$0.601464\pi$
$90$	−5.04585	−0.531880
$91$	−12.2904	−1.28838
$92$	3.49228	0.364095
$93$	−4.92622	−0.510825
$94$	7.94567	0.819533
$95$	−3.35793	−0.344516
$96$	8.90454	0.908816
$97$	1.45339	0.147569	0.0737845	−	0.997274i	$-0.476492\pi$
$97$	1.45339	0.147569	0.0737845	+	0.997274i	$0.476492\pi$
$98$	−5.71585	−0.577388
$99$	5.27094	0.529750
$100$	−7.80435	−0.780435
$101$	−0.811313	−0.0807287	−0.0403643	−	0.999185i	$-0.512852\pi$
$101$	−0.811313	−0.0807287	−0.0403643	+	0.999185i	$0.512852\pi$
$102$	17.6204	1.74468
$103$	−6.85244	−0.675191	−0.337596	−	0.941291i	$-0.609614\pi$
$103$	−6.85244	−0.675191	−0.337596	+	0.941291i	$0.609614\pi$
$104$	−3.94567	−0.386905
$105$	4.71585	0.460220
$106$	−3.11491	−0.302547
$107$	11.1887	1.08165	0.540826	−	0.841135i	$-0.318112\pi$
$107$	11.1887	1.08165	0.540826	+	0.841135i	$0.318112\pi$
$108$	−13.1149	−1.26198
$109$	−19.2361	−1.84248	−0.921240	−	0.388994i	$-0.872823\pi$
$109$	−19.2361	−1.84248	−0.921240	+	0.388994i	$0.872823\pi$
$110$	−8.61567	−0.821472
$111$	6.22982	0.591308
$112$	8.81756	0.833181
$113$	−14.5140	−1.36536	−0.682679	−	0.730718i	$-0.739185\pi$
$113$	−14.5140	−1.36536	−0.682679	+	0.730718i	$0.739185\pi$
$114$	−5.83076	−0.546101
$115$	−1.91774	−0.178830
$116$	−26.1817	−2.43091
$117$	−6.93246	−0.640907
$118$	−7.47283	−0.687930
$119$	23.2772	2.13382
$120$	1.51396	0.138205
$121$	−2.00000	−0.181818
$122$	−1.95887	−0.177348
$123$	9.03265	0.814447
$124$	−10.9262	−0.981204
$125$	11.0753	0.990605
$126$	−11.5745	−1.03114
$127$	5.87189	0.521046	0.260523	−	0.965468i	$-0.416105\pi$
$127$	5.87189	0.521046	0.260523	+	0.965468i	$0.416105\pi$
$128$	7.77643	0.687346
$129$	10.5466	0.928577
$130$	11.3315	0.993840
$131$	3.30359	0.288636	0.144318	−	0.989531i	$-0.453901\pi$
$131$	3.30359	0.288636	0.144318	+	0.989531i	$0.453901\pi$
$132$	−8.27094	−0.719893
$133$	−7.70265	−0.667904
$134$	0	0
$135$	7.20189	0.619840
$136$	7.47283	0.640790
$137$	6.15604	0.525946	0.262973	−	0.964803i	$-0.415297\pi$
$137$	6.15604	0.525946	0.262973	+	0.964803i	$0.415297\pi$
$138$	−3.33000	−0.283469
$139$	7.20813	0.611386	0.305693	−	0.952130i	$-0.401112\pi$
$139$	7.20813	0.611386	0.305693	+	0.952130i	$0.401112\pi$
$140$	10.4596	0.884000
$141$	−4.18869	−0.352751
$142$	11.0194	0.924731
$143$	−11.8370	−0.989860
$144$	4.97359	0.414466
$145$	14.3774	1.19398
$146$	−6.58774	−0.545205
$147$	3.01320	0.248525
$148$	13.8176	1.13580
$149$	−17.2841	−1.41597	−0.707986	−	0.706226i	$-0.750396\pi$
$149$	−17.2841	−1.41597	−0.707986	+	0.706226i	$0.750396\pi$
$150$	7.44170	0.607612
$151$	2.09546	0.170526	0.0852631	−	0.996358i	$-0.472827\pi$
$151$	2.09546	0.170526	0.0852631	+	0.996358i	$0.472827\pi$
$152$	−2.47283	−0.200573
$153$	13.1296	1.06147
$154$	−19.7632	−1.59257
$155$	6.00000	0.481932
$156$	10.8781	0.870948
$157$	−21.4247	−1.70988	−0.854940	−	0.518726i	$-0.826406\pi$
$157$	−21.4247	−1.70988	−0.854940	+	0.518726i	$0.826406\pi$
$158$	16.8455	1.34015
$159$	1.64207	0.130225
$160$	−10.8455	−0.857411
$161$	−4.39905	−0.346694
$162$	1.35793	0.106689
$163$	−19.4659	−1.52468	−0.762342	−	0.647174i	$-0.775951\pi$
$163$	−19.4659	−1.52468	−0.762342	+	0.647174i	$0.775951\pi$
$164$	20.0342	1.56441
$165$	4.54189	0.353585
$166$	−36.3246	−2.81933
$167$	16.3921	1.26846	0.634229	−	0.773145i	$-0.281318\pi$
$167$	16.3921	1.26846	0.634229	+	0.773145i	$0.281318\pi$
$168$	3.47283	0.267935
$169$	2.56829	0.197561
$170$	−21.4611	−1.64599
$171$	−4.34472	−0.332249
$172$	23.3921	1.78363
$173$	−24.5264	−1.86471	−0.932356	−	0.361542i	$-0.882250\pi$
$173$	−24.5264	−1.86471	−0.932356	+	0.361542i	$0.882250\pi$
$174$	24.9651	1.89260
$175$	9.83076	0.743136
$176$	8.49228	0.640130
$177$	3.93942	0.296105
$178$	12.5055	0.937326
$179$	24.3378	1.81909	0.909545	−	0.415606i	$-0.136430\pi$
$179$	24.3378	1.81909	0.909545	+	0.415606i	$0.136430\pi$
$180$	5.89981	0.439746
$181$	−13.6421	−1.01401	−0.507004	−	0.861944i	$-0.669247\pi$
$181$	−13.6421	−1.01401	−0.507004	+	0.861944i	$0.669247\pi$
$182$	25.9930	1.92673
$183$	1.03265	0.0763357
$184$	−1.41226	−0.104113
$185$	−7.58774	−0.557862
$186$	10.4185	0.763922
$187$	22.4185	1.63940
$188$	−9.29039	−0.677571
$189$	16.5202	1.20167
$190$	7.10170	0.515212
$191$	−3.78963	−0.274208	−0.137104	−	0.990557i	$-0.543779\pi$
$191$	−3.78963	−0.274208	−0.137104	+	0.990557i	$0.543779\pi$
$192$	−12.5202	−0.903568
$193$	−7.52021	−0.541316	−0.270658	−	0.962676i	$-0.587241\pi$
$193$	−7.52021	−0.541316	−0.270658	+	0.962676i	$0.587241\pi$
$194$	−3.07378	−0.220684
$195$	−5.97359	−0.427778
$196$	6.68320	0.477372
$197$	7.87189	0.560849	0.280424	−	0.959876i	$-0.409525\pi$
$197$	7.87189	0.560849	0.280424	+	0.959876i	$0.409525\pi$
$198$	−11.1476	−0.792222
$199$	−21.0342	−1.49107	−0.745536	−	0.666465i	$-0.767807\pi$
$199$	−21.0342	−1.49107	−0.745536	+	0.666465i	$0.767807\pi$
$200$	3.15604	0.223165
$201$	0	0
$202$	1.71585	0.120727
$203$	32.9798	2.31473
$204$	−20.6025	−1.44246
$205$	−11.0015	−0.768379
$206$	14.4923	1.00973
$207$	−2.48131	−0.172463
$208$	−11.1692	−0.774447
$209$	−7.41850	−0.513148
$210$	−9.97359	−0.688243
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.64207	0.250139
$213$	−5.80908	−0.398032
$214$	−23.6630	−1.61757
$215$	−12.8455	−0.876055
$216$	5.30359	0.360864
$217$	13.7632	0.934309
$218$	40.6825	2.75537
$219$	3.47283	0.234672
$220$	10.0738	0.679174
$221$	−29.4853	−1.98340
$222$	−13.1755	−0.884281
$223$	0.696406	0.0466348	0.0233174	−	0.999728i	$-0.492577\pi$
$223$	0.696406	0.0466348	0.0233174	+	0.999728i	$0.492577\pi$
$224$	−24.8781	−1.66224
$225$	5.54510	0.369673
$226$	30.6957	2.04185
$227$	−22.9387	−1.52250	−0.761248	−	0.648461i	$-0.775413\pi$
$227$	−22.9387	−1.52250	−0.761248	+	0.648461i	$0.775413\pi$
$228$	6.81756	0.451504
$229$	−7.41226	−0.489816	−0.244908	−	0.969546i	$-0.578758\pi$
$229$	−7.41226	−0.489816	−0.244908	+	0.969546i	$0.578758\pi$
$230$	4.05585	0.267435
$231$	10.4185	0.685487
$232$	10.5877	0.695119
$233$	0.406015	0.0265990	0.0132995	−	0.999912i	$-0.495767\pi$
$233$	0.406015	0.0265990	0.0132995	+	0.999912i	$0.495767\pi$
$234$	14.6615	0.958454
$235$	5.10170	0.332798
$236$	8.73753	0.568765
$237$	−8.88037	−0.576842
$238$	−49.2291	−3.19105
$239$	−26.3704	−1.70576	−0.852880	−	0.522107i	$-0.825146\pi$
$239$	−26.3704	−1.70576	−0.852880	+	0.522107i	$0.825146\pi$
$240$	4.28566	0.276638
$241$	12.9930	0.836955	0.418478	−	0.908227i	$-0.362564\pi$
$241$	12.9930	0.836955	0.418478	+	0.908227i	$0.362564\pi$
$242$	4.22982	0.271903
$243$	15.1949	0.974755
$244$	2.29039	0.146627
$245$	−3.67000	−0.234468
$246$	−19.1032	−1.21798
$247$	9.75698	0.620822
$248$	4.41850	0.280575
$249$	19.1491	1.21352
$250$	−23.4232	−1.48141
$251$	−11.3447	−0.716073	−0.358036	−	0.933708i	$-0.616554\pi$
$251$	−11.3447	−0.716073	−0.358036	+	0.933708i	$0.616554\pi$
$252$	13.5334	0.852525
$253$	−4.23678	−0.266364
$254$	−12.4185	−0.779206
$255$	11.3136	0.708484
$256$	6.01320	0.375825
$257$	−12.4053	−0.773821	−0.386911	−	0.922117i	$-0.626458\pi$
$257$	−12.4053	−0.773821	−0.386911	+	0.922117i	$0.626458\pi$
$258$	−22.3051	−1.38866
$259$	−17.4053	−1.08151
$260$	−13.2493	−0.821684
$261$	18.6025	1.15146
$262$	−6.98680	−0.431646
$263$	−6.81756	−0.420389	−0.210194	−	0.977660i	$-0.567410\pi$
$263$	−6.81756	−0.420389	−0.210194	+	0.977660i	$0.567410\pi$
$264$	3.34472	0.205853
$265$	−2.00000	−0.122859
$266$	16.2904	0.998828
$267$	−6.59247	−0.403452
$268$	0	0
$269$	−9.65528	−0.588693	−0.294346	−	0.955699i	$-0.595102\pi$
$269$	−9.65528	−0.588693	−0.294346	+	0.955699i	$0.595102\pi$
$270$	−15.2313	−0.926949
$271$	18.0000	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$271$	18.0000	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$272$	21.1538	1.28264
$273$	−13.7026	−0.829322
$274$	−13.0194	−0.786534
$275$	9.46811	0.570948
$276$	3.89357	0.234365
$277$	19.4185	1.16674	0.583372	−	0.812205i	$-0.301733\pi$
$277$	19.4185	1.16674	0.583372	+	0.812205i	$0.301733\pi$
$278$	−15.2445	−0.914307
$279$	7.76322	0.464772
$280$	−4.22982	−0.252780
$281$	7.96511	0.475159	0.237579	−	0.971368i	$-0.423646\pi$
$281$	7.96511	0.475159	0.237579	+	0.971368i	$0.423646\pi$
$282$	8.85868	0.527527
$283$	4.68945	0.278759	0.139379	−	0.990239i	$-0.455489\pi$
$283$	4.68945	0.278759	0.139379	+	0.990239i	$0.455489\pi$
$284$	−12.8844	−0.764547
$285$	−3.74378	−0.221762
$286$	25.0342	1.48030
$287$	−25.2361	−1.48964
$288$	−14.0327	−0.826882
$289$	38.8432	2.28490
$290$	−30.4068	−1.78555
$291$	1.62039	0.0949891
$292$	7.70265	0.450763
$293$	21.3161	1.24530	0.622649	−	0.782501i	$-0.286056\pi$
$293$	21.3161	1.24530	0.622649	+	0.782501i	$0.286056\pi$
$294$	−6.37265	−0.371660
$295$	−4.79811	−0.279357
$296$	−5.58774	−0.324781
$297$	15.9108	0.923237
$298$	36.5544	2.11754
$299$	5.57230	0.322255
$300$	−8.70113	−0.502360
$301$	−29.4659	−1.69838
$302$	−4.43171	−0.255016
$303$	−0.904539	−0.0519644
$304$	−7.00000	−0.401478
$305$	−1.25774	−0.0720180
$306$	−27.7680	−1.58739
$307$	−6.70961	−0.382938	−0.191469	−	0.981499i	$-0.561325\pi$
$307$	−6.70961	−0.382938	−0.191469	+	0.981499i	$0.561325\pi$
$308$	23.1079	1.31670
$309$	−7.63984	−0.434615
$310$	−12.6894	−0.720712
$311$	18.2834	1.03676	0.518379	−	0.855151i	$-0.326536\pi$
$311$	18.2834	1.03676	0.518379	+	0.855151i	$0.326536\pi$
$312$	−4.39905	−0.249047
$313$	−19.9325	−1.12665	−0.563325	−	0.826236i	$-0.690478\pi$
$313$	−19.9325	−1.12665	−0.563325	+	0.826236i	$0.690478\pi$
$314$	45.3114	2.55707
$315$	−7.43171	−0.418729
$316$	−19.6964	−1.10801
$317$	−12.9868	−0.729411	−0.364706	−	0.931123i	$-0.618830\pi$
$317$	−12.9868	−0.729411	−0.364706	+	0.931123i	$0.618830\pi$
$318$	−3.47283	−0.194747
$319$	31.7632	1.77840
$320$	15.2493	0.852460
$321$	12.4744	0.696250
$322$	9.30359	0.518469
$323$	−18.4791	−1.02820
$324$	−1.58774	−0.0882079
$325$	−12.4527	−0.690750
$326$	41.1685	2.28011
$327$	−21.4464	−1.18599
$328$	−8.10170	−0.447342
$329$	11.7026	0.645188
$330$	−9.60567	−0.528775
$331$	21.5613	1.18512	0.592559	−	0.805527i	$-0.298118\pi$
$331$	21.5613	1.18512	0.592559	+	0.805527i	$0.298118\pi$
$332$	42.4721	2.33096
$333$	−9.81756	−0.537999
$334$	−34.6678	−1.89694
$335$	0	0
$336$	9.83076	0.536312
$337$	−0.809079	−0.0440733	−0.0220367	−	0.999757i	$-0.507015\pi$
$337$	−0.809079	−0.0440733	−0.0220367	+	0.999757i	$0.507015\pi$
$338$	−5.43171	−0.295446
$339$	−16.1817	−0.878871
$340$	25.0932	1.36087
$341$	13.2555	0.717826
$342$	9.18869	0.496867
$343$	13.3859	0.722768
$344$	−9.45963	−0.510029
$345$	−2.13811	−0.115112
$346$	51.8712	2.78861
$347$	25.0342	1.34390	0.671952	−	0.740594i	$-0.265456\pi$
$347$	25.0342	1.34390	0.671952	+	0.740594i	$0.265456\pi$
$348$	−29.1902	−1.56476
$349$	−1.42698	−0.0763845	−0.0381922	−	0.999270i	$-0.512160\pi$
$349$	−1.42698	−0.0763845	−0.0381922	+	0.999270i	$0.512160\pi$
$350$	−20.7911	−1.11133
$351$	−20.9262	−1.11696
$352$	−23.9604	−1.27709
$353$	−4.89981	−0.260791	−0.130395	−	0.991462i	$-0.541625\pi$
$353$	−4.89981	−0.260791	−0.130395	+	0.991462i	$0.541625\pi$
$354$	−8.33152	−0.442815
$355$	7.07530	0.375518
$356$	−14.6219	−0.774960
$357$	25.9519	1.37352
$358$	−51.4721	−2.72039
$359$	6.31207	0.333138	0.166569	−	0.986030i	$-0.446731\pi$
$359$	6.31207	0.333138	0.166569	+	0.986030i	$0.446731\pi$
$360$	−2.38585	−0.125745
$361$	−12.8851	−0.678163
$362$	28.8517	1.51641
$363$	−2.22982	−0.117035
$364$	−30.3921	−1.59298
$365$	−4.22982	−0.221399
$366$	−2.18396	−0.114157
$367$	18.6630	0.974203	0.487101	−	0.873345i	$-0.338054\pi$
$367$	18.6630	0.974203	0.487101	+	0.873345i	$0.338054\pi$
$368$	−3.99777	−0.208398
$369$	−14.2345	−0.741021
$370$	16.0474	0.834263
$371$	−4.58774	−0.238184
$372$	−12.1817	−0.631593
$373$	−6.37041	−0.329847	−0.164924	−	0.986306i	$-0.552738\pi$
$373$	−6.37041	−0.329847	−0.164924	+	0.986306i	$0.552738\pi$
$374$	−47.4131	−2.45167
$375$	12.3479	0.637644
$376$	3.75698	0.193752
$377$	−41.7757	−2.15156
$378$	−34.9387	−1.79705
$379$	−37.7757	−1.94041	−0.970204	−	0.242290i	$-0.922102\pi$
$379$	−37.7757	−1.94041	−0.970204	+	0.242290i	$0.922102\pi$
$380$	−8.30359	−0.425965
$381$	6.54661	0.335393
$382$	8.01472	0.410069
$383$	31.8036	1.62509	0.812545	−	0.582899i	$-0.198082\pi$
$383$	31.8036	1.62509	0.812545	+	0.582899i	$0.198082\pi$
$384$	8.67000	0.442439
$385$	−12.6894	−0.646714
$386$	15.9045	0.809520
$387$	−16.6204	−0.844862
$388$	3.59398	0.182457
$389$	4.51396	0.228867	0.114433	−	0.993431i	$-0.463495\pi$
$389$	4.51396	0.228867	0.114433	+	0.993431i	$0.463495\pi$
$390$	12.6336	0.639727
$391$	−10.5536	−0.533717
$392$	−2.70265	−0.136504
$393$	3.68320	0.185793
$394$	−16.6483	−0.838730
$395$	10.8160	0.544214
$396$	13.0342	0.654992
$397$	0.147558	0.00740573	0.00370287	−	0.999993i	$-0.498821\pi$
$397$	0.147558	0.00740573	0.00370287	+	0.999993i	$0.498821\pi$
$398$	44.4853	2.22985
$399$	−8.58774	−0.429925
$400$	8.93398	0.446699
$401$	25.8260	1.28969	0.644845	−	0.764313i	$-0.276922\pi$
$401$	25.8260	1.28969	0.644845	+	0.764313i	$0.276922\pi$
$402$	0	0
$403$	−17.4339	−0.868446
$404$	−2.00624	−0.0998143
$405$	0.871889	0.0433245
$406$	−69.7493	−3.46160
$407$	−16.7632	−0.830922
$408$	8.33152	0.412472
$409$	27.3836	1.35403	0.677016	−	0.735968i	$-0.263273\pi$
$409$	27.3836	1.35403	0.677016	+	0.735968i	$0.263273\pi$
$410$	23.2672	1.14908
$411$	6.86341	0.338547
$412$	−16.9450	−0.834818
$413$	−11.0062	−0.541582
$414$	5.24774	0.257913
$415$	−23.3230	−1.14488
$416$	31.5132	1.54506
$417$	8.03640	0.393544
$418$	15.6894	0.767396
$419$	−12.5264	−0.611957	−0.305979	−	0.952038i	$-0.598984\pi$
$419$	−12.5264	−0.611957	−0.305979	+	0.952038i	$0.598984\pi$
$420$	11.6615	0.569024
$421$	−23.7438	−1.15720	−0.578600	−	0.815611i	$-0.696401\pi$
$421$	−23.7438	−1.15720	−0.578600	+	0.815611i	$0.696401\pi$
$422$	2.11491	0.102952
$423$	6.60095	0.320949
$424$	−1.47283	−0.0715271
$425$	23.5845	1.14402
$426$	12.2857	0.595242
$427$	−2.88509	−0.139619
$428$	27.6678	1.33737
$429$	−13.1972	−0.637165
$430$	27.1670	1.31011
$431$	−14.2361	−0.685727	−0.342863	−	0.939385i	$-0.611397\pi$
$431$	−14.2361	−0.685727	−0.342863	+	0.939385i	$0.611397\pi$
$432$	15.0132	0.722323
$433$	−0.486038	−0.0233575	−0.0116787	−	0.999932i	$-0.503718\pi$
$433$	−0.486038	−0.0233575	−0.0116787	+	0.999932i	$0.503718\pi$
$434$	−29.1079	−1.39723
$435$	16.0294	0.768553
$436$	−47.5676	−2.27807
$437$	3.49228	0.167058
$438$	−7.34472	−0.350944
$439$	19.6421	0.937465	0.468733	−	0.883340i	$-0.344711\pi$
$439$	19.6421	0.937465	0.468733	+	0.883340i	$0.344711\pi$
$440$	−4.07378	−0.194210
$441$	−4.74850	−0.226119
$442$	62.3587	2.96610
$443$	−1.43795	−0.0683190	−0.0341595	−	0.999416i	$-0.510875\pi$
$443$	−1.43795	−0.0683190	−0.0341595	+	0.999416i	$0.510875\pi$
$444$	15.4053	0.731103
$445$	8.02944	0.380632
$446$	−1.47283	−0.0697407
$447$	−19.2702	−0.911450
$448$	34.9798	1.65264
$449$	23.8021	1.12329	0.561646	−	0.827378i	$-0.310168\pi$
$449$	23.8021	1.12329	0.561646	+	0.827378i	$0.310168\pi$
$450$	−11.7274	−0.552833
$451$	−24.3051	−1.14448
$452$	−35.8906	−1.68815
$453$	2.33624	0.109766
$454$	48.5132	2.27684
$455$	16.6894	0.782413
$456$	−2.75698	−0.129107
$457$	−27.8168	−1.30122	−0.650608	−	0.759413i	$-0.725486\pi$
$457$	−27.8168	−1.30122	−0.650608	+	0.759413i	$0.725486\pi$
$458$	15.6762	0.732503
$459$	39.6329	1.84990
$460$	−4.74226	−0.221109
$461$	−21.3447	−0.994123	−0.497061	−	0.867715i	$-0.665588\pi$
$461$	−21.3447	−0.994123	−0.497061	+	0.867715i	$0.665588\pi$
$462$	−22.0342	−1.02512
$463$	−5.56205	−0.258490	−0.129245	−	0.991613i	$-0.541255\pi$
$463$	−5.56205	−0.258490	−0.129245	+	0.991613i	$0.541255\pi$
$464$	29.9714	1.39139
$465$	6.68945	0.310216
$466$	−0.858685	−0.0397778
$467$	25.5459	1.18212	0.591062	−	0.806626i	$-0.298709\pi$
$467$	25.5459	1.18212	0.591062	+	0.806626i	$0.298709\pi$
$468$	−17.1428	−0.792428
$469$	0	0
$470$	−10.7896	−0.497689
$471$	−23.8866	−1.10064
$472$	−3.53341	−0.162638
$473$	−28.3789	−1.30486
$474$	18.7812	0.862647
$475$	−7.80435	−0.358088
$476$	57.5606	2.63829
$477$	−2.58774	−0.118485
$478$	55.7710	2.55091
$479$	−0.0194469	−0.000888552 0	−0.000444276	−	1.00000i	$-0.500141\pi$
$479$	−0.0194469	−0.000888552 0	−0.000444276		1.00000i	$0.500141\pi$
$480$	−12.0917	−0.551908
$481$	22.0474	1.00527
$482$	−27.4791	−1.25164
$483$	−4.90454	−0.223164
$484$	−4.94567	−0.224803
$485$	−1.97359	−0.0896162
$486$	−32.1359	−1.45771
$487$	−1.62039	−0.0734270	−0.0367135	−	0.999326i	$-0.511689\pi$
$487$	−1.62039	−0.0734270	−0.0367135	+	0.999326i	$0.511689\pi$
$488$	−0.926221	−0.0419280
$489$	−21.7026	−0.981428
$490$	7.76171	0.350638
$491$	12.0543	0.544004	0.272002	−	0.962297i	$-0.412314\pi$
$491$	12.0543	0.544004	0.272002	+	0.962297i	$0.412314\pi$
$492$	22.3362	1.00700
$493$	79.1204	3.56341
$494$	−20.6351	−0.928418
$495$	−7.15755	−0.321708
$496$	12.5077	0.561613
$497$	16.2298	0.728007
$498$	−40.4985	−1.81478
$499$	−21.2794	−0.952598	−0.476299	−	0.879283i	$-0.658022\pi$
$499$	−21.2794	−0.952598	−0.476299	+	0.879283i	$0.658022\pi$
$500$	27.3874	1.22480
$501$	18.2757	0.816497
$502$	23.9930	1.07086
$503$	−26.2027	−1.16832	−0.584160	−	0.811638i	$-0.698576\pi$
$503$	−26.2027	−1.16832	−0.584160	+	0.811638i	$0.698576\pi$
$504$	−5.47283	−0.243779
$505$	1.10170	0.0490252
$506$	8.96039	0.398338
$507$	2.86341	0.127169
$508$	14.5202	0.644230
$509$	−8.85244	−0.392378	−0.196189	−	0.980566i	$-0.562857\pi$
$509$	−8.85244	−0.392378	−0.196189	+	0.980566i	$0.562857\pi$
$510$	−23.9272	−1.05951
$511$	−9.70265	−0.429220
$512$	−28.2702	−1.24938
$513$	−13.1149	−0.579037
$514$	26.2361	1.15722
$515$	9.30511	0.410032
$516$	26.0800	1.14811
$517$	11.2709	0.495696
$518$	36.8106	1.61736
$519$	−27.3447	−1.20030
$520$	5.35793	0.234961
$521$	−43.6803	−1.91367	−0.956833	−	0.290637i	$-0.906133\pi$
$521$	−43.6803	−1.91367	−0.956833	+	0.290637i	$0.906133\pi$
$522$	−39.3425	−1.72197
$523$	−1.33624	−0.0584299	−0.0292150	−	0.999573i	$-0.509301\pi$
$523$	−1.33624	−0.0584299	−0.0292150	+	0.999573i	$0.509301\pi$
$524$	8.16924	0.356875
$525$	10.9604	0.478351
$526$	14.4185	0.628677
$527$	33.0187	1.43832
$528$	9.46811	0.412047
$529$	−21.0055	−0.913284
$530$	4.22982	0.183731
$531$	−6.20813	−0.269410
$532$	−19.0474	−0.825808
$533$	31.9666	1.38463
$534$	13.9425	0.603349
$535$	−15.1934	−0.656869
$536$	0	0
$537$	27.1344	1.17093
$538$	20.4200	0.880370
$539$	−8.10795	−0.349234
$540$	17.8091	0.766381
$541$	39.1748	1.68425	0.842127	−	0.539279i	$-0.181303\pi$
$541$	39.1748	1.68425	0.842127	+	0.539279i	$0.181303\pi$
$542$	−38.0683	−1.63518
$543$	−15.2097	−0.652709
$544$	−59.6840	−2.55893
$545$	26.1212	1.11891
$546$	28.9798	1.24022
$547$	−30.1406	−1.28872	−0.644359	−	0.764723i	$-0.722876\pi$
$547$	−30.1406	−1.28872	−0.644359	+	0.764723i	$0.722876\pi$
$548$	15.2229	0.650288
$549$	−1.62735	−0.0694537
$550$	−20.0242	−0.853834
$551$	−26.1817	−1.11538
$552$	−1.57454	−0.0670168
$553$	24.8106	1.05505
$554$	−41.0683	−1.74483
$555$	−8.45963	−0.359091
$556$	17.8245	0.755928
$557$	18.6197	0.788941	0.394470	−	0.918909i	$-0.370928\pi$
$557$	18.6197	0.788941	0.394470	+	0.918909i	$0.370928\pi$
$558$	−16.4185	−0.695051
$559$	37.3246	1.57866
$560$	−11.9736	−0.505977
$561$	24.9946	1.05527
$562$	−16.8455	−0.710584
$563$	−13.3789	−0.563853	−0.281927	−	0.959436i	$-0.590973\pi$
$563$	−13.3789	−0.563853	−0.281927	+	0.959436i	$0.590973\pi$
$564$	−10.3579	−0.436147
$565$	19.7089	0.829159
$566$	−9.91774	−0.416874
$567$	2.00000	0.0839921
$568$	5.21037	0.218622
$569$	−4.93871	−0.207041	−0.103521	−	0.994627i	$-0.533011\pi$
$569$	−4.93871	−0.207041	−0.103521	+	0.994627i	$0.533011\pi$
$570$	7.91774	0.331638
$571$	−4.57526	−0.191468	−0.0957342	−	0.995407i	$-0.530520\pi$
$571$	−4.57526	−0.191468	−0.0957342	+	0.995407i	$0.530520\pi$
$572$	−29.2709	−1.22388
$573$	−4.22509	−0.176506
$574$	53.3719	2.22770
$575$	−4.45714	−0.185876
$576$	19.7306	0.822107
$577$	−38.7167	−1.61180	−0.805898	−	0.592055i	$-0.798317\pi$
$577$	−38.7167	−1.61180	−0.805898	+	0.592055i	$0.798317\pi$
$578$	−82.1499	−3.41698
$579$	−8.38433	−0.348441
$580$	35.5529	1.47625
$581$	−53.5000	−2.21956
$582$	−3.42698	−0.142053
$583$	−4.41850	−0.182996
$584$	−3.11491	−0.128896
$585$	9.41378	0.389212
$586$	−45.0815	−1.86230
$587$	−35.6568	−1.47171	−0.735857	−	0.677137i	$-0.763220\pi$
$587$	−35.6568	−1.47171	−0.735857	+	0.677137i	$0.763220\pi$
$588$	7.45115	0.307280
$589$	−10.9262	−0.450207
$590$	10.1476	0.417768
$591$	8.77643	0.361014
$592$	−15.8176	−0.650098
$593$	−20.1149	−0.826020	−0.413010	−	0.910726i	$-0.635523\pi$
$593$	−20.1149	−0.826020	−0.413010	+	0.910726i	$0.635523\pi$
$594$	−33.6498	−1.38067
$595$	−31.6087	−1.29583
$596$	−42.7408	−1.75073
$597$	−23.4512	−0.959792
$598$	−11.7849	−0.481921
$599$	18.3051	0.747927	0.373963	−	0.927444i	$-0.377999\pi$
$599$	18.3051	0.747927	0.373963	+	0.927444i	$0.377999\pi$
$600$	3.51869	0.143650
$601$	43.4846	1.77377	0.886887	−	0.461986i	$-0.152863\pi$
$601$	43.4846	1.77377	0.886887	+	0.461986i	$0.152863\pi$
$602$	62.3176	2.53988
$603$	0	0
$604$	5.18173	0.210841
$605$	2.71585	0.110415
$606$	1.91302	0.0777110
$607$	−19.4945	−0.791258	−0.395629	−	0.918410i	$-0.629473\pi$
$607$	−19.4945	−0.791258	−0.395629	+	0.918410i	$0.629473\pi$
$608$	19.7500	0.800969
$609$	36.7695	1.48997
$610$	2.66000	0.107700
$611$	−14.8238	−0.599707
$612$	32.4674	1.31242
$613$	19.1880	0.774995	0.387497	−	0.921871i	$-0.373340\pi$
$613$	19.1880	0.774995	0.387497	+	0.921871i	$0.373340\pi$
$614$	14.1902	0.572670
$615$	−12.2657	−0.494600
$616$	−9.34472	−0.376510
$617$	40.5155	1.63109	0.815546	−	0.578692i	$-0.196437\pi$
$617$	40.5155	1.63109	0.815546	+	0.578692i	$0.196437\pi$
$618$	16.1576	0.649952
$619$	8.71585	0.350320	0.175160	−	0.984540i	$-0.443956\pi$
$619$	8.71585	0.350320	0.175160	+	0.984540i	$0.443956\pi$
$620$	14.8370	0.595868
$621$	−7.49005	−0.300565
$622$	−38.6678	−1.55044
$623$	18.4185	0.737922
$624$	−12.4527	−0.498506
$625$	0.740743	0.0296297
$626$	42.1553	1.68487
$627$	−8.27094	−0.330310
$628$	−52.9798	−2.11413
$629$	−41.7563	−1.66493
$630$	15.7174	0.626195
$631$	43.5653	1.73431	0.867154	−	0.498039i	$-0.165946\pi$
$631$	43.5653	1.73431	0.867154	+	0.498039i	$0.165946\pi$
$632$	7.96511	0.316835
$633$	−1.11491	−0.0443136
$634$	27.4659	1.09081
$635$	−7.97359	−0.316422
$636$	4.06058	0.161012
$637$	10.6638	0.422513
$638$	−67.1763	−2.65953
$639$	9.15452	0.362147
$640$	−10.5598	−0.417413
$641$	−13.5598	−0.535581	−0.267790	−	0.963477i	$-0.586293\pi$
$641$	−13.5598	−0.535581	−0.267790	+	0.963477i	$0.586293\pi$
$642$	−26.3821	−1.04122
$643$	−22.0536	−0.869710	−0.434855	−	0.900501i	$-0.643200\pi$
$643$	−22.0536	−0.869710	−0.434855	+	0.900501i	$0.643200\pi$
$644$	−10.8781	−0.428658
$645$	−14.3215	−0.563909
$646$	39.0815	1.53764
$647$	25.7547	1.01252	0.506262	−	0.862380i	$-0.331027\pi$
$647$	25.7547	1.01252	0.506262	+	0.862380i	$0.331027\pi$
$648$	0.642074	0.0252230
$649$	−10.6002	−0.416095
$650$	26.3362	1.03299
$651$	15.3447	0.601407
$652$	−48.1359	−1.88515
$653$	34.0103	1.33092	0.665462	−	0.746432i	$-0.268235\pi$
$653$	34.0103	1.33092	0.665462	+	0.746432i	$0.268235\pi$
$654$	45.3572	1.77361
$655$	−4.48604	−0.175284
$656$	−22.9340	−0.895422
$657$	−5.47283	−0.213516
$658$	−24.7500	−0.964856
$659$	13.8844	0.540858	0.270429	−	0.962740i	$-0.412834\pi$
$659$	13.8844	0.540858	0.270429	+	0.962740i	$0.412834\pi$
$660$	11.2313	0.437179
$661$	−8.71362	−0.338920	−0.169460	−	0.985537i	$-0.554202\pi$
$661$	−8.71362	−0.338920	−0.169460	+	0.985537i	$0.554202\pi$
$662$	−45.6002	−1.77230
$663$	−32.8734	−1.27670
$664$	−17.1755	−0.666538
$665$	10.4596	0.405607
$666$	20.7632	0.804559
$667$	−14.9526	−0.578968
$668$	40.5349	1.56834
$669$	0.776428	0.0300184
$670$	0	0
$671$	−2.77866	−0.107269
$672$	−27.7368	−1.06997
$673$	27.5551	1.06217	0.531085	−	0.847318i	$-0.321784\pi$
$673$	27.5551	1.06217	0.531085	+	0.847318i	$0.321784\pi$
$674$	1.71113	0.0659101
$675$	16.7383	0.644259
$676$	6.35097	0.244268
$677$	−37.3943	−1.43718	−0.718590	−	0.695434i	$-0.755212\pi$
$677$	−37.3943	−1.43718	−0.718590	+	0.695434i	$0.755212\pi$
$678$	34.2229	1.31432
$679$	−4.52717	−0.173737
$680$	−10.1476	−0.389141
$681$	−25.5745	−0.980018
$682$	−28.0342	−1.07348
$683$	−17.5195	−0.670365	−0.335182	−	0.942153i	$-0.608798\pi$
$683$	−17.5195	−0.670365	−0.335182	+	0.942153i	$0.608798\pi$
$684$	−10.7438	−0.410799
$685$	−8.35944	−0.319398
$686$	−28.3098	−1.08087
$687$	−8.26398	−0.315291
$688$	−26.7779	−1.02090
$689$	5.81131	0.221393
$690$	4.52190	0.172146
$691$	13.4791	0.512768	0.256384	−	0.966575i	$-0.417469\pi$
$691$	13.4791	0.512768	0.256384	+	0.966575i	$0.417469\pi$
$692$	−60.6498	−2.30556
$693$	−16.4185	−0.623687
$694$	−52.9450	−2.00976
$695$	−9.78811	−0.371284
$696$	11.8044	0.447443
$697$	−60.5427	−2.29322
$698$	3.01793	0.114230
$699$	0.452670	0.0171215
$700$	24.3098	0.918825
$701$	−8.55910	−0.323273	−0.161636	−	0.986850i	$-0.551677\pi$
$701$	−8.55910	−0.323273	−0.161636	+	0.986850i	$0.551677\pi$
$702$	44.2570	1.67037
$703$	13.8176	0.521139
$704$	33.6894	1.26972
$705$	5.68793	0.214220
$706$	10.3627	0.390004
$707$	2.52717	0.0950439
$708$	9.74154	0.366110
$709$	−9.62887	−0.361620	−0.180810	−	0.983518i	$-0.557872\pi$
$709$	−9.62887	−0.361620	−0.180810	+	0.983518i	$0.557872\pi$
$710$	−14.9636	−0.561574
$711$	13.9946	0.524837
$712$	5.91302	0.221600
$713$	−6.24007	−0.233692
$714$	−54.8859	−2.05405
$715$	16.0738	0.601125
$716$	60.1832	2.24915
$717$	−29.4006	−1.09798
$718$	−13.3494	−0.498197
$719$	−15.3014	−0.570644	−0.285322	−	0.958432i	$-0.592101\pi$
$719$	−15.3014	−0.570644	−0.285322	+	0.958432i	$0.592101\pi$
$720$	−6.75377	−0.251698
$721$	21.3447	0.794919
$722$	27.2508	1.01417
$723$	14.4860	0.538742
$724$	−33.7346	−1.25374
$725$	33.4153	1.24101
$726$	4.71585	0.175022
$727$	−3.95887	−0.146826	−0.0734132	−	0.997302i	$-0.523389\pi$
$727$	−3.95887	−0.146826	−0.0734132	+	0.997302i	$0.523389\pi$
$728$	12.2904	0.455512
$729$	18.8672	0.698784
$730$	8.94567	0.331094
$731$	−70.6902	−2.61457
$732$	2.55357	0.0943828
$733$	−4.70041	−0.173614	−0.0868069	−	0.996225i	$-0.527666\pi$
$733$	−4.70041	−0.173614	−0.0868069	+	0.996225i	$0.527666\pi$
$734$	−39.4706	−1.45689
$735$	−4.09171	−0.150925
$736$	11.2794	0.415765
$737$	0	0
$738$	30.1047	1.10817
$739$	26.1887	0.963366	0.481683	−	0.876345i	$-0.340026\pi$
$739$	26.1887	0.963366	0.481683	+	0.876345i	$0.340026\pi$
$740$	−18.7632	−0.689750
$741$	10.8781	0.399618
$742$	9.70265	0.356195
$743$	−50.3246	−1.84623	−0.923114	−	0.384525i	$-0.874365\pi$
$743$	−50.3246	−1.84623	−0.923114	+	0.384525i	$0.874365\pi$
$744$	4.92622	0.180604
$745$	23.4706	0.859896
$746$	13.4728	0.493275
$747$	−30.1770	−1.10412
$748$	55.4372	2.02699
$749$	−34.8517	−1.27345
$750$	−26.1147	−0.953575
$751$	37.5551	1.37040	0.685202	−	0.728353i	$-0.259714\pi$
$751$	37.5551	1.37040	0.685202	+	0.728353i	$0.259714\pi$
$752$	10.6351	0.387823
$753$	−12.6483	−0.460930
$754$	88.3518	3.21758
$755$	−2.84548	−0.103558
$756$	40.8517	1.48576
$757$	38.4527	1.39759	0.698793	−	0.715324i	$-0.253721\pi$
$757$	38.4527	1.39759	0.698793	+	0.715324i	$0.253721\pi$
$758$	79.8921	2.90181
$759$	−4.72361	−0.171456
$760$	3.35793	0.121805
$761$	6.18396	0.224168	0.112084	−	0.993699i	$-0.464247\pi$
$761$	6.18396	0.224168	0.112084	+	0.993699i	$0.464247\pi$
$762$	−13.8455	−0.501569
$763$	59.9185	2.16920
$764$	−9.37113	−0.339036
$765$	−17.8291	−0.644611
$766$	−67.2617	−2.43027
$767$	13.9417	0.503404
$768$	6.70417	0.241916
$769$	−0.149075	−0.00537580	−0.00268790	−	0.999996i	$-0.500856\pi$
$769$	−0.149075	−0.00537580	−0.00268790	+	0.999996i	$0.500856\pi$
$770$	26.8370	0.967138
$771$	−13.8308	−0.498103
$772$	−18.5962	−0.669293
$773$	−30.1692	−1.08511	−0.542556	−	0.840020i	$-0.682543\pi$
$773$	−30.1692	−1.08511	−0.542556	+	0.840020i	$0.682543\pi$
$774$	35.1506	1.26346
$775$	13.9450	0.500917
$776$	−1.45339	−0.0521736
$777$	−19.4053	−0.696161
$778$	−9.54661	−0.342263
$779$	20.0342	0.717799
$780$	−14.7717	−0.528912
$781$	15.6311	0.559325
$782$	22.3198	0.798156
$783$	56.1531	2.00675
$784$	−7.65055	−0.273234
$785$	29.0932	1.03838
$786$	−7.78963	−0.277847
$787$	−41.2577	−1.47068	−0.735340	−	0.677699i	$-0.762977\pi$
$787$	−41.2577	−1.47068	−0.735340	+	0.677699i	$0.762977\pi$
$788$	19.4659	0.693443
$789$	−7.60095	−0.270601
$790$	−22.8749	−0.813853
$791$	45.2097	1.60747
$792$	−5.27094	−0.187295
$793$	3.65456	0.129777
$794$	−0.312072	−0.0110750
$795$	−2.22982	−0.0790834
$796$	−52.0140	−1.84359
$797$	−6.40378	−0.226834	−0.113417	−	0.993548i	$-0.536180\pi$
$797$	−6.40378	−0.226834	−0.113417	+	0.993548i	$0.536180\pi$
$798$	18.1623	0.642938
$799$	28.0753	0.993233
$800$	−25.2066	−0.891188
$801$	10.3891	0.367079
$802$	−54.6197	−1.92869
$803$	−9.34472	−0.329768
$804$	0	0
$805$	5.97359	0.210541
$806$	36.8712	1.29873
$807$	−10.7647	−0.378937
$808$	0.811313	0.0285419
$809$	1.84325	0.0648051	0.0324026	−	0.999475i	$-0.489684\pi$
$809$	1.84325	0.0648051	0.0324026	+	0.999475i	$0.489684\pi$
$810$	−1.84396	−0.0647903
$811$	8.64903	0.303709	0.151854	−	0.988403i	$-0.451476\pi$
$811$	8.64903	0.303709	0.151854	+	0.988403i	$0.451476\pi$
$812$	81.5537	2.86197
$813$	20.0683	0.703827
$814$	35.4527	1.24262
$815$	26.4332	0.925915
$816$	23.5845	0.825624
$817$	23.3921	0.818386
$818$	−57.9138	−2.02491
$819$	21.5940	0.754555
$820$	−27.2049	−0.950037
$821$	11.8781	0.414550	0.207275	−	0.978283i	$-0.433541\pi$
$821$	11.8781	0.414550	0.207275	+	0.978283i	$0.433541\pi$
$822$	−14.5155	−0.506285
$823$	−26.7375	−0.932012	−0.466006	−	0.884782i	$-0.654307\pi$
$823$	−26.7375	−0.932012	−0.466006	+	0.884782i	$0.654307\pi$
$824$	6.85244	0.238716
$825$	10.5561	0.367515
$826$	23.2772	0.809917
$827$	12.5885	0.437744	0.218872	−	0.975754i	$-0.429762\pi$
$827$	12.5885	0.437744	0.218872	+	0.975754i	$0.429762\pi$
$828$	−6.13587	−0.213236
$829$	42.2313	1.46675	0.733377	−	0.679822i	$-0.237943\pi$
$829$	42.2313	1.46675	0.733377	+	0.679822i	$0.237943\pi$
$830$	49.3261	1.71213
$831$	21.6498	0.751024
$832$	−44.3091	−1.53614
$833$	−20.1964	−0.699765
$834$	−16.9962	−0.588532
$835$	−22.2593	−0.770313
$836$	−18.3447	−0.634465
$837$	23.4339	0.809995
$838$	26.4923	0.915161
$839$	−35.0062	−1.20855	−0.604275	−	0.796776i	$-0.706537\pi$
$839$	−35.0062	−1.20855	−0.604275	+	0.796776i	$0.706537\pi$
$840$	−4.71585	−0.162712
$841$	83.1003	2.86553
$842$	50.2159	1.73055
$843$	8.88037	0.305856
$844$	−2.47283	−0.0851185
$845$	−3.48755	−0.119976
$846$	−13.9604	−0.479968
$847$	6.22982	0.214059
$848$	−4.16924	−0.143172
$849$	5.22830	0.179435
$850$	−49.8791	−1.71084
$851$	7.89134	0.270512
$852$	−14.3649	−0.492133
$853$	−7.86269	−0.269213	−0.134607	−	0.990899i	$-0.542977\pi$
$853$	−7.86269	−0.269213	−0.134607	+	0.990899i	$0.542977\pi$
$854$	6.10170	0.208796
$855$	5.89981	0.201769
$856$	−11.1887	−0.382421
$857$	34.1468	1.16643	0.583217	−	0.812316i	$-0.301794\pi$
$857$	34.1468	1.16643	0.583217	+	0.812316i	$0.301794\pi$
$858$	27.9108	0.952858
$859$	23.5287	0.802788	0.401394	−	0.915905i	$-0.368526\pi$
$859$	23.5287	0.802788	0.401394	+	0.915905i	$0.368526\pi$
$860$	−31.7647	−1.08317
$861$	−28.1359	−0.958868
$862$	30.1079	1.02548
$863$	54.3286	1.84937	0.924683	−	0.380738i	$-0.124330\pi$
$863$	54.3286	1.84937	0.924683	+	0.380738i	$0.124330\pi$
$864$	−42.3587	−1.44107
$865$	33.3051	1.13241
$866$	1.02792	0.0349303
$867$	43.3066	1.47077
$868$	34.0342	1.15519
$869$	23.8953	0.810594
$870$	−33.9008	−1.14934
$871$	0	0
$872$	19.2361	0.651415
$873$	−2.55357	−0.0864254
$874$	−7.38585	−0.249830
$875$	−34.4985	−1.16626
$876$	8.58774	0.290153
$877$	−23.7540	−0.802117	−0.401058	−	0.916053i	$-0.631358\pi$
$877$	−23.7540	−0.802117	−0.401058	+	0.916053i	$0.631358\pi$
$878$	−41.5412	−1.40195
$879$	23.7655	0.801589
$880$	−11.5319	−0.388740
$881$	−27.4355	−0.924324	−0.462162	−	0.886796i	$-0.652926\pi$
$881$	−27.4355	−0.924324	−0.462162	+	0.886796i	$0.652926\pi$
$882$	10.0426	0.338153
$883$	−23.6498	−0.795880	−0.397940	−	0.917411i	$-0.630275\pi$
$883$	−23.6498	−0.795880	−0.397940	+	0.917411i	$0.630275\pi$
$884$	−72.9123	−2.45231
$885$	−5.34945	−0.179820
$886$	3.04113	0.102169
$887$	−6.04809	−0.203075	−0.101537	−	0.994832i	$-0.532376\pi$
$887$	−6.04809	−0.203075	−0.101537	+	0.994832i	$0.532376\pi$
$888$	−6.22982	−0.209059
$889$	−18.2904	−0.613440
$890$	−16.9815	−0.569222
$891$	1.92622	0.0645308
$892$	1.72210	0.0576600
$893$	−9.29039	−0.310891
$894$	40.7547	1.36304
$895$	−33.0489	−1.10470
$896$	−24.2229	−0.809229
$897$	6.21260	0.207433
$898$	−50.3393	−1.67984
$899$	46.7820	1.56027
$900$	13.7121	0.457070
$901$	−11.0062	−0.366671
$902$	51.4031	1.71153
$903$	−32.8517	−1.09324
$904$	14.5140	0.482727
$905$	18.5249	0.615790
$906$	−4.94094	−0.164152
$907$	0.761707	0.0252921	0.0126460	−	0.999920i	$-0.495975\pi$
$907$	0.761707	0.0252921	0.0126460	+	0.999920i	$0.495975\pi$
$908$	−56.7236	−1.88244
$909$	1.42546	0.0472796
$910$	−35.2966	−1.17007
$911$	−47.0621	−1.55924	−0.779618	−	0.626255i	$-0.784587\pi$
$911$	−47.0621	−1.55924	−0.779618	+	0.626255i	$0.784587\pi$
$912$	−7.80435	−0.258428
$913$	−51.5264	−1.70528
$914$	58.8300	1.94592
$915$	−1.40226	−0.0463574
$916$	−18.3293	−0.605617
$917$	−10.2904	−0.339819
$918$	−83.8199	−2.76647
$919$	10.0319	0.330923	0.165461	−	0.986216i	$-0.447089\pi$
$919$	10.0319	0.330923	0.165461	+	0.986216i	$0.447089\pi$
$920$	1.91774	0.0632261
$921$	−7.48059	−0.246494
$922$	45.1421	1.48668
$923$	−20.5584	−0.676687
$924$	25.7632	0.847548
$925$	−17.6351	−0.579839
$926$	11.7632	0.386564
$927$	12.0396	0.395433
$928$	−84.5621	−2.77589
$929$	51.9883	1.70568	0.852841	−	0.522171i	$-0.174878\pi$
$929$	51.9883	1.70568	0.852841	+	0.522171i	$0.174878\pi$
$930$	−14.1476	−0.463917
$931$	6.68320	0.219033
$932$	1.00401	0.0328874
$933$	20.3843	0.667353
$934$	−54.0272	−1.76782
$935$	−30.4427	−0.995582
$936$	6.93246	0.226595
$937$	16.0878	0.525565	0.262782	−	0.964855i	$-0.415360\pi$
$937$	16.0878	0.525565	0.262782	+	0.964855i	$0.415360\pi$
$938$	0	0
$939$	−22.2229	−0.725215
$940$	12.6157	0.411478
$941$	−51.6234	−1.68288	−0.841438	−	0.540354i	$-0.818290\pi$
$941$	−51.6234	−1.68288	−0.841438	+	0.540354i	$0.818290\pi$
$942$	50.5180	1.64596
$943$	11.4417	0.372593
$944$	−10.0022	−0.325545
$945$	−22.4332	−0.729753
$946$	60.0187	1.95138
$947$	−1.10866	−0.0360268	−0.0180134	−	0.999838i	$-0.505734\pi$
$947$	−1.10866	−0.0360268	−0.0180134	+	0.999838i	$0.505734\pi$
$948$	−21.9597	−0.713217
$949$	12.2904	0.398963
$950$	16.5055	0.535509
$951$	−14.4791	−0.469516
$952$	−23.2772	−0.754418
$953$	57.1964	1.85277	0.926387	−	0.376572i	$-0.122897\pi$
$953$	57.1964	1.85277	0.926387	+	0.376572i	$0.122897\pi$
$954$	5.47283	0.177190
$955$	5.14604	0.166522
$956$	−65.2097	−2.10903
$957$	35.4131	1.14474
$958$	0.0411284	0.00132880
$959$	−19.1755	−0.619209
$960$	17.0015	0.548722
$961$	−11.4768	−0.370221
$962$	−46.6282	−1.50335
$963$	−19.6583	−0.633480
$964$	32.1296	1.03483
$965$	10.2119	0.328732
$966$	10.3726	0.333734
$967$	−19.4596	−0.625780	−0.312890	−	0.949789i	$-0.601297\pi$
$967$	−19.4596	−0.625780	−0.312890	+	0.949789i	$0.601297\pi$
$968$	2.00000	0.0642824
$969$	−20.6025	−0.661846
$970$	4.17397	0.134018
$971$	−24.6630	−0.791475	−0.395737	−	0.918364i	$-0.629511\pi$
$971$	−24.6630	−0.791475	−0.395737	+	0.918364i	$0.629511\pi$
$972$	37.5745	1.20520
$973$	−22.4527	−0.719800
$974$	3.42698	0.109808
$975$	−13.8836	−0.444630
$976$	−2.62191	−0.0839253
$977$	−2.89205	−0.0925250	−0.0462625	−	0.998929i	$-0.514731\pi$
$977$	−2.89205	−0.0925250	−0.0462625	+	0.998929i	$0.514731\pi$
$978$	45.8991	1.46769
$979$	17.7391	0.566943
$980$	−9.07530	−0.289900
$981$	33.7974	1.07907
$982$	−25.4938	−0.813540
$983$	26.7717	0.853885	0.426942	−	0.904279i	$-0.359591\pi$
$983$	26.7717	0.853885	0.426942	+	0.904279i	$0.359591\pi$
$984$	−9.03265	−0.287950
$985$	−10.6894	−0.340594
$986$	−167.332	−5.32895
$987$	13.0474	0.415302
$988$	24.1274	0.767595
$989$	13.3594	0.424806
$990$	15.1376	0.481103
$991$	−35.0691	−1.11401	−0.557003	−	0.830511i	$-0.688049\pi$
$991$	−35.0691	−1.11401	−0.557003	+	0.830511i	$0.688049\pi$
$992$	−35.2897	−1.12045
$993$	24.0389	0.762851
$994$	−34.3246	−1.08871
$995$	28.5629	0.905503
$996$	47.3525	1.50042
$997$	−37.3711	−1.18356	−0.591778	−	0.806101i	$-0.701574\pi$
$997$	−37.3711	−1.18356	−0.591778	+	0.806101i	$0.701574\pi$
$998$	45.0040	1.42458
$999$	−29.6351	−0.937613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.2.a.c.1.1	✓	3
3.2	odd	2		1899.2.a.e.1.3		3
4.3	odd	2		3376.2.a.m.1.1		3
5.4	even	2		5275.2.a.h.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.2.a.c.1.1	✓	3	1.1	even	1	trivial
1899.2.a.e.1.3		3	3.2	odd	2
3376.2.a.m.1.1		3	4.3	odd	2
5275.2.a.h.1.3		3	5.4	even	2

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:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	211.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11491 q^{2} +1.11491 q^{3} +2.47283 q^{4} -1.35793 q^{5} -2.35793 q^{6} -3.11491 q^{7} -1.00000 q^{8} -1.75698 q^{9} +O(q^{10})\)	\(q-2.11491 q^{2} +1.11491 q^{3} +2.47283 q^{4} -1.35793 q^{5} -2.35793 q^{6} -3.11491 q^{7} -1.00000 q^{8} -1.75698 q^{9} +2.87189 q^{10} -3.00000 q^{11} +2.75698 q^{12} +3.94567 q^{13} +6.58774 q^{14} -1.51396 q^{15} -2.83076 q^{16} -7.47283 q^{17} +3.71585 q^{18} +2.47283 q^{19} -3.35793 q^{20} -3.47283 q^{21} +6.34472 q^{22} +1.41226 q^{23} -1.11491 q^{24} -3.15604 q^{25} -8.34472 q^{26} -5.30359 q^{27} -7.70265 q^{28} -10.5877 q^{29} +3.20189 q^{30} -4.41850 q^{31} +7.98680 q^{32} -3.34472 q^{33} +15.8044 q^{34} +4.22982 q^{35} -4.34472 q^{36} +5.58774 q^{37} -5.22982 q^{38} +4.39905 q^{39} +1.35793 q^{40} +8.10170 q^{41} +7.34472 q^{42} +9.45963 q^{43} -7.41850 q^{44} +2.38585 q^{45} -2.98680 q^{46} -3.75698 q^{47} -3.15604 q^{48} +2.70265 q^{49} +6.67472 q^{50} -8.33152 q^{51} +9.75698 q^{52} +1.47283 q^{53} +11.2166 q^{54} +4.07378 q^{55} +3.11491 q^{56} +2.75698 q^{57} +22.3921 q^{58} +3.53341 q^{59} -3.74378 q^{60} +0.926221 q^{61} +9.34472 q^{62} +5.47283 q^{63} -11.2298 q^{64} -5.35793 q^{65} +7.07378 q^{66} -18.4791 q^{68} +1.57454 q^{69} -8.94567 q^{70} -5.21037 q^{71} +1.75698 q^{72} +3.11491 q^{73} -11.8176 q^{74} -3.51869 q^{75} +6.11491 q^{76} +9.34472 q^{77} -9.30359 q^{78} -7.96511 q^{79} +3.84396 q^{80} -0.642074 q^{81} -17.1344 q^{82} +17.1755 q^{83} -8.58774 q^{84} +10.1476 q^{85} -20.0062 q^{86} -11.8044 q^{87} +3.00000 q^{88} -5.91302 q^{89} -5.04585 q^{90} -12.2904 q^{91} +3.49228 q^{92} -4.92622 q^{93} +7.94567 q^{94} -3.35793 q^{95} +8.90454 q^{96} +1.45339 q^{97} -5.71585 q^{98} +5.27094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} + q^{12} + q^{13} + 8 q^{14} + 10 q^{15} - 4 q^{16} - 17 q^{17} + 13 q^{18} + 2 q^{19} - 11 q^{20} - 5 q^{21} + 16 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 5 q^{28} - 20 q^{29} + 26 q^{30} + 3 q^{31} + 4 q^{32} + 9 q^{33} + 3 q^{34} + 6 q^{36} + 5 q^{37} - 3 q^{38} + 5 q^{39} + 5 q^{40} - 2 q^{41} + 3 q^{42} + 3 q^{43} - 6 q^{44} - 21 q^{45} + 11 q^{46} - 4 q^{47} + 6 q^{48} - 10 q^{49} + 31 q^{50} + 14 q^{51} + 22 q^{52} - q^{53} + q^{54} + 15 q^{55} + 3 q^{56} + q^{57} + 11 q^{58} - 12 q^{59} + 16 q^{60} + 9 q^{62} + 11 q^{63} - 21 q^{64} - 17 q^{65} + 24 q^{66} - 22 q^{68} - 27 q^{69} - 16 q^{70} - 11 q^{71} - 2 q^{72} + 3 q^{73} - 11 q^{74} - 37 q^{75} + 12 q^{76} + 9 q^{77} - 18 q^{78} - 5 q^{79} + 27 q^{80} - q^{81} - 37 q^{82} + 28 q^{83} - 14 q^{84} + 36 q^{85} - 32 q^{86} + 9 q^{87} + 9 q^{88} + 5 q^{89} - 47 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 13 q^{94} - 11 q^{95} + 25 q^{96} + 7 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 + q^12 + q^13 + 8 * q^14 + 10 * q^15 - 4 * q^16 - 17 * q^17 + 13 * q^18 + 2 * q^19 - 11 * q^20 - 5 * q^21 + 16 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 5 * q^28 - 20 * q^29 + 26 * q^30 + 3 * q^31 + 4 * q^32 + 9 * q^33 + 3 * q^34 + 6 * q^36 + 5 * q^37 - 3 * q^38 + 5 * q^39 + 5 * q^40 - 2 * q^41 + 3 * q^42 + 3 * q^43 - 6 * q^44 - 21 * q^45 + 11 * q^46 - 4 * q^47 + 6 * q^48 - 10 * q^49 + 31 * q^50 + 14 * q^51 + 22 * q^52 - q^53 + q^54 + 15 * q^55 + 3 * q^56 + q^57 + 11 * q^58 - 12 * q^59 + 16 * q^60 + 9 * q^62 + 11 * q^63 - 21 * q^64 - 17 * q^65 + 24 * q^66 - 22 * q^68 - 27 * q^69 - 16 * q^70 - 11 * q^71 - 2 * q^72 + 3 * q^73 - 11 * q^74 - 37 * q^75 + 12 * q^76 + 9 * q^77 - 18 * q^78 - 5 * q^79 + 27 * q^80 - q^81 - 37 * q^82 + 28 * q^83 - 14 * q^84 + 36 * q^85 - 32 * q^86 + 9 * q^87 + 9 * q^88 + 5 * q^89 - 47 * q^90 - 7 * q^91 - 3 * q^92 - 12 * q^93 + 13 * q^94 - 11 * q^95 + 25 * q^96 + 7 * q^97 - 19 * q^98 - 6 * q^99

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