LMFDB - Embedded newform 6007.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, 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("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63584 q^{2} +2.53685 q^{3} +4.94764 q^{4} +0.682671 q^{5} -6.68672 q^{6} +1.00934 q^{7} -7.76949 q^{8} +3.43560 q^{9} +O(q^{10})$	\(q-2.63584 q^{2} +2.53685 q^{3} +4.94764 q^{4} +0.682671 q^{5} -6.68672 q^{6} +1.00934 q^{7} -7.76949 q^{8} +3.43560 q^{9} -1.79941 q^{10} -3.63422 q^{11} +12.5514 q^{12} +1.33180 q^{13} -2.66046 q^{14} +1.73183 q^{15} +10.5838 q^{16} +0.0448742 q^{17} -9.05568 q^{18} -7.25605 q^{19} +3.37761 q^{20} +2.56055 q^{21} +9.57922 q^{22} +2.66358 q^{23} -19.7100 q^{24} -4.53396 q^{25} -3.51041 q^{26} +1.10505 q^{27} +4.99386 q^{28} -2.96844 q^{29} -4.56483 q^{30} +2.00174 q^{31} -12.3583 q^{32} -9.21947 q^{33} -0.118281 q^{34} +0.689049 q^{35} +16.9981 q^{36} +10.2148 q^{37} +19.1258 q^{38} +3.37857 q^{39} -5.30400 q^{40} -7.29946 q^{41} -6.74919 q^{42} +1.51877 q^{43} -17.9808 q^{44} +2.34538 q^{45} -7.02077 q^{46} -1.71522 q^{47} +26.8496 q^{48} -5.98123 q^{49} +11.9508 q^{50} +0.113839 q^{51} +6.58926 q^{52} -5.95884 q^{53} -2.91273 q^{54} -2.48098 q^{55} -7.84208 q^{56} -18.4075 q^{57} +7.82433 q^{58} -11.5454 q^{59} +8.56847 q^{60} -6.47929 q^{61} -5.27626 q^{62} +3.46770 q^{63} +11.4067 q^{64} +0.909180 q^{65} +24.3010 q^{66} +10.1567 q^{67} +0.222021 q^{68} +6.75711 q^{69} -1.81622 q^{70} -8.80223 q^{71} -26.6928 q^{72} +12.8058 q^{73} -26.9246 q^{74} -11.5020 q^{75} -35.9003 q^{76} -3.66818 q^{77} -8.90537 q^{78} -2.85728 q^{79} +7.22527 q^{80} -7.50345 q^{81} +19.2402 q^{82} +10.8259 q^{83} +12.6687 q^{84} +0.0306343 q^{85} -4.00324 q^{86} -7.53049 q^{87} +28.2360 q^{88} +16.6420 q^{89} -6.18205 q^{90} +1.34424 q^{91} +13.1784 q^{92} +5.07811 q^{93} +4.52105 q^{94} -4.95349 q^{95} -31.3511 q^{96} +3.75093 q^{97} +15.7655 q^{98} -12.4857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.63584	−1.86382	−0.931909	−	0.362692i	$-0.881858\pi$
$2$	−2.63584	−1.86382	−0.931909	+	0.362692i	$0.881858\pi$
$3$	2.53685	1.46465	0.732325	−	0.680955i	$-0.238435\pi$
$3$	2.53685	1.46465	0.732325	+	0.680955i	$0.238435\pi$
$4$	4.94764	2.47382
$5$	0.682671	0.305300	0.152650	−	0.988280i	$-0.451219\pi$
$5$	0.682671	0.305300	0.152650	+	0.988280i	$0.451219\pi$
$6$	−6.68672	−2.72984
$7$	1.00934	0.381496	0.190748	−	0.981639i	$-0.438909\pi$
$7$	1.00934	0.381496	0.190748	+	0.981639i	$0.438909\pi$
$8$	−7.76949	−2.74693
$9$	3.43560	1.14520
$10$	−1.79941	−0.569023
$11$	−3.63422	−1.09576	−0.547880	−	0.836557i	$-0.684565\pi$
$11$	−3.63422	−1.09576	−0.547880	+	0.836557i	$0.684565\pi$
$12$	12.5514	3.62328
$13$	1.33180	0.369375	0.184687	−	0.982797i	$-0.440873\pi$
$13$	1.33180	0.369375	0.184687	+	0.982797i	$0.440873\pi$
$14$	−2.66046	−0.711039
$15$	1.73183	0.447157
$16$	10.5838	2.64596
$17$	0.0448742	0.0108836	0.00544180	−	0.999985i	$-0.498268\pi$
$17$	0.0448742	0.0108836	0.00544180	+	0.999985i	$0.498268\pi$
$18$	−9.05568	−2.13444
$19$	−7.25605	−1.66465	−0.832326	−	0.554287i	$-0.812991\pi$
$19$	−7.25605	−1.66465	−0.832326	+	0.554287i	$0.812991\pi$
$20$	3.37761	0.755256
$21$	2.56055	0.558758
$22$	9.57922	2.04230
$23$	2.66358	0.555396	0.277698	−	0.960668i	$-0.410429\pi$
$23$	2.66358	0.555396	0.277698	+	0.960668i	$0.410429\pi$
$24$	−19.7100	−4.02329
$25$	−4.53396	−0.906792
$26$	−3.51041	−0.688447
$27$	1.10505	0.212667
$28$	4.99386	0.943751
$29$	−2.96844	−0.551226	−0.275613	−	0.961269i	$-0.588881\pi$
$29$	−2.96844	−0.551226	−0.275613	+	0.961269i	$0.588881\pi$
$30$	−4.56483	−0.833419
$31$	2.00174	0.359523	0.179761	−	0.983710i	$-0.442467\pi$
$31$	2.00174	0.359523	0.179761	+	0.983710i	$0.442467\pi$
$32$	−12.3583	−2.18465
$33$	−9.21947	−1.60490
$34$	−0.118281	−0.0202851
$35$	0.689049	0.116471
$36$	16.9981	2.83302
$37$	10.2148	1.67931	0.839653	−	0.543124i	$-0.182759\pi$
$37$	10.2148	1.67931	0.839653	+	0.543124i	$0.182759\pi$
$38$	19.1258	3.10261
$39$	3.37857	0.541005
$40$	−5.30400	−0.838636
$41$	−7.29946	−1.13998	−0.569992	−	0.821650i	$-0.693054\pi$
$41$	−7.29946	−1.13998	−0.569992	+	0.821650i	$0.693054\pi$
$42$	−6.74919	−1.04142
$43$	1.51877	0.231611	0.115805	−	0.993272i	$-0.463055\pi$
$43$	1.51877	0.231611	0.115805	+	0.993272i	$0.463055\pi$
$44$	−17.9808	−2.71071
$45$	2.34538	0.349629
$46$	−7.02077	−1.03516
$47$	−1.71522	−0.250191	−0.125096	−	0.992145i	$-0.539924\pi$
$47$	−1.71522	−0.250191	−0.125096	+	0.992145i	$0.539924\pi$
$48$	26.8496	3.87540
$49$	−5.98123	−0.854461
$50$	11.9508	1.69010
$51$	0.113839	0.0159407
$52$	6.58926	0.913766
$53$	−5.95884	−0.818510	−0.409255	−	0.912420i	$-0.634211\pi$
$53$	−5.95884	−0.818510	−0.409255	+	0.912420i	$0.634211\pi$
$54$	−2.91273	−0.396373
$55$	−2.48098	−0.334535
$56$	−7.84208	−1.04794
$57$	−18.4075	−2.43813
$58$	7.82433	1.02739
$59$	−11.5454	−1.50309	−0.751544	−	0.659683i	$-0.770690\pi$
$59$	−11.5454	−1.50309	−0.751544	+	0.659683i	$0.770690\pi$
$60$	8.56847	1.10619
$61$	−6.47929	−0.829588	−0.414794	−	0.909915i	$-0.636146\pi$
$61$	−6.47929	−0.829588	−0.414794	+	0.909915i	$0.636146\pi$
$62$	−5.27626	−0.670085
$63$	3.46770	0.436889
$64$	11.4067	1.42584
$65$	0.909180	0.112770
$66$	24.3010	2.99125
$67$	10.1567	1.24084	0.620422	−	0.784268i	$-0.286961\pi$
$67$	10.1567	1.24084	0.620422	+	0.784268i	$0.286961\pi$
$68$	0.222021	0.0269240
$69$	6.75711	0.813460
$70$	−1.81622	−0.217080
$71$	−8.80223	−1.04463	−0.522316	−	0.852752i	$-0.674932\pi$
$71$	−8.80223	−1.04463	−0.522316	+	0.852752i	$0.674932\pi$
$72$	−26.6928	−3.14578
$73$	12.8058	1.49881	0.749404	−	0.662113i	$-0.230340\pi$
$73$	12.8058	1.49881	0.749404	+	0.662113i	$0.230340\pi$
$74$	−26.9246	−3.12992
$75$	−11.5020	−1.32813
$76$	−35.9003	−4.11804
$77$	−3.66818	−0.418028
$78$	−8.90537	−1.00833
$79$	−2.85728	−0.321469	−0.160735	−	0.986998i	$-0.551386\pi$
$79$	−2.85728	−0.321469	−0.160735	+	0.986998i	$0.551386\pi$
$80$	7.22527	0.807810
$81$	−7.50345	−0.833717
$82$	19.2402	2.12472
$83$	10.8259	1.18830	0.594150	−	0.804354i	$-0.297488\pi$
$83$	10.8259	1.18830	0.594150	+	0.804354i	$0.297488\pi$
$84$	12.6687	1.38227
$85$	0.0306343	0.00332276
$86$	−4.00324	−0.431680
$87$	−7.53049	−0.807353
$88$	28.2360	3.00997
$89$	16.6420	1.76404	0.882022	−	0.471209i	$-0.156182\pi$
$89$	16.6420	1.76404	0.882022	+	0.471209i	$0.156182\pi$
$90$	−6.18205	−0.651645
$91$	1.34424	0.140915
$92$	13.1784	1.37395
$93$	5.07811	0.526575
$94$	4.52105	0.466311
$95$	−4.95349	−0.508217
$96$	−31.3511	−3.19975
$97$	3.75093	0.380849	0.190425	−	0.981702i	$-0.439014\pi$
$97$	3.75093	0.380849	0.190425	+	0.981702i	$0.439014\pi$
$98$	15.7655	1.59256
$99$	−12.4857	−1.25486
$100$	−22.4324	−2.24324
$101$	−5.45676	−0.542968	−0.271484	−	0.962443i	$-0.587514\pi$
$101$	−5.45676	−0.542968	−0.271484	+	0.962443i	$0.587514\pi$
$102$	−0.300061	−0.0297105
$103$	−10.8258	−1.06670	−0.533350	−	0.845894i	$-0.679067\pi$
$103$	−10.8258	−1.06670	−0.533350	+	0.845894i	$0.679067\pi$
$104$	−10.3474	−1.01465
$105$	1.74801	0.170589
$106$	15.7065	1.52555
$107$	9.46919	0.915421	0.457710	−	0.889101i	$-0.348670\pi$
$107$	9.46919	0.915421	0.457710	+	0.889101i	$0.348670\pi$
$108$	5.46739	0.526100
$109$	−13.3671	−1.28034	−0.640169	−	0.768235i	$-0.721135\pi$
$109$	−13.3671	−1.28034	−0.640169	+	0.768235i	$0.721135\pi$
$110$	6.53945	0.623512
$111$	25.9134	2.45959
$112$	10.6827	1.00942
$113$	−2.78266	−0.261770	−0.130885	−	0.991398i	$-0.541782\pi$
$113$	−2.78266	−0.261770	−0.130885	+	0.991398i	$0.541782\pi$
$114$	48.5191	4.54423
$115$	1.81835	0.169562
$116$	−14.6868	−1.36363
$117$	4.57553	0.423008
$118$	30.4319	2.80148
$119$	0.0452935	0.00415205
$120$	−13.4554	−1.22831
$121$	2.20758	0.200689
$122$	17.0783	1.54620
$123$	−18.5176	−1.66968
$124$	9.90387	0.889394
$125$	−6.50855	−0.582143
$126$	−9.14029	−0.814282
$127$	−18.8759	−1.67497	−0.837484	−	0.546461i	$-0.815975\pi$
$127$	−18.8759	−1.67497	−0.837484	+	0.546461i	$0.815975\pi$
$128$	−5.34973	−0.472854
$129$	3.85290	0.339229
$130$	−2.39645	−0.210183
$131$	−21.3641	−1.86659	−0.933295	−	0.359112i	$-0.883080\pi$
$131$	−21.3641	−1.86659	−0.933295	+	0.359112i	$0.883080\pi$
$132$	−45.6146	−3.97024
$133$	−7.32384	−0.635058
$134$	−26.7715	−2.31271
$135$	0.754386	0.0649272
$136$	−0.348650	−0.0298965
$137$	0.0247402	0.00211370	0.00105685	−	0.999999i	$-0.499664\pi$
$137$	0.0247402	0.00211370	0.00105685	+	0.999999i	$0.499664\pi$
$138$	−17.8106	−1.51614
$139$	20.8778	1.77083	0.885415	−	0.464801i	$-0.153874\pi$
$139$	20.8778	1.77083	0.885415	+	0.464801i	$0.153874\pi$
$140$	3.40916	0.288127
$141$	−4.35126	−0.366443
$142$	23.2012	1.94701
$143$	−4.84006	−0.404746
$144$	36.3618	3.03015
$145$	−2.02647	−0.168289
$146$	−33.7541	−2.79351
$147$	−15.1735	−1.25149
$148$	50.5392	4.15430
$149$	−10.0060	−0.819724	−0.409862	−	0.912148i	$-0.634423\pi$
$149$	−10.0060	−0.819724	−0.409862	+	0.912148i	$0.634423\pi$
$150$	30.3173	2.47540
$151$	15.8735	1.29177	0.645883	−	0.763436i	$-0.276489\pi$
$151$	15.8735	1.29177	0.645883	+	0.763436i	$0.276489\pi$
$152$	56.3758	4.57268
$153$	0.154170	0.0124639
$154$	9.66872	0.779128
$155$	1.36653	0.109762
$156$	16.7159	1.33835
$157$	16.1695	1.29047	0.645234	−	0.763985i	$-0.276760\pi$
$157$	16.1695	1.29047	0.645234	+	0.763985i	$0.276760\pi$
$158$	7.53133	0.599161
$159$	−15.1167	−1.19883
$160$	−8.43663	−0.666974
$161$	2.68847	0.211881
$162$	19.7779	1.55390
$163$	−6.63363	−0.519586	−0.259793	−	0.965664i	$-0.583654\pi$
$163$	−6.63363	−0.519586	−0.259793	+	0.965664i	$0.583654\pi$
$164$	−36.1151	−2.82011
$165$	−6.29386	−0.489977
$166$	−28.5354	−2.21478
$167$	−22.5550	−1.74536	−0.872681	−	0.488291i	$-0.837620\pi$
$167$	−22.5550	−1.74536	−0.872681	+	0.488291i	$0.837620\pi$
$168$	−19.8942	−1.53487
$169$	−11.2263	−0.863562
$170$	−0.0807471	−0.00619302
$171$	−24.9289	−1.90636
$172$	7.51433	0.572962
$173$	−4.36338	−0.331742	−0.165871	−	0.986147i	$-0.553044\pi$
$173$	−4.36338	−0.331742	−0.165871	+	0.986147i	$0.553044\pi$
$174$	19.8491	1.50476
$175$	−4.57632	−0.345938
$176$	−38.4640	−2.89933
$177$	−29.2890	−2.20150
$178$	−43.8655	−3.28786
$179$	−1.31070	−0.0979662	−0.0489831	−	0.998800i	$-0.515598\pi$
$179$	−1.31070	−0.0979662	−0.0489831	+	0.998800i	$0.515598\pi$
$180$	11.6041	0.864919
$181$	−20.9087	−1.55413	−0.777064	−	0.629421i	$-0.783292\pi$
$181$	−20.9087	−1.55413	−0.777064	+	0.629421i	$0.783292\pi$
$182$	−3.54320	−0.262640
$183$	−16.4370	−1.21506
$184$	−20.6947	−1.52563
$185$	6.97335	0.512691
$186$	−13.3851	−0.981440
$187$	−0.163083	−0.0119258
$188$	−8.48631	−0.618927
$189$	1.11538	0.0811317
$190$	13.0566	0.947225
$191$	−24.7949	−1.79410	−0.897048	−	0.441932i	$-0.854293\pi$
$191$	−24.7949	−1.79410	−0.897048	+	0.441932i	$0.854293\pi$
$192$	28.9371	2.08836
$193$	−19.6807	−1.41665	−0.708325	−	0.705887i	$-0.750549\pi$
$193$	−19.6807	−1.41665	−0.708325	+	0.705887i	$0.750549\pi$
$194$	−9.88684	−0.709833
$195$	2.30645	0.165169
$196$	−29.5929	−2.11378
$197$	4.50282	0.320812	0.160406	−	0.987051i	$-0.448720\pi$
$197$	4.50282	0.320812	0.160406	+	0.987051i	$0.448720\pi$
$198$	32.9104	2.33884
$199$	16.3614	1.15983	0.579914	−	0.814678i	$-0.303086\pi$
$199$	16.3614	1.15983	0.579914	+	0.814678i	$0.303086\pi$
$200$	35.2265	2.49089
$201$	25.7661	1.81740
$202$	14.3831	1.01199
$203$	−2.99618	−0.210291
$204$	0.563235	0.0394343
$205$	−4.98313	−0.348037
$206$	28.5351	1.98814
$207$	9.15101	0.636039
$208$	14.0955	0.977350
$209$	26.3701	1.82406
$210$	−4.60748	−0.317946
$211$	−12.7008	−0.874356	−0.437178	−	0.899375i	$-0.644022\pi$
$211$	−12.7008	−0.874356	−0.437178	+	0.899375i	$0.644022\pi$
$212$	−29.4822	−2.02484
$213$	−22.3299	−1.53002
$214$	−24.9592	−1.70618
$215$	1.03682	0.0707106
$216$	−8.58568	−0.584181
$217$	2.02044	0.137156
$218$	35.2335	2.38632
$219$	32.4864	2.19523
$220$	−12.2750	−0.827578
$221$	0.0597635	0.00402013
$222$	−68.3036	−4.58424
$223$	14.8086	0.991658	0.495829	−	0.868420i	$-0.334864\pi$
$223$	14.8086	0.991658	0.495829	+	0.868420i	$0.334864\pi$
$224$	−12.4737	−0.833437
$225$	−15.5769	−1.03846
$226$	7.33463	0.487892
$227$	−12.5319	−0.831769	−0.415885	−	0.909417i	$-0.636528\pi$
$227$	−12.5319	−0.831769	−0.415885	+	0.909417i	$0.636528\pi$
$228$	−91.0736	−6.03149
$229$	23.8170	1.57387	0.786935	−	0.617036i	$-0.211667\pi$
$229$	23.8170	1.57387	0.786935	+	0.617036i	$0.211667\pi$
$230$	−4.79287	−0.316033
$231$	−9.30561	−0.612264
$232$	23.0633	1.51418
$233$	−25.2510	−1.65425	−0.827123	−	0.562021i	$-0.810024\pi$
$233$	−25.2510	−1.65425	−0.827123	+	0.562021i	$0.810024\pi$
$234$	−12.0604	−0.788410
$235$	−1.17093	−0.0763833
$236$	−57.1226	−3.71836
$237$	−7.24849	−0.470840
$238$	−0.119386	−0.00773867
$239$	−5.64524	−0.365160	−0.182580	−	0.983191i	$-0.558445\pi$
$239$	−5.64524	−0.365160	−0.182580	+	0.983191i	$0.558445\pi$
$240$	18.3294	1.18316
$241$	27.4135	1.76586	0.882930	−	0.469504i	$-0.155567\pi$
$241$	27.4135	1.76586	0.882930	+	0.469504i	$0.155567\pi$
$242$	−5.81881	−0.374047
$243$	−22.3503	−1.43377
$244$	−32.0572	−2.05225
$245$	−4.08321	−0.260867
$246$	48.8094	3.11198
$247$	−9.66360	−0.614880
$248$	−15.5525	−0.987583
$249$	27.4638	1.74045
$250$	17.1555	1.08501
$251$	−8.03896	−0.507415	−0.253707	−	0.967281i	$-0.581650\pi$
$251$	−8.03896	−0.507415	−0.253707	+	0.967281i	$0.581650\pi$
$252$	17.1569	1.08078
$253$	−9.68006	−0.608580
$254$	49.7539	3.12184
$255$	0.0777146	0.00486668
$256$	−8.71244	−0.544527
$257$	−9.82343	−0.612769	−0.306384	−	0.951908i	$-0.599119\pi$
$257$	−9.82343	−0.612769	−0.306384	+	0.951908i	$0.599119\pi$
$258$	−10.1556	−0.632260
$259$	10.3103	0.640648
$260$	4.49829	0.278972
$261$	−10.1984	−0.631264
$262$	56.3122	3.47898
$263$	−4.20827	−0.259493	−0.129747	−	0.991547i	$-0.541416\pi$
$263$	−4.20827	−0.259493	−0.129747	+	0.991547i	$0.541416\pi$
$264$	71.6306	4.40856
$265$	−4.06793	−0.249891
$266$	19.3045	1.18363
$267$	42.2181	2.58371
$268$	50.2519	3.06962
$269$	8.07733	0.492483	0.246242	−	0.969208i	$-0.420804\pi$
$269$	8.07733	0.492483	0.246242	+	0.969208i	$0.420804\pi$
$270$	−1.98844	−0.121012
$271$	−27.1860	−1.65143	−0.825715	−	0.564088i	$-0.809228\pi$
$271$	−27.1860	−1.65143	−0.825715	+	0.564088i	$0.809228\pi$
$272$	0.474941	0.0287975
$273$	3.41014	0.206391
$274$	−0.0652112	−0.00393955
$275$	16.4774	0.993626
$276$	33.4317	2.01235
$277$	−29.5449	−1.77518	−0.887591	−	0.460633i	$-0.847623\pi$
$277$	−29.5449	−1.77518	−0.887591	+	0.460633i	$0.847623\pi$
$278$	−55.0304	−3.30051
$279$	6.87717	0.411726
$280$	−5.35356	−0.319936
$281$	−23.0892	−1.37739	−0.688693	−	0.725053i	$-0.741815\pi$
$281$	−23.0892	−1.37739	−0.688693	+	0.725053i	$0.741815\pi$
$282$	11.4692	0.682982
$283$	17.9771	1.06863	0.534315	−	0.845286i	$-0.320570\pi$
$283$	17.9771	1.06863	0.534315	+	0.845286i	$0.320570\pi$
$284$	−43.5502	−2.58423
$285$	−12.5663	−0.744361
$286$	12.7576	0.754373
$287$	−7.36766	−0.434899
$288$	−42.4581	−2.50187
$289$	−16.9980	−0.999882
$290$	5.34144	0.313660
$291$	9.51554	0.557811
$292$	63.3586	3.70778
$293$	−23.2755	−1.35977	−0.679885	−	0.733319i	$-0.737970\pi$
$293$	−23.2755	−1.35977	−0.679885	+	0.733319i	$0.737970\pi$
$294$	39.9948	2.33254
$295$	−7.88173	−0.458892
$296$	−79.3639	−4.61293
$297$	−4.01600	−0.233032
$298$	26.3742	1.52782
$299$	3.54736	0.205149
$300$	−56.9076	−3.28556
$301$	1.53296	0.0883585
$302$	−41.8399	−2.40762
$303$	−13.8430	−0.795259
$304$	−76.7967	−4.40460
$305$	−4.42322	−0.253273
$306$	−0.406367	−0.0232304
$307$	26.3810	1.50565	0.752823	−	0.658223i	$-0.228692\pi$
$307$	26.3810	1.50565	0.752823	+	0.658223i	$0.228692\pi$
$308$	−18.1488	−1.03412
$309$	−27.4635	−1.56234
$310$	−3.60194	−0.204577
$311$	27.5692	1.56330	0.781652	−	0.623715i	$-0.214377\pi$
$311$	27.5692	1.56330	0.781652	+	0.623715i	$0.214377\pi$
$312$	−26.2498	−1.48610
$313$	22.2542	1.25788	0.628939	−	0.777454i	$-0.283489\pi$
$313$	22.2542	1.25788	0.628939	+	0.777454i	$0.283489\pi$
$314$	−42.6202	−2.40520
$315$	2.36730	0.133382
$316$	−14.1368	−0.795257
$317$	24.3423	1.36720	0.683600	−	0.729857i	$-0.260413\pi$
$317$	24.3423	1.36720	0.683600	+	0.729857i	$0.260413\pi$
$318$	39.8451	2.23440
$319$	10.7880	0.604011
$320$	7.78704	0.435309
$321$	24.0219	1.34077
$322$	−7.08637	−0.394908
$323$	−0.325610	−0.0181174
$324$	−37.1244	−2.06246
$325$	−6.03833	−0.334946
$326$	17.4852	0.968413
$327$	−33.9103	−1.87525
$328$	56.7131	3.13146
$329$	−1.73125	−0.0954469
$330$	16.5896	0.913227
$331$	26.7317	1.46931	0.734654	−	0.678442i	$-0.237345\pi$
$331$	26.7317	1.46931	0.734654	+	0.678442i	$0.237345\pi$
$332$	53.5628	2.93964
$333$	35.0940	1.92314
$334$	59.4514	3.25304
$335$	6.93371	0.378829
$336$	27.1004	1.47845
$337$	−20.2439	−1.10276	−0.551378	−	0.834255i	$-0.685898\pi$
$337$	−20.2439	−1.10276	−0.551378	+	0.834255i	$0.685898\pi$
$338$	29.5907	1.60952
$339$	−7.05918	−0.383402
$340$	0.151567	0.00821990
$341$	−7.27476	−0.393950
$342$	65.7084	3.55311
$343$	−13.1025	−0.707469
$344$	−11.8001	−0.636218
$345$	4.61288	0.248349
$346$	11.5012	0.618306
$347$	5.16047	0.277029	0.138514	−	0.990360i	$-0.455767\pi$
$347$	5.16047	0.277029	0.138514	+	0.990360i	$0.455767\pi$
$348$	−37.2581	−1.99725
$349$	−16.3641	−0.875949	−0.437975	−	0.898987i	$-0.644304\pi$
$349$	−16.3641	−0.875949	−0.437975	+	0.898987i	$0.644304\pi$
$350$	12.0624	0.644765
$351$	1.47171	0.0785539
$352$	44.9127	2.39386
$353$	21.5415	1.14654	0.573270	−	0.819366i	$-0.305674\pi$
$353$	21.5415	1.14654	0.573270	+	0.819366i	$0.305674\pi$
$354$	77.2011	4.10319
$355$	−6.00903	−0.318926
$356$	82.3383	4.36392
$357$	0.114903	0.00608130
$358$	3.45479	0.182591
$359$	15.5986	0.823264	0.411632	−	0.911350i	$-0.364959\pi$
$359$	15.5986	0.823264	0.411632	+	0.911350i	$0.364959\pi$
$360$	−18.2224	−0.960406
$361$	33.6502	1.77106
$362$	55.1118	2.89661
$363$	5.60028	0.293939
$364$	6.65082	0.348598
$365$	8.74216	0.457586
$366$	43.3252	2.26464
$367$	10.1469	0.529665	0.264832	−	0.964294i	$-0.414683\pi$
$367$	10.1469	0.529665	0.264832	+	0.964294i	$0.414683\pi$
$368$	28.1909	1.46955
$369$	−25.0780	−1.30551
$370$	−18.3806	−0.955563
$371$	−6.01452	−0.312258
$372$	25.1246	1.30265
$373$	−0.292684	−0.0151546	−0.00757729	−	0.999971i	$-0.502412\pi$
$373$	−0.292684	−0.0151546	−0.00757729	+	0.999971i	$0.502412\pi$
$374$	0.429860	0.0222275
$375$	−16.5112	−0.852636
$376$	13.3264	0.687257
$377$	−3.95337	−0.203609
$378$	−2.93995	−0.151215
$379$	6.95250	0.357126	0.178563	−	0.983928i	$-0.442855\pi$
$379$	6.95250	0.357126	0.178563	+	0.983928i	$0.442855\pi$
$380$	−24.5081	−1.25724
$381$	−47.8854	−2.45324
$382$	65.3553	3.34387
$383$	25.8061	1.31863	0.659316	−	0.751866i	$-0.270846\pi$
$383$	25.8061	1.31863	0.659316	+	0.751866i	$0.270846\pi$
$384$	−13.5715	−0.692565
$385$	−2.50416	−0.127624
$386$	51.8752	2.64038
$387$	5.21789	0.265240
$388$	18.5582	0.942151
$389$	−14.8021	−0.750497	−0.375249	−	0.926924i	$-0.622443\pi$
$389$	−14.8021	−0.750497	−0.375249	+	0.926924i	$0.622443\pi$
$390$	−6.07943	−0.307844
$391$	0.119526	0.00604470
$392$	46.4711	2.34714
$393$	−54.1975	−2.73390
$394$	−11.8687	−0.597936
$395$	−1.95058	−0.0981445
$396$	−61.7749	−3.10430
$397$	5.21116	0.261541	0.130770	−	0.991413i	$-0.458255\pi$
$397$	5.21116	0.261541	0.130770	+	0.991413i	$0.458255\pi$
$398$	−43.1259	−2.16171
$399$	−18.5795	−0.930137
$400$	−47.9867	−2.39933
$401$	6.29394	0.314304	0.157152	−	0.987574i	$-0.449769\pi$
$401$	6.29394	0.314304	0.157152	+	0.987574i	$0.449769\pi$
$402$	−67.9153	−3.38731
$403$	2.66591	0.132799
$404$	−26.9981	−1.34320
$405$	−5.12239	−0.254533
$406$	7.89744	0.391943
$407$	−37.1229	−1.84011
$408$	−0.884472	−0.0437879
$409$	6.06947	0.300116	0.150058	−	0.988677i	$-0.452054\pi$
$409$	6.06947	0.300116	0.150058	+	0.988677i	$0.452054\pi$
$410$	13.1347	0.648677
$411$	0.0627622	0.00309583
$412$	−53.5623	−2.63882
$413$	−11.6533	−0.573422
$414$	−24.1206	−1.18546
$415$	7.39055	0.362788
$416$	−16.4587	−0.806956
$417$	52.9638	2.59365
$418$	−69.5073	−3.39971
$419$	27.1975	1.32869	0.664343	−	0.747428i	$-0.268711\pi$
$419$	27.1975	1.32869	0.664343	+	0.747428i	$0.268711\pi$
$420$	8.64853	0.422005
$421$	−15.1885	−0.740244	−0.370122	−	0.928983i	$-0.620684\pi$
$421$	−15.1885	−0.740244	−0.370122	+	0.928983i	$0.620684\pi$
$422$	33.4771	1.62964
$423$	−5.89282	−0.286519
$424$	46.2971	2.24839
$425$	−0.203458	−0.00986917
$426$	58.8580	2.85168
$427$	−6.53983	−0.316484
$428$	46.8501	2.26458
$429$	−12.2785	−0.592811
$430$	−2.73289	−0.131792
$431$	18.8168	0.906371	0.453186	−	0.891416i	$-0.350287\pi$
$431$	18.8168	0.906371	0.453186	+	0.891416i	$0.350287\pi$
$432$	11.6957	0.562708
$433$	8.71142	0.418644	0.209322	−	0.977847i	$-0.432874\pi$
$433$	8.71142	0.418644	0.209322	+	0.977847i	$0.432874\pi$
$434$	−5.32555	−0.255635
$435$	−5.14084	−0.246485
$436$	−66.1356	−3.16732
$437$	−19.3271	−0.924540
$438$	−85.6290	−4.09151
$439$	2.72464	0.130040	0.0650200	−	0.997884i	$-0.479289\pi$
$439$	2.72464	0.130040	0.0650200	+	0.997884i	$0.479289\pi$
$440$	19.2759	0.918943
$441$	−20.5491	−0.978529
$442$	−0.157527	−0.00749279
$443$	−23.9316	−1.13702	−0.568512	−	0.822675i	$-0.692481\pi$
$443$	−23.9316	−1.13702	−0.568512	+	0.822675i	$0.692481\pi$
$444$	128.210	6.08459
$445$	11.3610	0.538562
$446$	−39.0331	−1.84827
$447$	−25.3837	−1.20061
$448$	11.5133	0.543952
$449$	30.4174	1.43549	0.717743	−	0.696308i	$-0.245175\pi$
$449$	30.4174	1.43549	0.717743	+	0.696308i	$0.245175\pi$
$450$	41.0581	1.93550
$451$	26.5279	1.24915
$452$	−13.7676	−0.647572
$453$	40.2686	1.89199
$454$	33.0320	1.55027
$455$	0.917675	0.0430213
$456$	143.017	6.69737
$457$	−17.0387	−0.797038	−0.398519	−	0.917160i	$-0.630476\pi$
$457$	−17.0387	−0.797038	−0.398519	+	0.917160i	$0.630476\pi$
$458$	−62.7777	−2.93341
$459$	0.0495883	0.00231458
$460$	8.99654	0.419466
$461$	3.52615	0.164229	0.0821145	−	0.996623i	$-0.473833\pi$
$461$	3.52615	0.164229	0.0821145	+	0.996623i	$0.473833\pi$
$462$	24.5281	1.14115
$463$	−19.9274	−0.926107	−0.463054	−	0.886330i	$-0.653246\pi$
$463$	−19.9274	−0.926107	−0.463054	+	0.886330i	$0.653246\pi$
$464$	−31.4175	−1.45852
$465$	3.46667	0.160763
$466$	66.5574	3.08321
$467$	25.3289	1.17208	0.586040	−	0.810282i	$-0.300686\pi$
$467$	25.3289	1.17208	0.586040	+	0.810282i	$0.300686\pi$
$468$	22.6381	1.04644
$469$	10.2516	0.473377
$470$	3.08639	0.142365
$471$	41.0196	1.89008
$472$	89.7021	4.12887
$473$	−5.51956	−0.253790
$474$	19.1058	0.877561
$475$	32.8986	1.50949
$476$	0.224096	0.0102714
$477$	−20.4722	−0.937358
$478$	14.8799	0.680592
$479$	−12.3834	−0.565813	−0.282906	−	0.959148i	$-0.591299\pi$
$479$	−12.3834	−0.565813	−0.282906	+	0.959148i	$0.591299\pi$
$480$	−21.4024	−0.976883
$481$	13.6041	0.620293
$482$	−72.2576	−3.29124
$483$	6.82024	0.310332
$484$	10.9223	0.496467
$485$	2.56065	0.116273
$486$	58.9117	2.67229
$487$	24.3178	1.10194	0.550972	−	0.834524i	$-0.314257\pi$
$487$	24.3178	1.10194	0.550972	+	0.834524i	$0.314257\pi$
$488$	50.3408	2.27882
$489$	−16.8285	−0.761011
$490$	10.7627	0.486208
$491$	−37.0832	−1.67354	−0.836771	−	0.547553i	$-0.815559\pi$
$491$	−37.0832	−1.67354	−0.836771	+	0.547553i	$0.815559\pi$
$492$	−91.6185	−4.13048
$493$	−0.133207	−0.00599933
$494$	25.4717	1.14602
$495$	−8.52364	−0.383109
$496$	21.1861	0.951282
$497$	−8.88447	−0.398523
$498$	−72.3900	−3.24387
$499$	−38.3834	−1.71828	−0.859139	−	0.511742i	$-0.829001\pi$
$499$	−38.3834	−1.71828	−0.859139	+	0.511742i	$0.829001\pi$
$500$	−32.2020	−1.44012
$501$	−57.2187	−2.55634
$502$	21.1894	0.945729
$503$	31.3648	1.39849	0.699244	−	0.714883i	$-0.253520\pi$
$503$	31.3648	1.39849	0.699244	+	0.714883i	$0.253520\pi$
$504$	−26.9422	−1.20010
$505$	−3.72517	−0.165768
$506$	25.5150	1.13428
$507$	−28.4794	−1.26482
$508$	−93.3913	−4.14357
$509$	−30.0595	−1.33236	−0.666182	−	0.745790i	$-0.732072\pi$
$509$	−30.0595	−1.33236	−0.666182	+	0.745790i	$0.732072\pi$
$510$	−0.204843	−0.00907061
$511$	12.9255	0.571789
$512$	33.6640	1.48775
$513$	−8.01830	−0.354017
$514$	25.8930	1.14209
$515$	−7.39048	−0.325663
$516$	19.0627	0.839190
$517$	6.23351	0.274149
$518$	−27.1762	−1.19405
$519$	−11.0692	−0.485886
$520$	−7.06386	−0.309771
$521$	8.89884	0.389865	0.194933	−	0.980817i	$-0.437551\pi$
$521$	8.89884	0.389865	0.194933	+	0.980817i	$0.437551\pi$
$522$	26.8813	1.17656
$523$	1.86878	0.0817160	0.0408580	−	0.999165i	$-0.486991\pi$
$523$	1.86878	0.0817160	0.0408580	+	0.999165i	$0.486991\pi$
$524$	−105.702	−4.61760
$525$	−11.6094	−0.506677
$526$	11.0923	0.483648
$527$	0.0898265	0.00391290
$528$	−97.5773	−4.24651
$529$	−15.9053	−0.691536
$530$	10.7224	0.465751
$531$	−39.6655	−1.72134
$532$	−36.2357	−1.57102
$533$	−9.72142	−0.421081
$534$	−111.280	−4.81556
$535$	6.46434	0.279478
$536$	−78.9127	−3.40851
$537$	−3.32504	−0.143486
$538$	−21.2905	−0.917899
$539$	21.7371	0.936284
$540$	3.73243	0.160618
$541$	19.7490	0.849074	0.424537	−	0.905410i	$-0.360437\pi$
$541$	19.7490	0.849074	0.424537	+	0.905410i	$0.360437\pi$
$542$	71.6577	3.07796
$543$	−53.0421	−2.27625
$544$	−0.554568	−0.0237769
$545$	−9.12533	−0.390886
$546$	−8.98857	−0.384675
$547$	20.6143	0.881403	0.440702	−	0.897654i	$-0.354730\pi$
$547$	20.6143	0.881403	0.440702	+	0.897654i	$0.354730\pi$
$548$	0.122406	0.00522891
$549$	−22.2602	−0.950044
$550$	−43.4318	−1.85194
$551$	21.5392	0.917599
$552$	−52.4993	−2.23452
$553$	−2.88398	−0.122639
$554$	77.8756	3.30862
$555$	17.6903	0.750913
$556$	103.296	4.38071
$557$	21.0085	0.890159	0.445079	−	0.895491i	$-0.353175\pi$
$557$	21.0085	0.890159	0.445079	+	0.895491i	$0.353175\pi$
$558$	−18.1271	−0.767381
$559$	2.02270	0.0855511
$560$	7.29278	0.308176
$561$	−0.413717	−0.0174671
$562$	60.8594	2.56720
$563$	−10.6447	−0.448620	−0.224310	−	0.974518i	$-0.572013\pi$
$563$	−10.6447	−0.448620	−0.224310	+	0.974518i	$0.572013\pi$
$564$	−21.5285	−0.906512
$565$	−1.89964	−0.0799184
$566$	−47.3848	−1.99173
$567$	−7.57356	−0.318060
$568$	68.3888	2.86953
$569$	−16.6579	−0.698337	−0.349169	−	0.937060i	$-0.613536\pi$
$569$	−16.6579	−0.698337	−0.349169	+	0.937060i	$0.613536\pi$
$570$	33.1226	1.38735
$571$	−3.52314	−0.147439	−0.0737195	−	0.997279i	$-0.523487\pi$
$571$	−3.52314	−0.147439	−0.0737195	+	0.997279i	$0.523487\pi$
$572$	−23.9468	−1.00127
$573$	−62.9009	−2.62772
$574$	19.4200	0.810573
$575$	−12.0766	−0.503628
$576$	39.1889	1.63287
$577$	−31.0034	−1.29069	−0.645344	−	0.763892i	$-0.723286\pi$
$577$	−31.0034	−1.29069	−0.645344	+	0.763892i	$0.723286\pi$
$578$	44.8039	1.86360
$579$	−49.9270	−2.07490
$580$	−10.0262	−0.416317
$581$	10.9271	0.453332
$582$	−25.0814	−1.03966
$583$	21.6558	0.896890
$584$	−99.4947	−4.11712
$585$	3.12358	0.129144
$586$	61.3504	2.53436
$587$	−33.4100	−1.37898	−0.689489	−	0.724296i	$-0.742165\pi$
$587$	−33.4100	−1.37898	−0.689489	+	0.724296i	$0.742165\pi$
$588$	−75.0728	−3.09595
$589$	−14.5247	−0.598480
$590$	20.7749	0.855291
$591$	11.4230	0.469878
$592$	108.112	4.44337
$593$	19.2227	0.789384	0.394692	−	0.918814i	$-0.370851\pi$
$593$	19.2227	0.789384	0.394692	+	0.918814i	$0.370851\pi$
$594$	10.5855	0.434329
$595$	0.0309206	0.00126762
$596$	−49.5061	−2.02785
$597$	41.5063	1.69874
$598$	−9.35026	−0.382361
$599$	−2.98475	−0.121954	−0.0609768	−	0.998139i	$-0.519422\pi$
$599$	−2.98475	−0.121954	−0.0609768	+	0.998139i	$0.519422\pi$
$600$	89.3644	3.64829
$601$	40.8685	1.66706	0.833530	−	0.552475i	$-0.186317\pi$
$601$	40.8685	1.66706	0.833530	+	0.552475i	$0.186317\pi$
$602$	−4.04064	−0.164684
$603$	34.8945	1.42101
$604$	78.5362	3.19559
$605$	1.50705	0.0612702
$606$	36.4878	1.48222
$607$	27.4864	1.11564	0.557819	−	0.829963i	$-0.311639\pi$
$607$	27.4864	1.11564	0.557819	+	0.829963i	$0.311639\pi$
$608$	89.6722	3.63669
$609$	−7.60085	−0.308002
$610$	11.6589	0.472055
$611$	−2.28433	−0.0924143
$612$	0.762777	0.0308334
$613$	−10.9754	−0.443292	−0.221646	−	0.975127i	$-0.571143\pi$
$613$	−10.9754	−0.443292	−0.221646	+	0.975127i	$0.571143\pi$
$614$	−69.5361	−2.80625
$615$	−12.6414	−0.509752
$616$	28.4999	1.14829
$617$	32.0939	1.29205	0.646025	−	0.763316i	$-0.276430\pi$
$617$	32.0939	1.29205	0.646025	+	0.763316i	$0.276430\pi$
$618$	72.3893	2.91192
$619$	−5.58229	−0.224371	−0.112186	−	0.993687i	$-0.535785\pi$
$619$	−5.58229	−0.224371	−0.112186	+	0.993687i	$0.535785\pi$
$620$	6.76108	0.271532
$621$	2.94340	0.118114
$622$	−72.6678	−2.91371
$623$	16.7974	0.672975
$624$	35.7582	1.43148
$625$	18.2266	0.729064
$626$	−58.6583	−2.34446
$627$	66.8969	2.67161
$628$	80.0009	3.19238
$629$	0.458382	0.0182769
$630$	−6.23981	−0.248600
$631$	8.29519	0.330226	0.165113	−	0.986275i	$-0.447201\pi$
$631$	8.29519	0.330226	0.165113	+	0.986275i	$0.447201\pi$
$632$	22.1996	0.883054
$633$	−32.2199	−1.28063
$634$	−64.1623	−2.54821
$635$	−12.8861	−0.511367
$636$	−74.7918	−2.96569
$637$	−7.96579	−0.315616
$638$	−28.4354	−1.12577
$639$	−30.2409	−1.19631
$640$	−3.65210	−0.144362
$641$	−18.5963	−0.734511	−0.367255	−	0.930120i	$-0.619702\pi$
$641$	−18.5963	−0.734511	−0.367255	+	0.930120i	$0.619702\pi$
$642$	−63.3178	−2.49895
$643$	26.8368	1.05834	0.529170	−	0.848516i	$-0.322503\pi$
$643$	26.8368	1.05834	0.529170	+	0.848516i	$0.322503\pi$
$644$	13.3016	0.524155
$645$	2.63026	0.103566
$646$	0.858254	0.0337675
$647$	37.1462	1.46037	0.730185	−	0.683250i	$-0.239434\pi$
$647$	37.1462	1.46037	0.730185	+	0.683250i	$0.239434\pi$
$648$	58.2980	2.29016
$649$	41.9587	1.64702
$650$	15.9160	0.624279
$651$	5.12555	0.200886
$652$	−32.8208	−1.28536
$653$	−38.8364	−1.51979	−0.759893	−	0.650049i	$-0.774748\pi$
$653$	−38.8364	−1.51979	−0.759893	+	0.650049i	$0.774748\pi$
$654$	89.3821	3.49512
$655$	−14.5846	−0.569869
$656$	−77.2563	−3.01635
$657$	43.9957	1.71644
$658$	4.56329	0.177896
$659$	13.9961	0.545209	0.272604	−	0.962126i	$-0.412115\pi$
$659$	13.9961	0.545209	0.272604	+	0.962126i	$0.412115\pi$
$660$	−31.1397	−1.21211
$661$	36.7047	1.42765	0.713824	−	0.700325i	$-0.246962\pi$
$661$	36.7047	1.42765	0.713824	+	0.700325i	$0.246962\pi$
$662$	−70.4604	−2.73852
$663$	0.151611	0.00588808
$664$	−84.1120	−3.26418
$665$	−4.99977	−0.193883
$666$	−92.5021	−3.58438
$667$	−7.90670	−0.306149
$668$	−111.594	−4.31771
$669$	37.5672	1.45243
$670$	−18.2761	−0.706069
$671$	23.5472	0.909029
$672$	−31.6440	−1.22069
$673$	−6.67149	−0.257167	−0.128584	−	0.991699i	$-0.541043\pi$
$673$	−6.67149	−0.257167	−0.128584	+	0.991699i	$0.541043\pi$
$674$	53.3597	2.05534
$675$	−5.01026	−0.192845
$676$	−55.5437	−2.13630
$677$	−1.48251	−0.0569774	−0.0284887	−	0.999594i	$-0.509069\pi$
$677$	−1.48251	−0.0569774	−0.0284887	+	0.999594i	$0.509069\pi$
$678$	18.6068	0.714591
$679$	3.78597	0.145292
$680$	−0.238013	−0.00912738
$681$	−31.7915	−1.21825
$682$	19.1751	0.734252
$683$	24.0333	0.919610	0.459805	−	0.888020i	$-0.347919\pi$
$683$	24.0333	0.919610	0.459805	+	0.888020i	$0.347919\pi$
$684$	−123.339	−4.71598
$685$	0.0168894	0.000645311 0
$686$	34.5361	1.31859
$687$	60.4201	2.30517
$688$	16.0744	0.612832
$689$	−7.93598	−0.302337
$690$	−12.1588	−0.462877
$691$	−18.5576	−0.705966	−0.352983	−	0.935630i	$-0.614833\pi$
$691$	−18.5576	−0.705966	−0.352983	+	0.935630i	$0.614833\pi$
$692$	−21.5884	−0.820669
$693$	−12.6024	−0.478725
$694$	−13.6022	−0.516331
$695$	14.2526	0.540634
$696$	58.5080	2.21774
$697$	−0.327558	−0.0124071
$698$	43.1330	1.63261
$699$	−64.0579	−2.42289
$700$	−22.6420	−0.855786
$701$	−20.5575	−0.776446	−0.388223	−	0.921565i	$-0.626911\pi$
$701$	−20.5575	−0.776446	−0.388223	+	0.921565i	$0.626911\pi$
$702$	−3.87918	−0.146410
$703$	−74.1192	−2.79546
$704$	−41.4546	−1.56238
$705$	−2.97048	−0.111875
$706$	−56.7800	−2.13694
$707$	−5.50775	−0.207140
$708$	−144.911	−5.44610
$709$	−19.0495	−0.715419	−0.357709	−	0.933833i	$-0.616442\pi$
$709$	−19.0495	−0.715419	−0.357709	+	0.933833i	$0.616442\pi$
$710$	15.8388	0.594420
$711$	−9.81648	−0.368147
$712$	−129.299	−4.84570
$713$	5.33180	0.199677
$714$	−0.302865	−0.0113344
$715$	−3.30416	−0.123569
$716$	−6.48486	−0.242350
$717$	−14.3211	−0.534832
$718$	−41.1154	−1.53441
$719$	39.3691	1.46822	0.734110	−	0.679031i	$-0.237600\pi$
$719$	39.3691	1.46822	0.734110	+	0.679031i	$0.237600\pi$
$720$	24.8231	0.925103
$721$	−10.9270	−0.406942
$722$	−88.6965	−3.30094
$723$	69.5440	2.58637
$724$	−103.448	−3.84463
$725$	13.4588	0.499848
$726$	−14.7614	−0.547848
$727$	−25.5103	−0.946125	−0.473062	−	0.881029i	$-0.656851\pi$
$727$	−25.5103	−0.946125	−0.473062	+	0.881029i	$0.656851\pi$
$728$	−10.4441	−0.387083
$729$	−34.1889	−1.26626
$730$	−23.0429	−0.852856
$731$	0.0681538	0.00252076
$732$	−81.3242	−3.00583
$733$	42.5715	1.57242	0.786208	−	0.617962i	$-0.212042\pi$
$733$	42.5715	1.57242	0.786208	+	0.617962i	$0.212042\pi$
$734$	−26.7456	−0.987199
$735$	−10.3585	−0.382078
$736$	−32.9173	−1.21335
$737$	−36.9119	−1.35967
$738$	66.1016	2.43323
$739$	−28.5898	−1.05169	−0.525847	−	0.850579i	$-0.676252\pi$
$739$	−28.5898	−1.05169	−0.525847	+	0.850579i	$0.676252\pi$
$740$	34.5016	1.26830
$741$	−24.5151	−0.900584
$742$	15.8533	0.581992
$743$	−7.84854	−0.287935	−0.143967	−	0.989582i	$-0.545986\pi$
$743$	−7.84854	−0.287935	−0.143967	+	0.989582i	$0.545986\pi$
$744$	−39.4543	−1.44646
$745$	−6.83081	−0.250261
$746$	0.771466	0.0282454
$747$	37.1936	1.36084
$748$	−0.806875	−0.0295023
$749$	9.55766	0.349229
$750$	43.5209	1.58916
$751$	26.4407	0.964835	0.482417	−	0.875941i	$-0.339759\pi$
$751$	26.4407	0.964835	0.482417	+	0.875941i	$0.339759\pi$
$752$	−18.1536	−0.661995
$753$	−20.3936	−0.743185
$754$	10.4204	0.379490
$755$	10.8364	0.394376
$756$	5.51847	0.200705
$757$	−9.58514	−0.348378	−0.174189	−	0.984712i	$-0.555730\pi$
$757$	−9.58514	−0.348378	−0.174189	+	0.984712i	$0.555730\pi$
$758$	−18.3256	−0.665618
$759$	−24.5568	−0.891357
$760$	38.4861	1.39604
$761$	−10.9750	−0.397844	−0.198922	−	0.980015i	$-0.563744\pi$
$761$	−10.9750	−0.397844	−0.198922	+	0.980015i	$0.563744\pi$
$762$	126.218	4.57240
$763$	−13.4920	−0.488443
$764$	−122.676	−4.43827
$765$	0.105247	0.00380522
$766$	−68.0208	−2.45769
$767$	−15.3762	−0.555202
$768$	−22.1021	−0.797542
$769$	−38.1702	−1.37645	−0.688226	−	0.725496i	$-0.741610\pi$
$769$	−38.1702	−1.37645	−0.688226	+	0.725496i	$0.741610\pi$
$770$	6.60055	0.237867
$771$	−24.9206	−0.897492
$772$	−97.3731	−3.50453
$773$	−28.8271	−1.03684	−0.518419	−	0.855127i	$-0.673479\pi$
$773$	−28.8271	−1.03684	−0.518419	+	0.855127i	$0.673479\pi$
$774$	−13.7535	−0.494360
$775$	−9.07580	−0.326012
$776$	−29.1428	−1.04617
$777$	26.1556	0.938325
$778$	39.0160	1.39879
$779$	52.9652	1.89768
$780$	11.4115	0.408597
$781$	31.9893	1.14467
$782$	−0.315052	−0.0112662
$783$	−3.28028	−0.117228
$784$	−63.3043	−2.26087
$785$	11.0385	0.393979
$786$	142.856	5.09549
$787$	−32.1460	−1.14588	−0.572940	−	0.819597i	$-0.694197\pi$
$787$	−32.1460	−1.14588	−0.572940	+	0.819597i	$0.694197\pi$
$788$	22.2783	0.793631
$789$	−10.6757	−0.380067
$790$	5.14142	0.182923
$791$	−2.80866	−0.0998643
$792$	97.0078	3.44702
$793$	−8.62911	−0.306429
$794$	−13.7358	−0.487464
$795$	−10.3197	−0.366002
$796$	80.9501	2.86920
$797$	−34.3482	−1.21668	−0.608338	−	0.793678i	$-0.708163\pi$
$797$	−34.3482	−1.21668	−0.608338	+	0.793678i	$0.708163\pi$
$798$	48.9725	1.73361
$799$	−0.0769694	−0.00272298
$800$	56.0319	1.98103
$801$	57.1751	2.02018
$802$	−16.5898	−0.585806
$803$	−46.5392	−1.64233
$804$	127.481	4.49592
$805$	1.83534	0.0646872
$806$	−7.02691	−0.247512
$807$	20.4910	0.721316
$808$	42.3963	1.49150
$809$	−23.2168	−0.816258	−0.408129	−	0.912924i	$-0.633819\pi$
$809$	−23.2168	−0.816258	−0.408129	+	0.912924i	$0.633819\pi$
$810$	13.5018	0.474404
$811$	−8.27505	−0.290576	−0.145288	−	0.989389i	$-0.546411\pi$
$811$	−8.27505	−0.290576	−0.145288	+	0.989389i	$0.546411\pi$
$812$	−14.8240	−0.520220
$813$	−68.9666	−2.41877
$814$	97.8499	3.42964
$815$	−4.52858	−0.158629
$816$	1.20485	0.0421783
$817$	−11.0203	−0.385551
$818$	−15.9981	−0.559362
$819$	4.61828	0.161376
$820$	−24.6547	−0.860980
$821$	−18.4036	−0.642289	−0.321144	−	0.947030i	$-0.604067\pi$
$821$	−18.4036	−0.642289	−0.321144	+	0.947030i	$0.604067\pi$
$822$	−0.165431	−0.00577006
$823$	9.94487	0.346656	0.173328	−	0.984864i	$-0.444548\pi$
$823$	9.94487	0.346656	0.173328	+	0.984864i	$0.444548\pi$
$824$	84.1111	2.93015
$825$	41.8007	1.45531
$826$	30.7162	1.06875
$827$	46.9834	1.63377	0.816886	−	0.576799i	$-0.195698\pi$
$827$	46.9834	1.63377	0.816886	+	0.576799i	$0.195698\pi$
$828$	45.2759	1.57344
$829$	−22.5066	−0.781687	−0.390844	−	0.920457i	$-0.627817\pi$
$829$	−22.5066	−0.781687	−0.390844	+	0.920457i	$0.627817\pi$
$830$	−19.4803	−0.676170
$831$	−74.9510	−2.60002
$832$	15.1915	0.526670
$833$	−0.268403	−0.00929961
$834$	−139.604	−4.83409
$835$	−15.3977	−0.532858
$836$	130.470	4.51239
$837$	2.21202	0.0764587
$838$	−71.6882	−2.47643
$839$	−42.2521	−1.45870	−0.729352	−	0.684138i	$-0.760178\pi$
$839$	−42.2521	−1.45870	−0.729352	+	0.684138i	$0.760178\pi$
$840$	−13.5812	−0.468595
$841$	−20.1883	−0.696150
$842$	40.0345	1.37968
$843$	−58.5738	−2.01739
$844$	−62.8387	−2.16300
$845$	−7.66387	−0.263645
$846$	15.5325	0.534019
$847$	2.22820	0.0765619
$848$	−63.0674	−2.16574
$849$	45.6053	1.56517
$850$	0.536282	0.0183943
$851$	27.2080	0.932679
$852$	−110.480	−3.78499
$853$	−15.3673	−0.526168	−0.263084	−	0.964773i	$-0.584740\pi$
$853$	−15.3673	−0.526168	−0.263084	+	0.964773i	$0.584740\pi$
$854$	17.2379	0.589869
$855$	−17.0182	−0.582010
$856$	−73.5707	−2.51460
$857$	−17.2880	−0.590548	−0.295274	−	0.955413i	$-0.595411\pi$
$857$	−17.2880	−0.590548	−0.295274	+	0.955413i	$0.595411\pi$
$858$	32.3641	1.10489
$859$	18.2167	0.621545	0.310772	−	0.950484i	$-0.399412\pi$
$859$	18.2167	0.621545	0.310772	+	0.950484i	$0.399412\pi$
$860$	5.12981	0.174925
$861$	−18.6906	−0.636975
$862$	−49.5979	−1.68931
$863$	10.8939	0.370831	0.185416	−	0.982660i	$-0.440637\pi$
$863$	10.8939	0.370831	0.185416	+	0.982660i	$0.440637\pi$
$864$	−13.6565	−0.464604
$865$	−2.97875	−0.101281
$866$	−22.9619	−0.780277
$867$	−43.1213	−1.46448
$868$	9.99641	0.339300
$869$	10.3840	0.352253
$870$	13.5504	0.459403
$871$	13.5268	0.458336
$872$	103.856	3.51699
$873$	12.8867	0.436148
$874$	50.9430	1.72317
$875$	−6.56937	−0.222085
$876$	160.731	5.43060
$877$	6.73072	0.227280	0.113640	−	0.993522i	$-0.463749\pi$
$877$	6.73072	0.227280	0.113640	+	0.993522i	$0.463749\pi$
$878$	−7.18170	−0.242371
$879$	−59.0464	−1.99159
$880$	−26.2582	−0.885165
$881$	48.1922	1.62364	0.811818	−	0.583910i	$-0.198478\pi$
$881$	48.1922	1.62364	0.811818	+	0.583910i	$0.198478\pi$
$882$	54.1641	1.82380
$883$	−11.8864	−0.400009	−0.200004	−	0.979795i	$-0.564096\pi$
$883$	−11.8864	−0.400009	−0.200004	+	0.979795i	$0.564096\pi$
$884$	0.295688	0.00994506
$885$	−19.9948	−0.672116
$886$	63.0798	2.11921
$887$	19.7880	0.664414	0.332207	−	0.943206i	$-0.392207\pi$
$887$	19.7880	0.664414	0.332207	+	0.943206i	$0.392207\pi$
$888$	−201.334	−6.75633
$889$	−19.0523	−0.638994
$890$	−29.9457	−1.00378
$891$	27.2692	0.913553
$892$	73.2676	2.45318
$893$	12.4457	0.416481
$894$	66.9073	2.23772
$895$	−0.894775	−0.0299090
$896$	−5.39971	−0.180392
$897$	8.99911	0.300472
$898$	−80.1753	−2.67548
$899$	−5.94205	−0.198178
$900$	−77.0687	−2.56896
$901$	−0.267399	−0.00890834
$902$	−69.9231	−2.32819
$903$	3.88889	0.129414
$904$	21.6198	0.719064
$905$	−14.2737	−0.474475
$906$	−106.142	−3.52632
$907$	−23.1333	−0.768129	−0.384064	−	0.923306i	$-0.625476\pi$
$907$	−23.1333	−0.768129	−0.384064	+	0.923306i	$0.625476\pi$
$908$	−62.0031	−2.05765
$909$	−18.7473	−0.621807
$910$	−2.41884	−0.0801838
$911$	12.6708	0.419802	0.209901	−	0.977723i	$-0.432686\pi$
$911$	12.6708	0.419802	0.209901	+	0.977723i	$0.432686\pi$
$912$	−194.822	−6.45119
$913$	−39.3439	−1.30209
$914$	44.9113	1.48553
$915$	−11.2210	−0.370956
$916$	117.838	3.89347
$917$	−21.5637	−0.712096
$918$	−0.130707	−0.00431397
$919$	−31.6063	−1.04260	−0.521298	−	0.853375i	$-0.674552\pi$
$919$	−31.6063	−1.04260	−0.521298	+	0.853375i	$0.674552\pi$
$920$	−14.1276	−0.465775
$921$	66.9247	2.20524
$922$	−9.29435	−0.306093
$923$	−11.7228	−0.385861
$924$	−46.0408	−1.51463
$925$	−46.3136	−1.52278
$926$	52.5255	1.72610
$927$	−37.1932	−1.22159
$928$	36.6848	1.20424
$929$	−22.3862	−0.734467	−0.367233	−	0.930129i	$-0.619695\pi$
$929$	−22.3862	−0.734467	−0.367233	+	0.930129i	$0.619695\pi$
$930$	−9.13759	−0.299633
$931$	43.4001	1.42238
$932$	−124.933	−4.09230
$933$	69.9388	2.28969
$934$	−66.7627	−2.18454
$935$	−0.111332	−0.00364094
$936$	−35.5495	−1.16197
$937$	10.1721	0.332309	0.166154	−	0.986100i	$-0.446865\pi$
$937$	10.1721	0.332309	0.166154	+	0.986100i	$0.446865\pi$
$938$	−27.0217	−0.882289
$939$	56.4554	1.84235
$940$	−5.79335	−0.188958
$941$	42.5080	1.38572	0.692860	−	0.721072i	$-0.256350\pi$
$941$	42.5080	1.38572	0.692860	+	0.721072i	$0.256350\pi$
$942$	−108.121	−3.52277
$943$	−19.4427	−0.633142
$944$	−122.195	−3.97710
$945$	0.761434	0.0247695
$946$	14.5487	0.473017
$947$	24.0906	0.782839	0.391420	−	0.920212i	$-0.371984\pi$
$947$	24.0906	0.782839	0.391420	+	0.920212i	$0.371984\pi$
$948$	−35.8629	−1.16477
$949$	17.0548	0.553622
$950$	−86.7154	−2.81342
$951$	61.7527	2.00247
$952$	−0.351907	−0.0114054
$953$	5.40062	0.174943	0.0874716	−	0.996167i	$-0.472121\pi$
$953$	5.40062	0.174943	0.0874716	+	0.996167i	$0.472121\pi$
$954$	53.9614	1.74706
$955$	−16.9268	−0.547737
$956$	−27.9306	−0.903340
$957$	27.3675	0.884665
$958$	32.6407	1.05457
$959$	0.0249714	0.000806367 0
$960$	19.7545	0.637575
$961$	−26.9930	−0.870743
$962$	−35.8581	−1.15611
$963$	32.5323	1.04834
$964$	135.632	4.36842
$965$	−13.4355	−0.432503
$966$	−17.9770	−0.578402
$967$	2.79466	0.0898702	0.0449351	−	0.998990i	$-0.485692\pi$
$967$	2.79466	0.0898702	0.0449351	+	0.998990i	$0.485692\pi$
$968$	−17.1517	−0.551277
$969$	−0.826022	−0.0265357
$970$	−6.74945	−0.216712
$971$	−48.9941	−1.57230	−0.786148	−	0.618039i	$-0.787927\pi$
$971$	−48.9941	−1.57230	−0.786148	+	0.618039i	$0.787927\pi$
$972$	−110.581	−3.54689
$973$	21.0728	0.675564
$974$	−64.0977	−2.05382
$975$	−15.3183	−0.490579
$976$	−68.5757	−2.19505
$977$	−16.3492	−0.523058	−0.261529	−	0.965196i	$-0.584227\pi$
$977$	−16.3492	−0.523058	−0.261529	+	0.965196i	$0.584227\pi$
$978$	44.3572	1.41839
$979$	−60.4806	−1.93297
$980$	−20.2022	−0.645336
$981$	−45.9240	−1.46624
$982$	97.7453	3.11918
$983$	−16.1344	−0.514606	−0.257303	−	0.966331i	$-0.582834\pi$
$983$	−16.1344	−0.514606	−0.257303	+	0.966331i	$0.582834\pi$
$984$	143.872	4.58649
$985$	3.07394	0.0979439
$986$	0.351111	0.0111817
$987$	−4.39192	−0.139796
$988$	−47.8120	−1.52110
$989$	4.04538	0.128636
$990$	22.4669	0.714046
$991$	−41.8644	−1.32987	−0.664933	−	0.746903i	$-0.731540\pi$
$991$	−41.8644	−1.32987	−0.664933	+	0.746903i	$0.731540\pi$
$992$	−24.7380	−0.785433
$993$	67.8143	2.15202
$994$	23.4180	0.742775
$995$	11.1694	0.354095
$996$	135.881	4.30554
$997$	10.2544	0.324759	0.162380	−	0.986728i	$-0.448083\pi$
$997$	10.2544	0.324759	0.162380	+	0.986728i	$0.448083\pi$
$998$	101.172	3.20256
$999$	11.2879	0.357133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.14	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.14	✓	237	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63584 q^{2} +2.53685 q^{3} +4.94764 q^{4} +0.682671 q^{5} -6.68672 q^{6} +1.00934 q^{7} -7.76949 q^{8} +3.43560 q^{9} +O(q^{10})\)	\(q-2.63584 q^{2} +2.53685 q^{3} +4.94764 q^{4} +0.682671 q^{5} -6.68672 q^{6} +1.00934 q^{7} -7.76949 q^{8} +3.43560 q^{9} -1.79941 q^{10} -3.63422 q^{11} +12.5514 q^{12} +1.33180 q^{13} -2.66046 q^{14} +1.73183 q^{15} +10.5838 q^{16} +0.0448742 q^{17} -9.05568 q^{18} -7.25605 q^{19} +3.37761 q^{20} +2.56055 q^{21} +9.57922 q^{22} +2.66358 q^{23} -19.7100 q^{24} -4.53396 q^{25} -3.51041 q^{26} +1.10505 q^{27} +4.99386 q^{28} -2.96844 q^{29} -4.56483 q^{30} +2.00174 q^{31} -12.3583 q^{32} -9.21947 q^{33} -0.118281 q^{34} +0.689049 q^{35} +16.9981 q^{36} +10.2148 q^{37} +19.1258 q^{38} +3.37857 q^{39} -5.30400 q^{40} -7.29946 q^{41} -6.74919 q^{42} +1.51877 q^{43} -17.9808 q^{44} +2.34538 q^{45} -7.02077 q^{46} -1.71522 q^{47} +26.8496 q^{48} -5.98123 q^{49} +11.9508 q^{50} +0.113839 q^{51} +6.58926 q^{52} -5.95884 q^{53} -2.91273 q^{54} -2.48098 q^{55} -7.84208 q^{56} -18.4075 q^{57} +7.82433 q^{58} -11.5454 q^{59} +8.56847 q^{60} -6.47929 q^{61} -5.27626 q^{62} +3.46770 q^{63} +11.4067 q^{64} +0.909180 q^{65} +24.3010 q^{66} +10.1567 q^{67} +0.222021 q^{68} +6.75711 q^{69} -1.81622 q^{70} -8.80223 q^{71} -26.6928 q^{72} +12.8058 q^{73} -26.9246 q^{74} -11.5020 q^{75} -35.9003 q^{76} -3.66818 q^{77} -8.90537 q^{78} -2.85728 q^{79} +7.22527 q^{80} -7.50345 q^{81} +19.2402 q^{82} +10.8259 q^{83} +12.6687 q^{84} +0.0306343 q^{85} -4.00324 q^{86} -7.53049 q^{87} +28.2360 q^{88} +16.6420 q^{89} -6.18205 q^{90} +1.34424 q^{91} +13.1784 q^{92} +5.07811 q^{93} +4.52105 q^{94} -4.95349 q^{95} -31.3511 q^{96} +3.75093 q^{97} +15.7655 q^{98} -12.4857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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