LMFDB - Embedded newform 6011.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72000 q^{2} -0.0742815 q^{3} +5.39842 q^{4} +2.94538 q^{5} +0.202046 q^{6} -4.01910 q^{7} -9.24371 q^{8} -2.99448 q^{9} +O(q^{10})$	\(q-2.72000 q^{2} -0.0742815 q^{3} +5.39842 q^{4} +2.94538 q^{5} +0.202046 q^{6} -4.01910 q^{7} -9.24371 q^{8} -2.99448 q^{9} -8.01145 q^{10} +0.175964 q^{11} -0.401003 q^{12} +2.05953 q^{13} +10.9320 q^{14} -0.218787 q^{15} +14.3461 q^{16} +2.55130 q^{17} +8.14500 q^{18} -5.31403 q^{19} +15.9004 q^{20} +0.298545 q^{21} -0.478623 q^{22} +4.28750 q^{23} +0.686637 q^{24} +3.67528 q^{25} -5.60194 q^{26} +0.445279 q^{27} -21.6968 q^{28} -4.65475 q^{29} +0.595102 q^{30} +9.61061 q^{31} -20.5340 q^{32} -0.0130709 q^{33} -6.93955 q^{34} -11.8378 q^{35} -16.1655 q^{36} +2.07456 q^{37} +14.4542 q^{38} -0.152985 q^{39} -27.2263 q^{40} -9.29820 q^{41} -0.812044 q^{42} +2.74328 q^{43} +0.949928 q^{44} -8.81989 q^{45} -11.6620 q^{46} -12.9229 q^{47} -1.06565 q^{48} +9.15320 q^{49} -9.99676 q^{50} -0.189515 q^{51} +11.1182 q^{52} +8.42563 q^{53} -1.21116 q^{54} +0.518281 q^{55} +37.1514 q^{56} +0.394734 q^{57} +12.6609 q^{58} +6.11985 q^{59} -1.18111 q^{60} -6.14854 q^{61} -26.1409 q^{62} +12.0351 q^{63} +27.1603 q^{64} +6.06611 q^{65} +0.0355528 q^{66} +7.23065 q^{67} +13.7730 q^{68} -0.318482 q^{69} +32.1989 q^{70} +6.96513 q^{71} +27.6801 q^{72} -2.05662 q^{73} -5.64282 q^{74} -0.273005 q^{75} -28.6874 q^{76} -0.707218 q^{77} +0.416120 q^{78} -3.58015 q^{79} +42.2547 q^{80} +8.95037 q^{81} +25.2911 q^{82} +7.19798 q^{83} +1.61167 q^{84} +7.51456 q^{85} -7.46173 q^{86} +0.345761 q^{87} -1.62656 q^{88} +1.69870 q^{89} +23.9901 q^{90} -8.27748 q^{91} +23.1457 q^{92} -0.713891 q^{93} +35.1505 q^{94} -15.6518 q^{95} +1.52529 q^{96} -18.3815 q^{97} -24.8967 q^{98} -0.526921 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.72000	−1.92333	−0.961666	−	0.274222i	$-0.911580\pi$
$2$	−2.72000	−1.92333	−0.961666	+	0.274222i	$0.911580\pi$
$3$	−0.0742815	−0.0428864	−0.0214432	−	0.999770i	$-0.506826\pi$
$3$	−0.0742815	−0.0428864	−0.0214432	+	0.999770i	$0.506826\pi$
$4$	5.39842	2.69921
$5$	2.94538	1.31721	0.658607	−	0.752487i	$-0.271146\pi$
$5$	2.94538	1.31721	0.658607	+	0.752487i	$0.271146\pi$
$6$	0.202046	0.0824849
$7$	−4.01910	−1.51908	−0.759539	−	0.650461i	$-0.774576\pi$
$7$	−4.01910	−1.51908	−0.759539	+	0.650461i	$0.774576\pi$
$8$	−9.24371	−3.26814
$9$	−2.99448	−0.998161
$10$	−8.01145	−2.53344
$11$	0.175964	0.0530552	0.0265276	−	0.999648i	$-0.491555\pi$
$11$	0.175964	0.0530552	0.0265276	+	0.999648i	$0.491555\pi$
$12$	−0.401003	−0.115759
$13$	2.05953	0.571212	0.285606	−	0.958347i	$-0.407805\pi$
$13$	2.05953	0.571212	0.285606	+	0.958347i	$0.407805\pi$
$14$	10.9320	2.92169
$15$	−0.218787	−0.0564907
$16$	14.3461	3.58652
$17$	2.55130	0.618782	0.309391	−	0.950935i	$-0.399875\pi$
$17$	2.55130	0.618782	0.309391	+	0.950935i	$0.399875\pi$
$18$	8.14500	1.91980
$19$	−5.31403	−1.21912	−0.609561	−	0.792739i	$-0.708654\pi$
$19$	−5.31403	−1.21912	−0.609561	+	0.792739i	$0.708654\pi$
$20$	15.9004	3.55544
$21$	0.298545	0.0651479
$22$	−0.478623	−0.102043
$23$	4.28750	0.894006	0.447003	−	0.894533i	$-0.352491\pi$
$23$	4.28750	0.894006	0.447003	+	0.894533i	$0.352491\pi$
$24$	0.686637	0.140159
$25$	3.67528	0.735055
$26$	−5.60194	−1.09863
$27$	0.445279	0.0856940
$28$	−21.6968	−4.10031
$29$	−4.65475	−0.864364	−0.432182	−	0.901786i	$-0.642256\pi$
$29$	−4.65475	−0.864364	−0.432182	+	0.901786i	$0.642256\pi$
$30$	0.595102	0.108650
$31$	9.61061	1.72612	0.863058	−	0.505104i	$-0.168546\pi$
$31$	9.61061	1.72612	0.863058	+	0.505104i	$0.168546\pi$
$32$	−20.5340	−3.62993
$33$	−0.0130709	−0.00227535
$34$	−6.93955	−1.19012
$35$	−11.8378	−2.00095
$36$	−16.1655	−2.69424
$37$	2.07456	0.341056	0.170528	−	0.985353i	$-0.445453\pi$
$37$	2.07456	0.341056	0.170528	+	0.985353i	$0.445453\pi$
$38$	14.4542	2.34478
$39$	−0.152985	−0.0244972
$40$	−27.2263	−4.30485
$41$	−9.29820	−1.45214	−0.726068	−	0.687623i	$-0.758654\pi$
$41$	−9.29820	−1.45214	−0.726068	+	0.687623i	$0.758654\pi$
$42$	−0.812044	−0.125301
$43$	2.74328	0.418346	0.209173	−	0.977879i	$-0.432923\pi$
$43$	2.74328	0.418346	0.209173	+	0.977879i	$0.432923\pi$
$44$	0.949928	0.143207
$45$	−8.81989	−1.31479
$46$	−11.6620	−1.71947
$47$	−12.9229	−1.88501	−0.942503	−	0.334198i	$-0.891534\pi$
$47$	−12.9229	−1.88501	−0.942503	+	0.334198i	$0.891534\pi$
$48$	−1.06565	−0.153813
$49$	9.15320	1.30760
$50$	−9.99676	−1.41376
$51$	−0.189515	−0.0265374
$52$	11.1182	1.54182
$53$	8.42563	1.15735	0.578675	−	0.815558i	$-0.303570\pi$
$53$	8.42563	1.15735	0.578675	+	0.815558i	$0.303570\pi$
$54$	−1.21116	−0.164818
$55$	0.518281	0.0698850
$56$	37.1514	4.96457
$57$	0.394734	0.0522838
$58$	12.6609	1.66246
$59$	6.11985	0.796737	0.398369	−	0.917225i	$-0.369576\pi$
$59$	6.11985	0.796737	0.398369	+	0.917225i	$0.369576\pi$
$60$	−1.18111	−0.152480
$61$	−6.14854	−0.787239	−0.393620	−	0.919273i	$-0.628777\pi$
$61$	−6.14854	−0.787239	−0.393620	+	0.919273i	$0.628777\pi$
$62$	−26.1409	−3.31990
$63$	12.0351	1.51628
$64$	27.1603	3.39504
$65$	6.06611	0.752409
$66$	0.0355528	0.00437625
$67$	7.23065	0.883365	0.441682	−	0.897172i	$-0.354382\pi$
$67$	7.23065	0.883365	0.441682	+	0.897172i	$0.354382\pi$
$68$	13.7730	1.67022
$69$	−0.318482	−0.0383407
$70$	32.1989	3.84850
$71$	6.96513	0.826608	0.413304	−	0.910593i	$-0.364375\pi$
$71$	6.96513	0.826608	0.413304	+	0.910593i	$0.364375\pi$
$72$	27.6801	3.26213
$73$	−2.05662	−0.240710	−0.120355	−	0.992731i	$-0.538403\pi$
$73$	−2.05662	−0.240710	−0.120355	+	0.992731i	$0.538403\pi$
$74$	−5.64282	−0.655965
$75$	−0.273005	−0.0315239
$76$	−28.6874	−3.29066
$77$	−0.707218	−0.0805950
$78$	0.416120	0.0471163
$79$	−3.58015	−0.402799	−0.201399	−	0.979509i	$-0.564549\pi$
$79$	−3.58015	−0.402799	−0.201399	+	0.979509i	$0.564549\pi$
$80$	42.2547	4.72422
$81$	8.95037	0.994486
$82$	25.2911	2.79294
$83$	7.19798	0.790081	0.395040	−	0.918664i	$-0.370731\pi$
$83$	7.19798	0.790081	0.395040	+	0.918664i	$0.370731\pi$
$84$	1.61167	0.175848
$85$	7.51456	0.815069
$86$	−7.46173	−0.804619
$87$	0.345761	0.0370695
$88$	−1.62656	−0.173392
$89$	1.69870	0.180062	0.0900311	−	0.995939i	$-0.471303\pi$
$89$	1.69870	0.180062	0.0900311	+	0.995939i	$0.471303\pi$
$90$	23.9901	2.52878
$91$	−8.27748	−0.867715
$92$	23.1457	2.41311
$93$	−0.713891	−0.0740270
$94$	35.1505	3.62549
$95$	−15.6518	−1.60585
$96$	1.52529	0.155675
$97$	−18.3815	−1.86636	−0.933180	−	0.359410i	$-0.882978\pi$
$97$	−18.3815	−1.86636	−0.933180	+	0.359410i	$0.882978\pi$
$98$	−24.8967	−2.51495
$99$	−0.526921	−0.0529576
$100$	19.8407	1.98407
$101$	−4.41058	−0.438869	−0.219435	−	0.975627i	$-0.570421\pi$
$101$	−4.41058	−0.438869	−0.219435	+	0.975627i	$0.570421\pi$
$102$	0.515481	0.0510402
$103$	14.7650	1.45483	0.727417	−	0.686195i	$-0.240720\pi$
$103$	14.7650	1.45483	0.727417	+	0.686195i	$0.240720\pi$
$104$	−19.0377	−1.86680
$105$	0.879329	0.0858138
$106$	−22.9178	−2.22597
$107$	2.65787	0.256946	0.128473	−	0.991713i	$-0.458992\pi$
$107$	2.65787	0.256946	0.128473	+	0.991713i	$0.458992\pi$
$108$	2.40380	0.231306
$109$	1.54634	0.148113	0.0740565	−	0.997254i	$-0.476405\pi$
$109$	1.54634	0.148113	0.0740565	+	0.997254i	$0.476405\pi$
$110$	−1.40973	−0.134412
$111$	−0.154102	−0.0146267
$112$	−57.6584	−5.44821
$113$	5.01050	0.471348	0.235674	−	0.971832i	$-0.424270\pi$
$113$	5.01050	0.471348	0.235674	+	0.971832i	$0.424270\pi$
$114$	−1.07368	−0.100559
$115$	12.6283	1.17760
$116$	−25.1283	−2.33310
$117$	−6.16723	−0.570161
$118$	−16.6460	−1.53239
$119$	−10.2540	−0.939979
$120$	2.02241	0.184620
$121$	−10.9690	−0.997185
$122$	16.7240	1.51412
$123$	0.690685	0.0622769
$124$	51.8821	4.65915
$125$	−3.90182	−0.348989
$126$	−32.7356	−2.91632
$127$	−19.6947	−1.74762	−0.873809	−	0.486269i	$-0.838358\pi$
$127$	−19.6947	−1.74762	−0.873809	+	0.486269i	$0.838358\pi$
$128$	−32.8082	−2.89986
$129$	−0.203775	−0.0179414
$130$	−16.4998	−1.44713
$131$	−0.484623	−0.0423417	−0.0211708	−	0.999776i	$-0.506739\pi$
$131$	−0.484623	−0.0423417	−0.0211708	+	0.999776i	$0.506739\pi$
$132$	−0.0705620	−0.00614164
$133$	21.3576	1.85194
$134$	−19.6674	−1.69900
$135$	1.31152	0.112877
$136$	−23.5835	−2.02227
$137$	−16.9630	−1.44925	−0.724625	−	0.689144i	$-0.757987\pi$
$137$	−16.9630	−1.44925	−0.724625	+	0.689144i	$0.757987\pi$
$138$	0.866272	0.0737420
$139$	3.11757	0.264429	0.132215	−	0.991221i	$-0.457791\pi$
$139$	3.11757	0.264429	0.132215	+	0.991221i	$0.457791\pi$
$140$	−63.9054	−5.40099
$141$	0.959936	0.0808412
$142$	−18.9452	−1.58984
$143$	0.362404	0.0303057
$144$	−42.9591	−3.57992
$145$	−13.7100	−1.13855
$146$	5.59403	0.462965
$147$	−0.679913	−0.0560783
$148$	11.1994	0.920582
$149$	−4.01061	−0.328562	−0.164281	−	0.986414i	$-0.552530\pi$
$149$	−4.01061	−0.328562	−0.164281	+	0.986414i	$0.552530\pi$
$150$	0.742575	0.0606310
$151$	16.5206	1.34443	0.672215	−	0.740356i	$-0.265343\pi$
$151$	16.5206	1.34443	0.672215	+	0.740356i	$0.265343\pi$
$152$	49.1213	3.98427
$153$	−7.63983	−0.617644
$154$	1.92363	0.155011
$155$	28.3069	2.27367
$156$	−0.825878	−0.0661232
$157$	21.1093	1.68471	0.842353	−	0.538926i	$-0.181170\pi$
$157$	21.1093	1.68471	0.842353	+	0.538926i	$0.181170\pi$
$158$	9.73802	0.774716
$159$	−0.625869	−0.0496346
$160$	−60.4804	−4.78140
$161$	−17.2319	−1.35806
$162$	−24.3450	−1.91273
$163$	−8.27494	−0.648143	−0.324072	−	0.946033i	$-0.605052\pi$
$163$	−8.27494	−0.648143	−0.324072	+	0.946033i	$0.605052\pi$
$164$	−50.1956	−3.91962
$165$	−0.0384987	−0.00299712
$166$	−19.5785	−1.51959
$167$	9.53022	0.737470	0.368735	−	0.929535i	$-0.379791\pi$
$167$	9.53022	0.737470	0.368735	+	0.929535i	$0.379791\pi$
$168$	−2.75966	−0.212913
$169$	−8.75832	−0.673717
$170$	−20.4396	−1.56765
$171$	15.9128	1.21688
$172$	14.8094	1.12920
$173$	−18.3468	−1.39488	−0.697442	−	0.716642i	$-0.745678\pi$
$173$	−18.3468	−1.39488	−0.697442	+	0.716642i	$0.745678\pi$
$174$	−0.940472	−0.0712970
$175$	−14.7713	−1.11661
$176$	2.52439	0.190283
$177$	−0.454592	−0.0341692
$178$	−4.62048	−0.346320
$179$	0.616257	0.0460612	0.0230306	−	0.999735i	$-0.492668\pi$
$179$	0.616257	0.0460612	0.0230306	+	0.999735i	$0.492668\pi$
$180$	−47.6135	−3.54890
$181$	−17.1198	−1.27251	−0.636253	−	0.771480i	$-0.719517\pi$
$181$	−17.1198	−1.27251	−0.636253	+	0.771480i	$0.719517\pi$
$182$	22.5148	1.66891
$183$	0.456722	0.0337619
$184$	−39.6324	−2.92174
$185$	6.11038	0.449244
$186$	1.94179	0.142379
$187$	0.448938	0.0328296
$188$	−69.7635	−5.08802
$189$	−1.78962	−0.130176
$190$	42.5731	3.08858
$191$	−4.06515	−0.294144	−0.147072	−	0.989126i	$-0.546985\pi$
$191$	−4.06515	−0.294144	−0.147072	+	0.989126i	$0.546985\pi$
$192$	−2.01751	−0.145601
$193$	−3.46154	−0.249167	−0.124583	−	0.992209i	$-0.539759\pi$
$193$	−3.46154	−0.249167	−0.124583	+	0.992209i	$0.539759\pi$
$194$	49.9978	3.58963
$195$	−0.450600	−0.0322681
$196$	49.4128	3.52949
$197$	7.89053	0.562177	0.281088	−	0.959682i	$-0.409305\pi$
$197$	7.89053	0.562177	0.281088	+	0.959682i	$0.409305\pi$
$198$	1.43323	0.101855
$199$	4.07987	0.289215	0.144607	−	0.989489i	$-0.453808\pi$
$199$	4.07987	0.289215	0.144607	+	0.989489i	$0.453808\pi$
$200$	−33.9732	−2.40227
$201$	−0.537104	−0.0378844
$202$	11.9968	0.844092
$203$	18.7079	1.31304
$204$	−1.02308	−0.0716299
$205$	−27.3868	−1.91277
$206$	−40.1607	−2.79813
$207$	−12.8388	−0.892361
$208$	29.5462	2.04866
$209$	−0.935078	−0.0646807
$210$	−2.39178	−0.165048
$211$	−20.8688	−1.43667	−0.718334	−	0.695698i	$-0.755095\pi$
$211$	−20.8688	−1.43667	−0.718334	+	0.695698i	$0.755095\pi$
$212$	45.4851	3.12393
$213$	−0.517380	−0.0354503
$214$	−7.22941	−0.494192
$215$	8.08000	0.551052
$216$	−4.11603	−0.280060
$217$	−38.6261	−2.62211
$218$	−4.20606	−0.284870
$219$	0.152769	0.0103232
$220$	2.79790	0.188634
$221$	5.25449	0.353455
$222$	0.419157	0.0281320
$223$	1.56044	0.104495	0.0522474	−	0.998634i	$-0.483362\pi$
$223$	1.56044	0.104495	0.0522474	+	0.998634i	$0.483362\pi$
$224$	82.5282	5.51415
$225$	−11.0056	−0.733703
$226$	−13.6286	−0.906559
$227$	2.85142	0.189256	0.0946278	−	0.995513i	$-0.469834\pi$
$227$	2.85142	0.189256	0.0946278	+	0.995513i	$0.469834\pi$
$228$	2.13094	0.141125
$229$	−25.7516	−1.70172	−0.850858	−	0.525396i	$-0.823917\pi$
$229$	−25.7516	−1.70172	−0.850858	+	0.525396i	$0.823917\pi$
$230$	−34.3491	−2.26491
$231$	0.0525332	0.00345643
$232$	43.0271	2.82487
$233$	17.9978	1.17907	0.589537	−	0.807742i	$-0.299310\pi$
$233$	17.9978	1.17907	0.589537	+	0.807742i	$0.299310\pi$
$234$	16.7749	1.09661
$235$	−38.0630	−2.48296
$236$	33.0375	2.15056
$237$	0.265939	0.0172746
$238$	27.8908	1.80789
$239$	−10.0047	−0.647148	−0.323574	−	0.946203i	$-0.604885\pi$
$239$	−10.0047	−0.647148	−0.323574	+	0.946203i	$0.604885\pi$
$240$	−3.13874	−0.202605
$241$	−15.2415	−0.981791	−0.490895	−	0.871219i	$-0.663330\pi$
$241$	−15.2415	−0.981791	−0.490895	+	0.871219i	$0.663330\pi$
$242$	29.8358	1.91792
$243$	−2.00068	−0.128344
$244$	−33.1924	−2.12492
$245$	26.9597	1.72239
$246$	−1.87866	−0.119779
$247$	−10.9444	−0.696377
$248$	−88.8377	−5.64120
$249$	−0.534677	−0.0338838
$250$	10.6130	0.671222
$251$	−5.65888	−0.357186	−0.178593	−	0.983923i	$-0.557154\pi$
$251$	−5.65888	−0.357186	−0.178593	+	0.983923i	$0.557154\pi$
$252$	64.9707	4.09277
$253$	0.754446	0.0474316
$254$	53.5696	3.36125
$255$	−0.558193	−0.0349554
$256$	34.9178	2.18236
$257$	26.2133	1.63514	0.817570	−	0.575829i	$-0.195321\pi$
$257$	26.2133	1.63514	0.817570	+	0.575829i	$0.195321\pi$
$258$	0.554268	0.0345072
$259$	−8.33789	−0.518091
$260$	32.7474	2.03091
$261$	13.9386	0.862775
$262$	1.31818	0.0814372
$263$	30.6753	1.89152	0.945760	−	0.324867i	$-0.105320\pi$
$263$	30.6753	1.89152	0.945760	+	0.324867i	$0.105320\pi$
$264$	0.120823	0.00743616
$265$	24.8167	1.52448
$266$	−58.0928	−3.56190
$267$	−0.126182	−0.00772223
$268$	39.0341	2.38439
$269$	−14.9897	−0.913937	−0.456968	−	0.889483i	$-0.651065\pi$
$269$	−14.9897	−0.913937	−0.456968	+	0.889483i	$0.651065\pi$
$270$	−3.56733	−0.217101
$271$	−7.73805	−0.470053	−0.235027	−	0.971989i	$-0.575518\pi$
$271$	−7.73805	−0.470053	−0.235027	+	0.971989i	$0.575518\pi$
$272$	36.6012	2.21927
$273$	0.614863	0.0372132
$274$	46.1395	2.78739
$275$	0.646716	0.0389985
$276$	−1.71930	−0.103490
$277$	−0.108694	−0.00653080	−0.00326540	−	0.999995i	$-0.501039\pi$
$277$	−0.108694	−0.00653080	−0.00326540	+	0.999995i	$0.501039\pi$
$278$	−8.47981	−0.508585
$279$	−28.7788	−1.72294
$280$	109.425	6.53940
$281$	3.93804	0.234924	0.117462	−	0.993077i	$-0.462524\pi$
$281$	3.93804	0.234924	0.117462	+	0.993077i	$0.462524\pi$
$282$	−2.61103	−0.155484
$283$	−16.5903	−0.986193	−0.493096	−	0.869975i	$-0.664135\pi$
$283$	−16.5903	−0.986193	−0.493096	+	0.869975i	$0.664135\pi$
$284$	37.6007	2.23119
$285$	1.16264	0.0688690
$286$	−0.985739	−0.0582880
$287$	37.3705	2.20591
$288$	61.4886	3.62325
$289$	−10.4908	−0.617109
$290$	37.2913	2.18982
$291$	1.36541	0.0800415
$292$	−11.1025	−0.649726
$293$	2.31571	0.135285	0.0676425	−	0.997710i	$-0.478452\pi$
$293$	2.31571	0.135285	0.0676425	+	0.997710i	$0.478452\pi$
$294$	1.84937	0.107857
$295$	18.0253	1.04947
$296$	−19.1767	−1.11462
$297$	0.0783531	0.00454651
$298$	10.9089	0.631935
$299$	8.83025	0.510666
$300$	−1.47380	−0.0850896
$301$	−11.0255	−0.635501
$302$	−44.9362	−2.58579
$303$	0.327625	0.0188215
$304$	−76.2355	−4.37241
$305$	−18.1098	−1.03696
$306$	20.7804	1.18793
$307$	−14.3668	−0.819955	−0.409977	−	0.912096i	$-0.634463\pi$
$307$	−14.3668	−0.819955	−0.409977	+	0.912096i	$0.634463\pi$
$308$	−3.81786	−0.217543
$309$	−1.09676	−0.0623927
$310$	−76.9949	−4.37302
$311$	−20.6180	−1.16914	−0.584570	−	0.811343i	$-0.698737\pi$
$311$	−20.6180	−1.16914	−0.584570	+	0.811343i	$0.698737\pi$
$312$	1.41415	0.0800605
$313$	−0.174310	−0.00985259	−0.00492629	−	0.999988i	$-0.501568\pi$
$313$	−0.174310	−0.00985259	−0.00492629	+	0.999988i	$0.501568\pi$
$314$	−57.4174	−3.24025
$315$	35.4481	1.99727
$316$	−19.3272	−1.08724
$317$	−33.5432	−1.88397	−0.941987	−	0.335651i	$-0.891044\pi$
$317$	−33.5432	−1.88397	−0.941987	+	0.335651i	$0.891044\pi$
$318$	1.70237	0.0954639
$319$	−0.819068	−0.0458590
$320$	79.9975	4.47200
$321$	−0.197430	−0.0110195
$322$	46.8709	2.61201
$323$	−13.5577	−0.754371
$324$	48.3178	2.68432
$325$	7.56935	0.419872
$326$	22.5079	1.24660
$327$	−0.114865	−0.00635204
$328$	85.9499	4.74579
$329$	51.9387	2.86347
$330$	0.104717	0.00576446
$331$	5.23089	0.287516	0.143758	−	0.989613i	$-0.454081\pi$
$331$	5.23089	0.287516	0.143758	+	0.989613i	$0.454081\pi$
$332$	38.8577	2.13259
$333$	−6.21224	−0.340429
$334$	−25.9222	−1.41840
$335$	21.2970	1.16358
$336$	4.28295	0.233654
$337$	−28.5102	−1.55305	−0.776524	−	0.630088i	$-0.783019\pi$
$337$	−28.5102	−1.55305	−0.776524	+	0.630088i	$0.783019\pi$
$338$	23.8227	1.29578
$339$	−0.372187	−0.0202144
$340$	40.5668	2.20004
$341$	1.69112	0.0915794
$342$	−43.2828	−2.34046
$343$	−8.65394	−0.467269
$344$	−25.3581	−1.36722
$345$	−0.938051	−0.0505030
$346$	49.9034	2.68282
$347$	18.3213	0.983539	0.491769	−	0.870726i	$-0.336350\pi$
$347$	18.3213	0.983539	0.491769	+	0.870726i	$0.336350\pi$
$348$	1.86657	0.100058
$349$	−6.37940	−0.341481	−0.170741	−	0.985316i	$-0.554616\pi$
$349$	−6.37940	−0.341481	−0.170741	+	0.985316i	$0.554616\pi$
$350$	40.1780	2.14761
$351$	0.917067	0.0489494
$352$	−3.61324	−0.192586
$353$	10.8156	0.575656	0.287828	−	0.957682i	$-0.407067\pi$
$353$	10.8156	0.575656	0.287828	+	0.957682i	$0.407067\pi$
$354$	1.23649	0.0657188
$355$	20.5150	1.08882
$356$	9.17031	0.486026
$357$	0.761679	0.0403123
$358$	−1.67622	−0.0885911
$359$	3.58759	0.189346	0.0946729	−	0.995508i	$-0.469819\pi$
$359$	3.58759	0.189346	0.0946729	+	0.995508i	$0.469819\pi$
$360$	81.5285	4.29693
$361$	9.23891	0.486258
$362$	46.5660	2.44745
$363$	0.814796	0.0427657
$364$	−44.6853	−2.34215
$365$	−6.05755	−0.317066
$366$	−1.24229	−0.0649354
$367$	2.72323	0.142152	0.0710758	−	0.997471i	$-0.477357\pi$
$367$	2.72323	0.142152	0.0710758	+	0.997471i	$0.477357\pi$
$368$	61.5088	3.20637
$369$	27.8433	1.44946
$370$	−16.6203	−0.864046
$371$	−33.8635	−1.75811
$372$	−3.85388	−0.199814
$373$	15.8587	0.821133	0.410567	−	0.911831i	$-0.365331\pi$
$373$	15.8587	0.821133	0.410567	+	0.911831i	$0.365331\pi$
$374$	−1.22111	−0.0631422
$375$	0.289833	0.0149669
$376$	119.456	6.16047
$377$	−9.58660	−0.493735
$378$	4.86778	0.250372
$379$	−8.81086	−0.452583	−0.226292	−	0.974060i	$-0.572660\pi$
$379$	−8.81086	−0.452583	−0.226292	+	0.974060i	$0.572660\pi$
$380$	−84.4952	−4.33451
$381$	1.46295	0.0749492
$382$	11.0572	0.565737
$383$	−3.36424	−0.171905	−0.0859524	−	0.996299i	$-0.527393\pi$
$383$	−3.36424	−0.171905	−0.0859524	+	0.996299i	$0.527393\pi$
$384$	2.43704	0.124365
$385$	−2.08303	−0.106161
$386$	9.41539	0.479231
$387$	−8.21470	−0.417577
$388$	−99.2311	−5.03770
$389$	−3.70202	−0.187700	−0.0938501	−	0.995586i	$-0.529917\pi$
$389$	−3.70202	−0.187700	−0.0938501	+	0.995586i	$0.529917\pi$
$390$	1.22563	0.0620623
$391$	10.9387	0.553195
$392$	−84.6095	−4.27343
$393$	0.0359985	0.00181588
$394$	−21.4623	−1.08125
$395$	−10.5449	−0.530572
$396$	−2.84454	−0.142944
$397$	−11.5156	−0.577951	−0.288976	−	0.957336i	$-0.593315\pi$
$397$	−11.5156	−0.577951	−0.288976	+	0.957336i	$0.593315\pi$
$398$	−11.0973	−0.556256
$399$	−1.58648	−0.0794232
$400$	52.7258	2.63629
$401$	8.39657	0.419305	0.209652	−	0.977776i	$-0.432767\pi$
$401$	8.39657	0.419305	0.209652	+	0.977776i	$0.432767\pi$
$402$	1.46092	0.0728642
$403$	19.7934	0.985978
$404$	−23.8102	−1.18460
$405$	26.3623	1.30995
$406$	−50.8856	−2.52541
$407$	0.365049	0.0180948
$408$	1.75182	0.0867279
$409$	−36.3779	−1.79877	−0.899385	−	0.437156i	$-0.855986\pi$
$409$	−36.3779	−1.79877	−0.899385	+	0.437156i	$0.855986\pi$
$410$	74.4921	3.67890
$411$	1.26004	0.0621532
$412$	79.7074	3.92690
$413$	−24.5963	−1.21031
$414$	34.9217	1.71631
$415$	21.2008	1.04071
$416$	−42.2904	−2.07346
$417$	−0.231578	−0.0113404
$418$	2.54342	0.124403
$419$	5.15624	0.251899	0.125949	−	0.992037i	$-0.459802\pi$
$419$	5.15624	0.251899	0.125949	+	0.992037i	$0.459802\pi$
$420$	4.74699	0.231629
$421$	22.0195	1.07317	0.536583	−	0.843848i	$-0.319715\pi$
$421$	22.0195	1.07317	0.536583	+	0.843848i	$0.319715\pi$
$422$	56.7632	2.76319
$423$	38.6975	1.88154
$424$	−77.8841	−3.78239
$425$	9.37675	0.454839
$426$	1.40728	0.0681827
$427$	24.7116	1.19588
$428$	14.3483	0.693550
$429$	−0.0269199	−0.00129970
$430$	−21.9776	−1.05986
$431$	−4.62634	−0.222843	−0.111421	−	0.993773i	$-0.535540\pi$
$431$	−4.62634	−0.222843	−0.111421	+	0.993773i	$0.535540\pi$
$432$	6.38801	0.307343
$433$	−15.7440	−0.756610	−0.378305	−	0.925681i	$-0.623493\pi$
$433$	−15.7440	−0.756610	−0.378305	+	0.925681i	$0.623493\pi$
$434$	105.063	5.04319
$435$	1.01840	0.0488285
$436$	8.34781	0.399788
$437$	−22.7839	−1.08990
$438$	−0.415533	−0.0198549
$439$	25.9548	1.23876	0.619378	−	0.785093i	$-0.287385\pi$
$439$	25.9548	1.23876	0.619378	+	0.785093i	$0.287385\pi$
$440$	−4.79084	−0.228394
$441$	−27.4091	−1.30520
$442$	−14.2922	−0.679813
$443$	−34.0905	−1.61969	−0.809844	−	0.586645i	$-0.800449\pi$
$443$	−34.0905	−1.61969	−0.809844	+	0.586645i	$0.800449\pi$
$444$	−0.831905	−0.0394805
$445$	5.00333	0.237181
$446$	−4.24440	−0.200978
$447$	0.297914	0.0140909
$448$	−109.160	−5.15733
$449$	−21.3262	−1.00644	−0.503222	−	0.864157i	$-0.667852\pi$
$449$	−21.3262	−1.00644	−0.503222	+	0.864157i	$0.667852\pi$
$450$	29.9351	1.41116
$451$	−1.63615	−0.0770433
$452$	27.0488	1.27227
$453$	−1.22718	−0.0576578
$454$	−7.75588	−0.364002
$455$	−24.3803	−1.14297
$456$	−3.64881	−0.170871
$457$	25.7482	1.20445	0.602226	−	0.798326i	$-0.294281\pi$
$457$	25.7482	1.20445	0.602226	+	0.798326i	$0.294281\pi$
$458$	70.0445	3.27297
$459$	1.13604	0.0530259
$460$	68.1730	3.17858
$461$	17.7264	0.825603	0.412801	−	0.910821i	$-0.364550\pi$
$461$	17.7264	0.825603	0.412801	+	0.910821i	$0.364550\pi$
$462$	−0.142890	−0.00664787
$463$	−37.0490	−1.72181	−0.860907	−	0.508762i	$-0.830103\pi$
$463$	−37.0490	−1.72181	−0.860907	+	0.508762i	$0.830103\pi$
$464$	−66.7774	−3.10006
$465$	−2.10268	−0.0975095
$466$	−48.9540	−2.26775
$467$	−32.5673	−1.50704	−0.753518	−	0.657427i	$-0.771645\pi$
$467$	−32.5673	−1.50704	−0.753518	+	0.657427i	$0.771645\pi$
$468$	−33.2933	−1.53898
$469$	−29.0607	−1.34190
$470$	103.532	4.77555
$471$	−1.56803	−0.0722511
$472$	−56.5702	−2.60385
$473$	0.482718	0.0221954
$474$	−0.723355	−0.0332248
$475$	−19.5305	−0.896122
$476$	−55.3551	−2.53720
$477$	−25.2304	−1.15522
$478$	27.2127	1.24468
$479$	0.289082	0.0132085	0.00660424	−	0.999978i	$-0.497898\pi$
$479$	0.289082	0.0132085	0.00660424	+	0.999978i	$0.497898\pi$
$480$	4.49258	0.205057
$481$	4.27263	0.194815
$482$	41.4569	1.88831
$483$	1.28001	0.0582426
$484$	−59.2154	−2.69161
$485$	−54.1406	−2.45840
$486$	5.44187	0.246848
$487$	−29.9101	−1.35535	−0.677677	−	0.735360i	$-0.737013\pi$
$487$	−29.9101	−1.35535	−0.677677	+	0.735360i	$0.737013\pi$
$488$	56.8353	2.57281
$489$	0.614675	0.0277966
$490$	−73.3304	−3.31273
$491$	7.37462	0.332812	0.166406	−	0.986057i	$-0.446784\pi$
$491$	7.37462	0.332812	0.166406	+	0.986057i	$0.446784\pi$
$492$	3.72860	0.168098
$493$	−11.8757	−0.534853
$494$	29.7689	1.33936
$495$	−1.55198	−0.0697565
$496$	137.875	6.19075
$497$	−27.9936	−1.25568
$498$	1.45432	0.0651697
$499$	−30.9424	−1.38517	−0.692586	−	0.721335i	$-0.743529\pi$
$499$	−30.9424	−1.38517	−0.692586	+	0.721335i	$0.743529\pi$
$500$	−21.0636	−0.941995
$501$	−0.707919	−0.0316275
$502$	15.3922	0.686987
$503$	30.3675	1.35402	0.677009	−	0.735975i	$-0.263276\pi$
$503$	30.3675	1.35402	0.677009	+	0.735975i	$0.263276\pi$
$504$	−111.249	−4.95544
$505$	−12.9908	−0.578085
$506$	−2.05210	−0.0912268
$507$	0.650581	0.0288933
$508$	−106.320	−4.71719
$509$	−15.5837	−0.690736	−0.345368	−	0.938467i	$-0.612246\pi$
$509$	−15.5837	−0.690736	−0.345368	+	0.938467i	$0.612246\pi$
$510$	1.51829	0.0672309
$511$	8.26579	0.365657
$512$	−29.3601	−1.29755
$513$	−2.36623	−0.104471
$514$	−71.3003	−3.14492
$515$	43.4885	1.91633
$516$	−1.10006	−0.0484275
$517$	−2.27397	−0.100009
$518$	22.6791	0.996462
$519$	1.36283	0.0598216
$520$	−56.0734	−2.45898
$521$	−20.8686	−0.914269	−0.457135	−	0.889397i	$-0.651124\pi$
$521$	−20.8686	−0.914269	−0.457135	+	0.889397i	$0.651124\pi$
$522$	−37.9129	−1.65940
$523$	6.10102	0.266779	0.133389	−	0.991064i	$-0.457414\pi$
$523$	6.10102	0.266779	0.133389	+	0.991064i	$0.457414\pi$
$524$	−2.61620	−0.114289
$525$	1.09724	0.0478873
$526$	−83.4369	−3.63802
$527$	24.5196	1.06809
$528$	−0.187516	−0.00816058
$529$	−4.61734	−0.200754
$530$	−67.5015	−2.93208
$531$	−18.3258	−0.795272
$532$	115.297	4.99878
$533$	−19.1500	−0.829477
$534$	0.343216	0.0148524
$535$	7.82843	0.338453
$536$	−66.8380	−2.88696
$537$	−0.0457765	−0.00197540
$538$	40.7720	1.75780
$539$	1.61063	0.0693749
$540$	7.08012	0.304680
$541$	−46.1784	−1.98536	−0.992682	−	0.120761i	$-0.961467\pi$
$541$	−46.1784	−1.98536	−0.992682	+	0.120761i	$0.961467\pi$
$542$	21.0475	0.904069
$543$	1.27169	0.0545733
$544$	−52.3884	−2.24613
$545$	4.55458	0.195097
$546$	−1.67243	−0.0715734
$547$	28.1061	1.20173	0.600864	−	0.799351i	$-0.294823\pi$
$547$	28.1061	1.20173	0.600864	+	0.799351i	$0.294823\pi$
$548$	−91.5735	−3.91183
$549$	18.4117	0.785791
$550$	−1.75907	−0.0750070
$551$	24.7355	1.05377
$552$	2.94395	0.125303
$553$	14.3890	0.611883
$554$	0.295648	0.0125609
$555$	−0.453888	−0.0192665
$556$	16.8300	0.713750
$557$	24.2423	1.02718	0.513589	−	0.858036i	$-0.328316\pi$
$557$	24.2423	1.02718	0.513589	+	0.858036i	$0.328316\pi$
$558$	78.2785	3.31379
$559$	5.64987	0.238964
$560$	−169.826	−7.17646
$561$	−0.0333478	−0.00140794
$562$	−10.7115	−0.451837
$563$	21.7276	0.915711	0.457856	−	0.889027i	$-0.348618\pi$
$563$	21.7276	0.915711	0.457856	+	0.889027i	$0.348618\pi$
$564$	5.18214	0.218207
$565$	14.7578	0.620867
$566$	45.1258	1.89678
$567$	−35.9725	−1.51070
$568$	−64.3836	−2.70148
$569$	−37.0590	−1.55359	−0.776797	−	0.629752i	$-0.783157\pi$
$569$	−37.0590	−1.55359	−0.776797	+	0.629752i	$0.783157\pi$
$570$	−3.16239	−0.132458
$571$	16.2591	0.680422	0.340211	−	0.940349i	$-0.389501\pi$
$571$	16.2591	0.680422	0.340211	+	0.940349i	$0.389501\pi$
$572$	1.95641	0.0818015
$573$	0.301965	0.0126148
$574$	−101.648	−4.24270
$575$	15.7577	0.657144
$576$	−81.3311	−3.38880
$577$	10.1992	0.424599	0.212299	−	0.977205i	$-0.431905\pi$
$577$	10.1992	0.424599	0.212299	+	0.977205i	$0.431905\pi$
$578$	28.5351	1.18691
$579$	0.257128	0.0106859
$580$	−74.0123	−3.07320
$581$	−28.9294	−1.20019
$582$	−3.71391	−0.153947
$583$	1.48261	0.0614034
$584$	19.0108	0.786674
$585$	−18.1649	−0.751025
$586$	−6.29873	−0.260198
$587$	−22.0889	−0.911708	−0.455854	−	0.890054i	$-0.650666\pi$
$587$	−22.0889	−0.911708	−0.455854	+	0.890054i	$0.650666\pi$
$588$	−3.67046	−0.151367
$589$	−51.0711	−2.10435
$590$	−49.0289	−2.01849
$591$	−0.586120	−0.0241098
$592$	29.7619	1.22321
$593$	18.8177	0.772751	0.386376	−	0.922342i	$-0.373727\pi$
$593$	18.8177	0.772751	0.386376	+	0.922342i	$0.373727\pi$
$594$	−0.213121	−0.00874445
$595$	−30.2018	−1.23815
$596$	−21.6510	−0.886858
$597$	−0.303059	−0.0124034
$598$	−24.0183	−0.982181
$599$	17.7403	0.724850	0.362425	−	0.932013i	$-0.381949\pi$
$599$	17.7403	0.724850	0.362425	+	0.932013i	$0.381949\pi$
$600$	2.52358	0.103025
$601$	−32.0732	−1.30830	−0.654148	−	0.756367i	$-0.726972\pi$
$601$	−32.0732	−1.30830	−0.654148	+	0.756367i	$0.726972\pi$
$602$	29.9895	1.22228
$603$	−21.6521	−0.881740
$604$	89.1853	3.62890
$605$	−32.3080	−1.31351
$606$	−0.891140	−0.0362001
$607$	−6.88669	−0.279522	−0.139761	−	0.990185i	$-0.544633\pi$
$607$	−6.88669	−0.279522	−0.139761	+	0.990185i	$0.544633\pi$
$608$	109.118	4.42533
$609$	−1.38965	−0.0563115
$610$	49.2587	1.99443
$611$	−26.6152	−1.07674
$612$	−41.2430	−1.66715
$613$	−0.398312	−0.0160877	−0.00804384	−	0.999968i	$-0.502560\pi$
$613$	−0.398312	−0.0160877	−0.00804384	+	0.999968i	$0.502560\pi$
$614$	39.0777	1.57705
$615$	2.03433	0.0820321
$616$	6.53732	0.263396
$617$	11.5550	0.465188	0.232594	−	0.972574i	$-0.425279\pi$
$617$	11.5550	0.465188	0.232594	+	0.972574i	$0.425279\pi$
$618$	2.98320	0.120002
$619$	−1.66475	−0.0669121	−0.0334560	−	0.999440i	$-0.510651\pi$
$619$	−1.66475	−0.0669121	−0.0334560	+	0.999440i	$0.510651\pi$
$620$	152.813	6.13710
$621$	1.90913	0.0766109
$622$	56.0810	2.24865
$623$	−6.82727	−0.273529
$624$	−2.19474	−0.0878599
$625$	−29.8687	−1.19475
$626$	0.474124	0.0189498
$627$	0.0694590	0.00277393
$628$	113.957	4.54737
$629$	5.29284	0.211039
$630$	−96.4189	−3.84142
$631$	−35.9725	−1.43204	−0.716021	−	0.698079i	$-0.754038\pi$
$631$	−35.9725	−1.43204	−0.716021	+	0.698079i	$0.754038\pi$
$632$	33.0939	1.31640
$633$	1.55017	0.0616136
$634$	91.2376	3.62351
$635$	−58.0083	−2.30199
$636$	−3.37870	−0.133974
$637$	18.8513	0.746916
$638$	2.22787	0.0882021
$639$	−20.8569	−0.825088
$640$	−96.6327	−3.81974
$641$	25.7499	1.01706	0.508530	−	0.861044i	$-0.330189\pi$
$641$	25.7499	1.01706	0.508530	+	0.861044i	$0.330189\pi$
$642$	0.537011	0.0211941
$643$	−25.1821	−0.993086	−0.496543	−	0.868012i	$-0.665397\pi$
$643$	−25.1821	−0.993086	−0.496543	+	0.868012i	$0.665397\pi$
$644$	−93.0251	−3.66570
$645$	−0.600195	−0.0236326
$646$	36.8770	1.45091
$647$	49.4206	1.94293	0.971463	−	0.237192i	$-0.0762270\pi$
$647$	49.4206	1.94293	0.971463	+	0.237192i	$0.0762270\pi$
$648$	−82.7346	−3.25012
$649$	1.07687	0.0422710
$650$	−20.5887	−0.807554
$651$	2.86920	0.112453
$652$	−44.6716	−1.74947
$653$	−31.5041	−1.23285	−0.616426	−	0.787413i	$-0.711420\pi$
$653$	−31.5041	−1.23285	−0.616426	+	0.787413i	$0.711420\pi$
$654$	0.312433	0.0122171
$655$	−1.42740	−0.0557731
$656$	−133.393	−5.20811
$657$	6.15853	0.240267
$658$	−141.273	−5.50741
$659$	−7.30122	−0.284415	−0.142208	−	0.989837i	$-0.545420\pi$
$659$	−7.30122	−0.284415	−0.142208	+	0.989837i	$0.545420\pi$
$660$	−0.207832	−0.00808986
$661$	6.74301	0.262273	0.131136	−	0.991364i	$-0.458137\pi$
$661$	6.74301	0.262273	0.131136	+	0.991364i	$0.458137\pi$
$662$	−14.2280	−0.552988
$663$	−0.390312	−0.0151584
$664$	−66.5360	−2.58210
$665$	62.9064	2.43941
$666$	16.8973	0.654758
$667$	−19.9572	−0.772747
$668$	51.4481	1.99059
$669$	−0.115912	−0.00448141
$670$	−57.9280	−2.23795
$671$	−1.08192	−0.0417671
$672$	−6.13032	−0.236482
$673$	−23.7395	−0.915092	−0.457546	−	0.889186i	$-0.651271\pi$
$673$	−23.7395	−0.915092	−0.457546	+	0.889186i	$0.651271\pi$
$674$	77.5478	2.98703
$675$	1.63652	0.0629898
$676$	−47.2811	−1.81850
$677$	2.23974	0.0860800	0.0430400	−	0.999073i	$-0.486296\pi$
$677$	2.23974	0.0860800	0.0430400	+	0.999073i	$0.486296\pi$
$678$	1.01235	0.0388791
$679$	73.8772	2.83515
$680$	−69.4624	−2.66376
$681$	−0.211808	−0.00811650
$682$	−4.59986	−0.176138
$683$	20.5001	0.784414	0.392207	−	0.919877i	$-0.371712\pi$
$683$	20.5001	0.784414	0.392207	+	0.919877i	$0.371712\pi$
$684$	85.9038	3.28461
$685$	−49.9626	−1.90897
$686$	23.5387	0.898713
$687$	1.91287	0.0729805
$688$	39.3553	1.50041
$689$	17.3529	0.661092
$690$	2.55150	0.0971340
$691$	−7.46697	−0.284057	−0.142028	−	0.989863i	$-0.545362\pi$
$691$	−7.46697	−0.284057	−0.142028	+	0.989863i	$0.545362\pi$
$692$	−99.0438	−3.76508
$693$	2.11775	0.0804467
$694$	−49.8340	−1.89167
$695$	9.18245	0.348310
$696$	−3.19612	−0.121149
$697$	−23.7225	−0.898555
$698$	17.3520	0.656782
$699$	−1.33690	−0.0505663
$700$	−79.7418	−3.01396
$701$	48.1951	1.82030	0.910152	−	0.414275i	$-0.135965\pi$
$701$	48.1951	1.82030	0.910152	+	0.414275i	$0.135965\pi$
$702$	−2.49443	−0.0941460
$703$	−11.0243	−0.415789
$704$	4.77924	0.180124
$705$	2.82738	0.106485
$706$	−29.4185	−1.10718
$707$	17.7266	0.666677
$708$	−2.45408	−0.0922299
$709$	−48.8429	−1.83434	−0.917168	−	0.398501i	$-0.869530\pi$
$709$	−48.8429	−1.83434	−0.917168	+	0.398501i	$0.869530\pi$
$710$	−55.8008	−2.09417
$711$	10.7207	0.402058
$712$	−15.7023	−0.588469
$713$	41.2055	1.54316
$714$	−2.07177	−0.0775340
$715$	1.06742	0.0399192
$716$	3.32681	0.124329
$717$	0.743162	0.0277539
$718$	−9.75826	−0.364175
$719$	34.9344	1.30283	0.651417	−	0.758720i	$-0.274175\pi$
$719$	34.9344	1.30283	0.651417	+	0.758720i	$0.274175\pi$
$720$	−126.531	−4.71553
$721$	−59.3419	−2.21001
$722$	−25.1299	−0.935236
$723$	1.13216	0.0421055
$724$	−92.4200	−3.43476
$725$	−17.1075	−0.635356
$726$	−2.21625	−0.0822527
$727$	26.7684	0.992786	0.496393	−	0.868098i	$-0.334657\pi$
$727$	26.7684	0.992786	0.496393	+	0.868098i	$0.334657\pi$
$728$	76.5146	2.83582
$729$	−26.7025	−0.988981
$730$	16.4765	0.609824
$731$	6.99894	0.258865
$732$	2.46558	0.0911304
$733$	35.9527	1.32794	0.663971	−	0.747758i	$-0.268870\pi$
$733$	35.9527	1.32794	0.663971	+	0.747758i	$0.268870\pi$
$734$	−7.40720	−0.273405
$735$	−2.00260	−0.0738672
$736$	−88.0394	−3.24518
$737$	1.27233	0.0468670
$738$	−75.7339	−2.78780
$739$	−19.4321	−0.714821	−0.357410	−	0.933947i	$-0.616340\pi$
$739$	−19.4321	−0.714821	−0.357410	+	0.933947i	$0.616340\pi$
$740$	32.9864	1.21260
$741$	0.812968	0.0298651
$742$	92.1088	3.38142
$743$	10.7911	0.395888	0.197944	−	0.980213i	$-0.436574\pi$
$743$	10.7911	0.395888	0.197944	+	0.980213i	$0.436574\pi$
$744$	6.59900	0.241931
$745$	−11.8128	−0.432787
$746$	−43.1358	−1.57931
$747$	−21.5542	−0.788628
$748$	2.42355	0.0886139
$749$	−10.6822	−0.390321
$750$	−0.788346	−0.0287863
$751$	−52.2025	−1.90490	−0.952449	−	0.304699i	$-0.901444\pi$
$751$	−52.2025	−1.90490	−0.952449	+	0.304699i	$0.901444\pi$
$752$	−185.394	−6.76061
$753$	0.420350	0.0153184
$754$	26.0756	0.949617
$755$	48.6596	1.77090
$756$	−9.66114	−0.351372
$757$	24.8280	0.902388	0.451194	−	0.892426i	$-0.350998\pi$
$757$	24.8280	0.902388	0.451194	+	0.892426i	$0.350998\pi$
$758$	23.9656	0.870468
$759$	−0.0560414	−0.00203417
$760$	144.681	5.24814
$761$	−38.7658	−1.40526	−0.702630	−	0.711555i	$-0.747991\pi$
$761$	−38.7658	−1.40526	−0.702630	+	0.711555i	$0.747991\pi$
$762$	−3.97923	−0.144152
$763$	−6.21492	−0.224995
$764$	−21.9454	−0.793956
$765$	−22.5022	−0.813570
$766$	9.15075	0.330630
$767$	12.6040	0.455106
$768$	−2.59375	−0.0935938
$769$	46.7707	1.68659	0.843297	−	0.537448i	$-0.180611\pi$
$769$	46.7707	1.68659	0.843297	+	0.537448i	$0.180611\pi$
$770$	5.66584	0.204183
$771$	−1.94716	−0.0701254
$772$	−18.6868	−0.672554
$773$	54.6081	1.96412	0.982058	−	0.188577i	$-0.0603875\pi$
$773$	54.6081	1.96412	0.982058	+	0.188577i	$0.0603875\pi$
$774$	22.3440	0.803139
$775$	35.3217	1.26879
$776$	169.913	6.09953
$777$	0.619351	0.0222191
$778$	10.0695	0.361010
$779$	49.4109	1.77033
$780$	−2.43253	−0.0870984
$781$	1.22561	0.0438558
$782$	−29.7533	−1.06398
$783$	−2.07266	−0.0740709
$784$	131.313	4.68974
$785$	62.1750	2.21912
$786$	−0.0979161	−0.00349255
$787$	2.24860	0.0801538	0.0400769	−	0.999197i	$-0.487240\pi$
$787$	2.24860	0.0801538	0.0400769	+	0.999197i	$0.487240\pi$
$788$	42.5964	1.51743
$789$	−2.27861	−0.0811205
$790$	28.6822	1.02047
$791$	−20.1377	−0.716015
$792$	4.87071	0.173073
$793$	−12.6631	−0.449680
$794$	31.3225	1.11159
$795$	−1.84342	−0.0653795
$796$	22.0249	0.780651
$797$	−27.4046	−0.970721	−0.485360	−	0.874314i	$-0.661312\pi$
$797$	−27.4046	−0.970721	−0.485360	+	0.874314i	$0.661312\pi$
$798$	4.31522	0.152757
$799$	−32.9704	−1.16641
$800$	−75.4680	−2.66820
$801$	−5.08674	−0.179731
$802$	−22.8387	−0.806463
$803$	−0.361892	−0.0127709
$804$	−2.89951	−0.102258
$805$	−50.7546	−1.78886
$806$	−53.8380	−1.89636
$807$	1.11346	0.0391955
$808$	40.7701	1.43429
$809$	−34.0452	−1.19697	−0.598484	−	0.801135i	$-0.704230\pi$
$809$	−34.0452	−1.19697	−0.598484	+	0.801135i	$0.704230\pi$
$810$	−71.7054	−2.51947
$811$	−1.09076	−0.0383017	−0.0191508	−	0.999817i	$-0.506096\pi$
$811$	−1.09076	−0.0383017	−0.0191508	+	0.999817i	$0.506096\pi$
$812$	100.993	3.54416
$813$	0.574794	0.0201589
$814$	−0.992933	−0.0348023
$815$	−24.3729	−0.853744
$816$	−2.71879	−0.0951768
$817$	−14.5779	−0.510015
$818$	98.9480	3.45964
$819$	24.7868	0.866120
$820$	−147.845	−5.16298
$821$	−16.0902	−0.561553	−0.280776	−	0.959773i	$-0.590592\pi$
$821$	−16.0902	−0.561553	−0.280776	+	0.959773i	$0.590592\pi$
$822$	−3.42731	−0.119541
$823$	−16.2639	−0.566925	−0.283463	−	0.958983i	$-0.591483\pi$
$823$	−16.2639	−0.566925	−0.283463	+	0.958983i	$0.591483\pi$
$824$	−136.483	−4.75461
$825$	−0.0480391	−0.00167251
$826$	66.9021	2.32782
$827$	−31.0958	−1.08131	−0.540653	−	0.841246i	$-0.681823\pi$
$827$	−31.0958	−1.08131	−0.540653	+	0.841246i	$0.681823\pi$
$828$	−69.3094	−2.40867
$829$	29.4022	1.02118	0.510591	−	0.859824i	$-0.329427\pi$
$829$	29.4022	1.02118	0.510591	+	0.859824i	$0.329427\pi$
$830$	−57.6662	−2.00162
$831$	0.00807396	0.000280083 0
$832$	55.9376	1.93929
$833$	23.3526	0.809119
$834$	0.629893	0.0218114
$835$	28.0701	0.971407
$836$	−5.04794	−0.174587
$837$	4.27940	0.147918
$838$	−14.0250	−0.484485
$839$	−35.5758	−1.22821	−0.614107	−	0.789223i	$-0.710484\pi$
$839$	−35.5758	−1.22821	−0.614107	+	0.789223i	$0.710484\pi$
$840$	−8.12827	−0.280452
$841$	−7.33335	−0.252874
$842$	−59.8932	−2.06405
$843$	−0.292524	−0.0100750
$844$	−112.659	−3.87787
$845$	−25.7966	−0.887430
$846$	−105.257	−3.61882
$847$	44.0857	1.51480
$848$	120.875	4.15086
$849$	1.23235	0.0422943
$850$	−25.5048	−0.874807
$851$	8.89469	0.304906
$852$	−2.79303	−0.0956878
$853$	45.0618	1.54289	0.771444	−	0.636298i	$-0.219535\pi$
$853$	45.0618	1.54289	0.771444	+	0.636298i	$0.219535\pi$
$854$	−67.2157	−2.30007
$855$	46.8692	1.60289
$856$	−24.5685	−0.839736
$857$	−23.3069	−0.796150	−0.398075	−	0.917353i	$-0.630322\pi$
$857$	−23.3069	−0.796150	−0.398075	+	0.917353i	$0.630322\pi$
$858$	0.0732222	0.00249976
$859$	−43.5223	−1.48496	−0.742481	−	0.669867i	$-0.766351\pi$
$859$	−43.5223	−1.48496	−0.742481	+	0.669867i	$0.766351\pi$
$860$	43.6192	1.48740
$861$	−2.77593	−0.0946036
$862$	12.5837	0.428601
$863$	−53.9484	−1.83643	−0.918213	−	0.396088i	$-0.870368\pi$
$863$	−53.9484	−1.83643	−0.918213	+	0.396088i	$0.870368\pi$
$864$	−9.14335	−0.311063
$865$	−54.0384	−1.83736
$866$	42.8238	1.45521
$867$	0.779276	0.0264656
$868$	−208.520	−7.07762
$869$	−0.629978	−0.0213705
$870$	−2.77005	−0.0939135
$871$	14.8918	0.504588
$872$	−14.2940	−0.484055
$873$	55.0431	1.86293
$874$	61.9723	2.09624
$875$	15.6818	0.530142
$876$	0.824712	0.0278644
$877$	27.4412	0.926622	0.463311	−	0.886196i	$-0.346661\pi$
$877$	27.4412	0.926622	0.463311	+	0.886196i	$0.346661\pi$
$878$	−70.5972	−2.38254
$879$	−0.172014	−0.00580189
$880$	7.43531	0.250644
$881$	37.1099	1.25026	0.625131	−	0.780520i	$-0.285045\pi$
$881$	37.1099	1.25026	0.625131	+	0.780520i	$0.285045\pi$
$882$	74.5528	2.51032
$883$	15.1584	0.510122	0.255061	−	0.966925i	$-0.417904\pi$
$883$	15.1584	0.510122	0.255061	+	0.966925i	$0.417904\pi$
$884$	28.3660	0.954050
$885$	−1.33895	−0.0450082
$886$	92.7263	3.11520
$887$	17.8193	0.598313	0.299157	−	0.954204i	$-0.403295\pi$
$887$	17.8193	0.598313	0.299157	+	0.954204i	$0.403295\pi$
$888$	1.42447	0.0478021
$889$	79.1549	2.65477
$890$	−13.6091	−0.456177
$891$	1.57494	0.0527626
$892$	8.42391	0.282053
$893$	68.6729	2.29805
$894$	−0.810328	−0.0271014
$895$	1.81511	0.0606725
$896$	131.860	4.40512
$897$	−0.655924	−0.0219007
$898$	58.0073	1.93573
$899$	−44.7350	−1.49199
$900$	−59.4126	−1.98042
$901$	21.4963	0.716147
$902$	4.45033	0.148180
$903$	0.818992	0.0272544
$904$	−46.3156	−1.54043
$905$	−50.4244	−1.67616
$906$	3.33793	0.110895
$907$	8.56994	0.284560	0.142280	−	0.989826i	$-0.454557\pi$
$907$	8.56994	0.284560	0.142280	+	0.989826i	$0.454557\pi$
$908$	15.3932	0.510840
$909$	13.2074	0.438062
$910$	66.3146	2.19831
$911$	35.1286	1.16386	0.581931	−	0.813238i	$-0.302297\pi$
$911$	35.1286	1.16386	0.581931	+	0.813238i	$0.302297\pi$
$912$	5.66289	0.187517
$913$	1.26659	0.0419179
$914$	−70.0353	−2.31656
$915$	1.34522	0.0444717
$916$	−139.018	−4.59329
$917$	1.94775	0.0643204
$918$	−3.09004	−0.101986
$919$	−36.4720	−1.20310	−0.601551	−	0.798835i	$-0.705450\pi$
$919$	−36.4720	−1.20310	−0.601551	+	0.798835i	$0.705450\pi$
$920$	−116.733	−3.84856
$921$	1.06719	0.0351649
$922$	−48.2160	−1.58791
$923$	14.3449	0.472168
$924$	0.283596	0.00932963
$925$	7.62459	0.250695
$926$	100.773	3.31162
$927$	−44.2134	−1.45216
$928$	95.5804	3.13758
$929$	23.1274	0.758784	0.379392	−	0.925236i	$-0.376133\pi$
$929$	23.1274	0.758784	0.379392	+	0.925236i	$0.376133\pi$
$930$	5.71930	0.187543
$931$	−48.6404	−1.59412
$932$	97.1595	3.18257
$933$	1.53154	0.0501403
$934$	88.5832	2.89853
$935$	1.32229	0.0432436
$936$	57.0081	1.86337
$937$	5.03170	0.164378	0.0821892	−	0.996617i	$-0.473809\pi$
$937$	5.03170	0.164378	0.0821892	+	0.996617i	$0.473809\pi$
$938$	79.0453	2.58092
$939$	0.0129480	0.000422543 0
$940$	−205.480	−6.70202
$941$	−32.5595	−1.06141	−0.530705	−	0.847557i	$-0.678073\pi$
$941$	−32.5595	−1.06141	−0.530705	+	0.847557i	$0.678073\pi$
$942$	4.26505	0.138963
$943$	−39.8661	−1.29822
$944$	87.7960	2.85751
$945$	−5.27112	−0.171470
$946$	−1.31300	−0.0426892
$947$	−4.19207	−0.136224	−0.0681119	−	0.997678i	$-0.521698\pi$
$947$	−4.19207	−0.136224	−0.0681119	+	0.997678i	$0.521698\pi$
$948$	1.43565	0.0466277
$949$	−4.23569	−0.137496
$950$	53.1231	1.72354
$951$	2.49164	0.0807969
$952$	94.7846	3.07199
$953$	−27.8897	−0.903436	−0.451718	−	0.892161i	$-0.649189\pi$
$953$	−27.8897	−0.903436	−0.451718	+	0.892161i	$0.649189\pi$
$954$	68.6268	2.22187
$955$	−11.9734	−0.387451
$956$	−54.0094	−1.74679
$957$	0.0608416	0.00196673
$958$	−0.786303	−0.0254043
$959$	68.1762	2.20152
$960$	−5.94234	−0.191788
$961$	61.3639	1.97948
$962$	−11.6216	−0.374695
$963$	−7.95893	−0.256473
$964$	−82.2799	−2.65006
$965$	−10.1955	−0.328206
$966$	−3.48164	−0.112020
$967$	45.3969	1.45987	0.729933	−	0.683519i	$-0.239551\pi$
$967$	45.3969	1.45987	0.729933	+	0.683519i	$0.239551\pi$
$968$	101.395	3.25895
$969$	1.00709	0.0323523
$970$	147.263	4.72832
$971$	20.3086	0.651734	0.325867	−	0.945416i	$-0.394344\pi$
$971$	20.3086	0.651734	0.325867	+	0.945416i	$0.394344\pi$
$972$	−10.8005	−0.346427
$973$	−12.5299	−0.401689
$974$	81.3554	2.60680
$975$	−0.562263	−0.0180068
$976$	−88.2074	−2.82345
$977$	−44.7819	−1.43270	−0.716351	−	0.697740i	$-0.754189\pi$
$977$	−44.7819	−1.43270	−0.716351	+	0.697740i	$0.754189\pi$
$978$	−1.67192	−0.0534620
$979$	0.298911	0.00955323
$980$	145.540	4.64909
$981$	−4.63050	−0.147841
$982$	−20.0590	−0.640108
$983$	−12.7669	−0.407200	−0.203600	−	0.979054i	$-0.565264\pi$
$983$	−12.7669	−0.407200	−0.203600	+	0.979054i	$0.565264\pi$
$984$	−6.38449	−0.203530
$985$	23.2406	0.740508
$986$	32.3019	1.02870
$987$	−3.85808	−0.122804
$988$	−59.0825	−1.87967
$989$	11.7618	0.374004
$990$	4.22140	0.134165
$991$	28.5733	0.907662	0.453831	−	0.891088i	$-0.350057\pi$
$991$	28.5733	0.907662	0.453831	+	0.891088i	$0.350057\pi$
$992$	−197.344	−6.26568
$993$	−0.388558	−0.0123305
$994$	76.1426	2.41510
$995$	12.0168	0.380958
$996$	−2.88641	−0.0914593
$997$	32.5915	1.03218	0.516091	−	0.856534i	$-0.327387\pi$
$997$	32.5915	1.03218	0.516091	+	0.856534i	$0.327387\pi$
$998$	84.1634	2.66415
$999$	0.923760	0.0292265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.4	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.4	✓	221	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72000 q^{2} -0.0742815 q^{3} +5.39842 q^{4} +2.94538 q^{5} +0.202046 q^{6} -4.01910 q^{7} -9.24371 q^{8} -2.99448 q^{9} +O(q^{10})\)	\(q-2.72000 q^{2} -0.0742815 q^{3} +5.39842 q^{4} +2.94538 q^{5} +0.202046 q^{6} -4.01910 q^{7} -9.24371 q^{8} -2.99448 q^{9} -8.01145 q^{10} +0.175964 q^{11} -0.401003 q^{12} +2.05953 q^{13} +10.9320 q^{14} -0.218787 q^{15} +14.3461 q^{16} +2.55130 q^{17} +8.14500 q^{18} -5.31403 q^{19} +15.9004 q^{20} +0.298545 q^{21} -0.478623 q^{22} +4.28750 q^{23} +0.686637 q^{24} +3.67528 q^{25} -5.60194 q^{26} +0.445279 q^{27} -21.6968 q^{28} -4.65475 q^{29} +0.595102 q^{30} +9.61061 q^{31} -20.5340 q^{32} -0.0130709 q^{33} -6.93955 q^{34} -11.8378 q^{35} -16.1655 q^{36} +2.07456 q^{37} +14.4542 q^{38} -0.152985 q^{39} -27.2263 q^{40} -9.29820 q^{41} -0.812044 q^{42} +2.74328 q^{43} +0.949928 q^{44} -8.81989 q^{45} -11.6620 q^{46} -12.9229 q^{47} -1.06565 q^{48} +9.15320 q^{49} -9.99676 q^{50} -0.189515 q^{51} +11.1182 q^{52} +8.42563 q^{53} -1.21116 q^{54} +0.518281 q^{55} +37.1514 q^{56} +0.394734 q^{57} +12.6609 q^{58} +6.11985 q^{59} -1.18111 q^{60} -6.14854 q^{61} -26.1409 q^{62} +12.0351 q^{63} +27.1603 q^{64} +6.06611 q^{65} +0.0355528 q^{66} +7.23065 q^{67} +13.7730 q^{68} -0.318482 q^{69} +32.1989 q^{70} +6.96513 q^{71} +27.6801 q^{72} -2.05662 q^{73} -5.64282 q^{74} -0.273005 q^{75} -28.6874 q^{76} -0.707218 q^{77} +0.416120 q^{78} -3.58015 q^{79} +42.2547 q^{80} +8.95037 q^{81} +25.2911 q^{82} +7.19798 q^{83} +1.61167 q^{84} +7.51456 q^{85} -7.46173 q^{86} +0.345761 q^{87} -1.62656 q^{88} +1.69870 q^{89} +23.9901 q^{90} -8.27748 q^{91} +23.1457 q^{92} -0.713891 q^{93} +35.1505 q^{94} -15.6518 q^{95} +1.52529 q^{96} -18.3815 q^{97} -24.8967 q^{98} -0.526921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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