LMFDB - Embedded newform 6011.2.a.f.1.14

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:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.61605 q^{2} -0.908380 q^{3} +4.84374 q^{4} -1.38921 q^{5} +2.37637 q^{6} +2.01973 q^{7} -7.43937 q^{8} -2.17484 q^{9} +O(q^{10})$	\(q-2.61605 q^{2} -0.908380 q^{3} +4.84374 q^{4} -1.38921 q^{5} +2.37637 q^{6} +2.01973 q^{7} -7.43937 q^{8} -2.17484 q^{9} +3.63425 q^{10} -3.10444 q^{11} -4.39996 q^{12} +6.92822 q^{13} -5.28372 q^{14} +1.26193 q^{15} +9.77431 q^{16} -1.38446 q^{17} +5.68951 q^{18} -6.85939 q^{19} -6.72897 q^{20} -1.83468 q^{21} +8.12138 q^{22} -5.18663 q^{23} +6.75778 q^{24} -3.07009 q^{25} -18.1246 q^{26} +4.70073 q^{27} +9.78305 q^{28} +4.77374 q^{29} -3.30128 q^{30} +1.48072 q^{31} -10.6914 q^{32} +2.82001 q^{33} +3.62183 q^{34} -2.80583 q^{35} -10.5344 q^{36} +1.06338 q^{37} +17.9445 q^{38} -6.29346 q^{39} +10.3349 q^{40} -7.51569 q^{41} +4.79963 q^{42} -2.10462 q^{43} -15.0371 q^{44} +3.02132 q^{45} +13.5685 q^{46} -5.65750 q^{47} -8.87880 q^{48} -2.92069 q^{49} +8.03153 q^{50} +1.25762 q^{51} +33.5585 q^{52} +7.02284 q^{53} -12.2974 q^{54} +4.31272 q^{55} -15.0255 q^{56} +6.23093 q^{57} -12.4884 q^{58} -11.3644 q^{59} +6.11247 q^{60} +8.72258 q^{61} -3.87364 q^{62} -4.39260 q^{63} +8.42063 q^{64} -9.62476 q^{65} -7.37730 q^{66} -15.5722 q^{67} -6.70597 q^{68} +4.71143 q^{69} +7.34021 q^{70} +6.41118 q^{71} +16.1795 q^{72} +8.59609 q^{73} -2.78186 q^{74} +2.78881 q^{75} -33.2251 q^{76} -6.27013 q^{77} +16.4640 q^{78} +0.922615 q^{79} -13.5786 q^{80} +2.25449 q^{81} +19.6615 q^{82} +12.1081 q^{83} -8.88673 q^{84} +1.92331 q^{85} +5.50580 q^{86} -4.33637 q^{87} +23.0951 q^{88} +0.971268 q^{89} -7.90393 q^{90} +13.9931 q^{91} -25.1227 q^{92} -1.34506 q^{93} +14.8003 q^{94} +9.52914 q^{95} +9.71185 q^{96} +19.1610 q^{97} +7.64067 q^{98} +6.75167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.61605	−1.84983	−0.924915	−	0.380175i	$-0.875864\pi$
$2$	−2.61605	−1.84983	−0.924915	+	0.380175i	$0.875864\pi$
$3$	−0.908380	−0.524454	−0.262227	−	0.965006i	$-0.584457\pi$
$3$	−0.908380	−0.524454	−0.262227	+	0.965006i	$0.584457\pi$
$4$	4.84374	2.42187
$5$	−1.38921	−0.621274	−0.310637	−	0.950529i	$-0.600542\pi$
$5$	−1.38921	−0.621274	−0.310637	+	0.950529i	$0.600542\pi$
$6$	2.37637	0.970150
$7$	2.01973	0.763387	0.381693	−	0.924289i	$-0.375341\pi$
$7$	2.01973	0.763387	0.381693	+	0.924289i	$0.375341\pi$
$8$	−7.43937	−2.63021
$9$	−2.17484	−0.724948
$10$	3.63425	1.14925
$11$	−3.10444	−0.936024	−0.468012	−	0.883722i	$-0.655030\pi$
$11$	−3.10444	−0.936024	−0.468012	+	0.883722i	$0.655030\pi$
$12$	−4.39996	−1.27016
$13$	6.92822	1.92154	0.960772	−	0.277341i	$-0.0894530\pi$
$13$	6.92822	1.92154	0.960772	+	0.277341i	$0.0894530\pi$
$14$	−5.28372	−1.41213
$15$	1.26193	0.325829
$16$	9.77431	2.44358
$17$	−1.38446	−0.335782	−0.167891	−	0.985806i	$-0.553696\pi$
$17$	−1.38446	−0.335782	−0.167891	+	0.985806i	$0.553696\pi$
$18$	5.68951	1.34103
$19$	−6.85939	−1.57365	−0.786826	−	0.617175i	$-0.788277\pi$
$19$	−6.85939	−1.57365	−0.786826	+	0.617175i	$0.788277\pi$
$20$	−6.72897	−1.50464
$21$	−1.83468	−0.400361
$22$	8.12138	1.73148
$23$	−5.18663	−1.08149	−0.540744	−	0.841187i	$-0.681857\pi$
$23$	−5.18663	−1.08149	−0.540744	+	0.841187i	$0.681857\pi$
$24$	6.75778	1.37943
$25$	−3.07009	−0.614019
$26$	−18.1246	−3.55453
$27$	4.70073	0.904656
$28$	9.78305	1.84882
$29$	4.77374	0.886461	0.443230	−	0.896408i	$-0.353832\pi$
$29$	4.77374	0.886461	0.443230	+	0.896408i	$0.353832\pi$
$30$	−3.30128	−0.602729
$31$	1.48072	0.265945	0.132972	−	0.991120i	$-0.457548\pi$
$31$	1.48072	0.265945	0.132972	+	0.991120i	$0.457548\pi$
$32$	−10.6914	−1.88999
$33$	2.82001	0.490901
$34$	3.62183	0.621139
$35$	−2.80583	−0.474272
$36$	−10.5344	−1.75573
$37$	1.06338	0.174819	0.0874093	−	0.996172i	$-0.472141\pi$
$37$	1.06338	0.174819	0.0874093	+	0.996172i	$0.472141\pi$
$38$	17.9445	2.91099
$39$	−6.29346	−1.00776
$40$	10.3349	1.63408
$41$	−7.51569	−1.17375	−0.586877	−	0.809676i	$-0.699643\pi$
$41$	−7.51569	−1.17375	−0.586877	+	0.809676i	$0.699643\pi$
$42$	4.79963	0.740599
$43$	−2.10462	−0.320952	−0.160476	−	0.987040i	$-0.551303\pi$
$43$	−2.10462	−0.320952	−0.160476	+	0.987040i	$0.551303\pi$
$44$	−15.0371	−2.26693
$45$	3.02132	0.450392
$46$	13.5685	2.00057
$47$	−5.65750	−0.825231	−0.412616	−	0.910905i	$-0.635385\pi$
$47$	−5.65750	−0.825231	−0.412616	+	0.910905i	$0.635385\pi$
$48$	−8.87880	−1.28154
$49$	−2.92069	−0.417241
$50$	8.03153	1.13583
$51$	1.25762	0.176102
$52$	33.5585	4.65373
$53$	7.02284	0.964661	0.482331	−	0.875989i	$-0.339790\pi$
$53$	7.02284	0.964661	0.482331	+	0.875989i	$0.339790\pi$
$54$	−12.2974	−1.67346
$55$	4.31272	0.581527
$56$	−15.0255	−2.00787
$57$	6.23093	0.825307
$58$	−12.4884	−1.63980
$59$	−11.3644	−1.47952	−0.739760	−	0.672871i	$-0.765061\pi$
$59$	−11.3644	−1.47952	−0.739760	+	0.672871i	$0.765061\pi$
$60$	6.11247	0.789116
$61$	8.72258	1.11681	0.558406	−	0.829568i	$-0.311413\pi$
$61$	8.72258	1.11681	0.558406	+	0.829568i	$0.311413\pi$
$62$	−3.87364	−0.491952
$63$	−4.39260	−0.553416
$64$	8.42063	1.05258
$65$	−9.62476	−1.19381
$66$	−7.37730	−0.908083
$67$	−15.5722	−1.90244	−0.951222	−	0.308507i	$-0.900171\pi$
$67$	−15.5722	−1.90244	−0.951222	+	0.308507i	$0.900171\pi$
$68$	−6.70597	−0.813219
$69$	4.71143	0.567190
$70$	7.34021	0.877323
$71$	6.41118	0.760867	0.380434	−	0.924808i	$-0.375775\pi$
$71$	6.41118	0.760867	0.380434	+	0.924808i	$0.375775\pi$
$72$	16.1795	1.90677
$73$	8.59609	1.00610	0.503048	−	0.864258i	$-0.332212\pi$
$73$	8.59609	1.00610	0.503048	+	0.864258i	$0.332212\pi$
$74$	−2.78186	−0.323385
$75$	2.78881	0.322024
$76$	−33.2251	−3.81118
$77$	−6.27013	−0.714548
$78$	16.4640	1.86419
$79$	0.922615	0.103802	0.0519012	−	0.998652i	$-0.483472\pi$
$79$	0.922615	0.103802	0.0519012	+	0.998652i	$0.483472\pi$
$80$	−13.5786	−1.51813
$81$	2.25449	0.250498
$82$	19.6615	2.17125
$83$	12.1081	1.32904	0.664519	−	0.747271i	$-0.268636\pi$
$83$	12.1081	1.32904	0.664519	+	0.747271i	$0.268636\pi$
$84$	−8.88673	−0.969622
$85$	1.92331	0.208612
$86$	5.50580	0.593706
$87$	−4.33637	−0.464908
$88$	23.0951	2.46194
$89$	0.971268	0.102954	0.0514771	−	0.998674i	$-0.483607\pi$
$89$	0.971268	0.102954	0.0514771	+	0.998674i	$0.483607\pi$
$90$	−7.90393	−0.833148
$91$	13.9931	1.46688
$92$	−25.1227	−2.61922
$93$	−1.34506	−0.139476
$94$	14.8003	1.52654
$95$	9.52914	0.977669
$96$	9.71185	0.991212
$97$	19.1610	1.94551	0.972753	−	0.231843i	$-0.0744756\pi$
$97$	19.1610	1.94551	0.972753	+	0.231843i	$0.0744756\pi$
$98$	7.64067	0.771824
$99$	6.75167	0.678569
$100$	−14.8707	−1.48707
$101$	−10.3050	−1.02538	−0.512691	−	0.858573i	$-0.671351\pi$
$101$	−10.3050	−1.02538	−0.512691	+	0.858573i	$0.671351\pi$
$102$	−3.29000	−0.325758
$103$	−5.12808	−0.505285	−0.252643	−	0.967560i	$-0.581300\pi$
$103$	−5.12808	−0.505285	−0.252643	+	0.967560i	$0.581300\pi$
$104$	−51.5416	−5.05407
$105$	2.54876	0.248734
$106$	−18.3721	−1.78446
$107$	−9.64330	−0.932253	−0.466127	−	0.884718i	$-0.654351\pi$
$107$	−9.64330	−0.932253	−0.466127	+	0.884718i	$0.654351\pi$
$108$	22.7691	2.19096
$109$	−15.6965	−1.50345	−0.751727	−	0.659475i	$-0.770779\pi$
$109$	−15.6965	−1.50345	−0.751727	+	0.659475i	$0.770779\pi$
$110$	−11.2823	−1.07573
$111$	−0.965954	−0.0916843
$112$	19.7415	1.86539
$113$	−13.4779	−1.26789	−0.633947	−	0.773376i	$-0.718566\pi$
$113$	−13.4779	−1.26789	−0.633947	+	0.773376i	$0.718566\pi$
$114$	−16.3005	−1.52668
$115$	7.20533	0.671900
$116$	23.1227	2.14689
$117$	−15.0678	−1.39302
$118$	29.7299	2.73686
$119$	−2.79624	−0.256331
$120$	−9.38798	−0.857001
$121$	−1.36246	−0.123860
$122$	−22.8187	−2.06591
$123$	6.82711	0.615580
$124$	7.17221	0.644083
$125$	11.2111	1.00275
$126$	11.4913	1.02372
$127$	−6.92131	−0.614167	−0.307083	−	0.951683i	$-0.599353\pi$
$127$	−6.92131	−0.614167	−0.307083	+	0.951683i	$0.599353\pi$
$128$	−0.646031	−0.0571016
$129$	1.91180	0.168324
$130$	25.1789	2.20834
$131$	10.9408	0.955900	0.477950	−	0.878387i	$-0.341380\pi$
$131$	10.9408	0.955900	0.477950	+	0.878387i	$0.341380\pi$
$132$	13.6594	1.18890
$133$	−13.8541	−1.20130
$134$	40.7377	3.51920
$135$	−6.53030	−0.562039
$136$	10.2995	0.883177
$137$	17.6981	1.51205	0.756025	−	0.654543i	$-0.227139\pi$
$137$	17.6981	1.51205	0.756025	+	0.654543i	$0.227139\pi$
$138$	−12.3254	−1.04920
$139$	−15.6139	−1.32436	−0.662178	−	0.749347i	$-0.730368\pi$
$139$	−15.6139	−1.32436	−0.662178	+	0.749347i	$0.730368\pi$
$140$	−13.5907	−1.14863
$141$	5.13916	0.432796
$142$	−16.7720	−1.40747
$143$	−21.5082	−1.79861
$144$	−21.2576	−1.77147
$145$	−6.63173	−0.550735
$146$	−22.4878	−1.86111
$147$	2.65309	0.218824
$148$	5.15073	0.423388
$149$	−4.49702	−0.368410	−0.184205	−	0.982888i	$-0.558971\pi$
$149$	−4.49702	−0.368410	−0.184205	+	0.982888i	$0.558971\pi$
$150$	−7.29568	−0.595690
$151$	20.0399	1.63082	0.815410	−	0.578883i	$-0.196511\pi$
$151$	20.0399	1.63082	0.815410	+	0.578883i	$0.196511\pi$
$152$	51.0295	4.13904
$153$	3.01099	0.243424
$154$	16.4030	1.32179
$155$	−2.05703	−0.165225
$156$	−30.4839	−2.44066
$157$	15.1413	1.20841	0.604205	−	0.796829i	$-0.293491\pi$
$157$	15.1413	1.20841	0.604205	+	0.796829i	$0.293491\pi$
$158$	−2.41361	−0.192017
$159$	−6.37941	−0.505920
$160$	14.8526	1.17420
$161$	−10.4756	−0.825593
$162$	−5.89785	−0.463379
$163$	−11.6654	−0.913706	−0.456853	−	0.889542i	$-0.651023\pi$
$163$	−11.6654	−0.913706	−0.456853	+	0.889542i	$0.651023\pi$
$164$	−36.4040	−2.84268
$165$	−3.91759	−0.304984
$166$	−31.6755	−2.45849
$167$	17.0335	1.31810	0.659048	−	0.752101i	$-0.270960\pi$
$167$	17.0335	1.31810	0.659048	+	0.752101i	$0.270960\pi$
$168$	13.6489	1.05303
$169$	35.0003	2.69233
$170$	−5.03149	−0.385897
$171$	14.9181	1.14082
$172$	−10.1942	−0.777303
$173$	−7.67764	−0.583720	−0.291860	−	0.956461i	$-0.594274\pi$
$173$	−7.67764	−0.583720	−0.291860	+	0.956461i	$0.594274\pi$
$174$	11.3442	0.860000
$175$	−6.20076	−0.468734
$176$	−30.3438	−2.28725
$177$	10.3232	0.775940
$178$	−2.54089	−0.190448
$179$	−0.0223994	−0.00167421	−0.000837104	−	1.00000i	$-0.500266\pi$
$179$	−0.0223994	−0.00167421	−0.000837104		1.00000i	$0.500266\pi$
$180$	14.6345	1.09079
$181$	26.4258	1.96421	0.982106	−	0.188327i	$-0.0603064\pi$
$181$	26.4258	1.96421	0.982106	+	0.188327i	$0.0603064\pi$
$182$	−36.6068	−2.71348
$183$	−7.92342	−0.585716
$184$	38.5853	2.84454
$185$	−1.47726	−0.108610
$186$	3.51874	0.258006
$187$	4.29798	0.314299
$188$	−27.4034	−1.99860
$189$	9.49421	0.690602
$190$	−24.9287	−1.80852
$191$	−0.0823220	−0.00595661	−0.00297830	−	0.999996i	$-0.500948\pi$
$191$	−0.0823220	−0.00595661	−0.00297830	+	0.999996i	$0.500948\pi$
$192$	−7.64913	−0.552029
$193$	−1.51694	−0.109192	−0.0545959	−	0.998509i	$-0.517387\pi$
$193$	−1.51694	−0.109192	−0.0545959	+	0.998509i	$0.517387\pi$
$194$	−50.1262	−3.59885
$195$	8.74295	0.626096
$196$	−14.1470	−1.01050
$197$	−0.194024	−0.0138236	−0.00691181	−	0.999976i	$-0.502200\pi$
$197$	−0.194024	−0.0138236	−0.00691181	+	0.999976i	$0.502200\pi$
$198$	−17.6627	−1.25524
$199$	0.512178	0.0363073	0.0181537	−	0.999835i	$-0.494221\pi$
$199$	0.512178	0.0363073	0.0181537	+	0.999835i	$0.494221\pi$
$200$	22.8396	1.61500
$201$	14.1455	0.997744
$202$	26.9583	1.89678
$203$	9.64167	0.676712
$204$	6.09158	0.426496
$205$	10.4409	0.729223
$206$	13.4153	0.934691
$207$	11.2801	0.784022
$208$	67.7186	4.69544
$209$	21.2946	1.47298
$210$	−6.66770	−0.460115
$211$	−21.9411	−1.51049	−0.755245	−	0.655443i	$-0.772482\pi$
$211$	−21.9411	−1.51049	−0.755245	+	0.655443i	$0.772482\pi$
$212$	34.0168	2.33628
$213$	−5.82379	−0.399040
$214$	25.2274	1.72451
$215$	2.92376	0.199399
$216$	−34.9704	−2.37944
$217$	2.99065	0.203019
$218$	41.0629	2.78113
$219$	−7.80852	−0.527651
$220$	20.8897	1.40838
$221$	−9.59187	−0.645219
$222$	2.52699	0.169600
$223$	−10.1363	−0.678779	−0.339389	−	0.940646i	$-0.610220\pi$
$223$	−10.1363	−0.678779	−0.339389	+	0.940646i	$0.610220\pi$
$224$	−21.5937	−1.44279
$225$	6.67698	0.445132
$226$	35.2589	2.34539
$227$	−22.0811	−1.46558	−0.732788	−	0.680457i	$-0.761781\pi$
$227$	−22.0811	−1.46558	−0.732788	+	0.680457i	$0.761781\pi$
$228$	30.1810	1.99879
$229$	13.9531	0.922049	0.461024	−	0.887387i	$-0.347482\pi$
$229$	13.9531	0.922049	0.461024	+	0.887387i	$0.347482\pi$
$230$	−18.8495	−1.24290
$231$	5.69567	0.374747
$232$	−35.5136	−2.33158
$233$	−15.8536	−1.03860	−0.519301	−	0.854591i	$-0.673808\pi$
$233$	−15.8536	−1.03860	−0.519301	+	0.854591i	$0.673808\pi$
$234$	39.4182	2.57685
$235$	7.85946	0.512695
$236$	−55.0462	−3.58320
$237$	−0.838086	−0.0544395
$238$	7.31512	0.474169
$239$	−15.7819	−1.02085	−0.510423	−	0.859923i	$-0.670511\pi$
$239$	−15.7819	−1.02085	−0.510423	+	0.859923i	$0.670511\pi$
$240$	12.3345	0.796190
$241$	7.78388	0.501404	0.250702	−	0.968064i	$-0.419339\pi$
$241$	7.78388	0.501404	0.250702	+	0.968064i	$0.419339\pi$
$242$	3.56427	0.229120
$243$	−16.1501	−1.03603
$244$	42.2499	2.70477
$245$	4.05745	0.259221
$246$	−17.8601	−1.13872
$247$	−47.5234	−3.02384
$248$	−11.0156	−0.699492
$249$	−10.9988	−0.697019
$250$	−29.3287	−1.85491
$251$	−12.5416	−0.791617	−0.395808	−	0.918333i	$-0.629536\pi$
$251$	−12.5416	−0.791617	−0.395808	+	0.918333i	$0.629536\pi$
$252$	−21.2766	−1.34030
$253$	16.1016	1.01230
$254$	18.1065	1.13610
$255$	−1.74710	−0.109408
$256$	−15.1512	−0.946950
$257$	9.81532	0.612263	0.306132	−	0.951989i	$-0.400965\pi$
$257$	9.81532	0.612263	0.306132	+	0.951989i	$0.400965\pi$
$258$	−5.00137	−0.311371
$259$	2.14774	0.133454
$260$	−46.6198	−2.89124
$261$	−10.3821	−0.642638
$262$	−28.6216	−1.76825
$263$	19.3929	1.19582	0.597909	−	0.801564i	$-0.295998\pi$
$263$	19.3929	1.19582	0.597909	+	0.801564i	$0.295998\pi$
$264$	−20.9791	−1.29117
$265$	−9.75621	−0.599319
$266$	36.2431	2.22221
$267$	−0.882281	−0.0539947
$268$	−75.4275	−4.60747
$269$	2.77941	0.169463	0.0847317	−	0.996404i	$-0.472997\pi$
$269$	2.77941	0.169463	0.0847317	+	0.996404i	$0.472997\pi$
$270$	17.0836	1.03968
$271$	3.85307	0.234057	0.117029	−	0.993129i	$-0.462663\pi$
$271$	3.85307	0.234057	0.117029	+	0.993129i	$0.462663\pi$
$272$	−13.5322	−0.820509
$273$	−12.7111	−0.769311
$274$	−46.2992	−2.79703
$275$	9.53092	0.574736
$276$	22.8210	1.37366
$277$	−4.99013	−0.299828	−0.149914	−	0.988699i	$-0.547900\pi$
$277$	−4.99013	−0.299828	−0.149914	+	0.988699i	$0.547900\pi$
$278$	40.8469	2.44983
$279$	−3.22033	−0.192796
$280$	20.8736	1.24744
$281$	−2.00913	−0.119855	−0.0599275	−	0.998203i	$-0.519087\pi$
$281$	−2.00913	−0.119855	−0.0599275	+	0.998203i	$0.519087\pi$
$282$	−13.4443	−0.800598
$283$	−9.92704	−0.590101	−0.295051	−	0.955482i	$-0.595337\pi$
$283$	−9.92704	−0.590101	−0.295051	+	0.955482i	$0.595337\pi$
$284$	31.0541	1.84272
$285$	−8.65608	−0.512742
$286$	56.2667	3.32712
$287$	−15.1797	−0.896028
$288$	23.2521	1.37014
$289$	−15.0833	−0.887251
$290$	17.3490	1.01877
$291$	−17.4055	−1.02033
$292$	41.6372	2.43663
$293$	9.53773	0.557200	0.278600	−	0.960407i	$-0.410130\pi$
$293$	9.53773	0.557200	0.278600	+	0.960407i	$0.410130\pi$
$294$	−6.94064	−0.404786
$295$	15.7876	0.919188
$296$	−7.91088	−0.459810
$297$	−14.5931	−0.846779
$298$	11.7644	0.681496
$299$	−35.9341	−2.07813
$300$	13.5083	0.779900
$301$	−4.25077	−0.245010
$302$	−52.4254	−3.01674
$303$	9.36083	0.537766
$304$	−67.0458	−3.84534
$305$	−12.1175	−0.693846
$306$	−7.87692	−0.450293
$307$	−22.3227	−1.27402	−0.637011	−	0.770854i	$-0.719830\pi$
$307$	−22.3227	−1.27402	−0.637011	+	0.770854i	$0.719830\pi$
$308$	−30.3709	−1.73054
$309$	4.65825	0.264999
$310$	5.38130	0.305637
$311$	5.89912	0.334508	0.167254	−	0.985914i	$-0.446510\pi$
$311$	5.89912	0.334508	0.167254	+	0.985914i	$0.446510\pi$
$312$	46.8194	2.65063
$313$	−10.8709	−0.614460	−0.307230	−	0.951635i	$-0.599402\pi$
$313$	−10.8709	−0.614460	−0.307230	+	0.951635i	$0.599402\pi$
$314$	−39.6105	−2.23535
$315$	6.10225	0.343823
$316$	4.46891	0.251396
$317$	−16.6243	−0.933714	−0.466857	−	0.884333i	$-0.654614\pi$
$317$	−16.6243	−0.933714	−0.466857	+	0.884333i	$0.654614\pi$
$318$	16.6889	0.935866
$319$	−14.8198	−0.829748
$320$	−11.6980	−0.653940
$321$	8.75979	0.488924
$322$	27.4047	1.52721
$323$	9.49657	0.528403
$324$	10.9201	0.606674
$325$	−21.2703	−1.17986
$326$	30.5174	1.69020
$327$	14.2584	0.788492
$328$	55.9120	3.08723
$329$	−11.4266	−0.629970
$330$	10.2486	0.564168
$331$	14.9534	0.821914	0.410957	−	0.911655i	$-0.365195\pi$
$331$	14.9534	0.821914	0.410957	+	0.911655i	$0.365195\pi$
$332$	58.6485	3.21876
$333$	−2.31269	−0.126734
$334$	−44.5607	−2.43825
$335$	21.6330	1.18194
$336$	−17.9328	−0.978313
$337$	−13.5200	−0.736483	−0.368242	−	0.929730i	$-0.620040\pi$
$337$	−13.5200	−0.736483	−0.368242	+	0.929730i	$0.620040\pi$
$338$	−91.5626	−4.98035
$339$	12.2431	0.664952
$340$	9.31601	0.505232
$341$	−4.59680	−0.248931
$342$	−39.0266	−2.11032
$343$	−20.0371	−1.08190
$344$	15.6571	0.844172
$345$	−6.54518	−0.352381
$346$	20.0851	1.07978
$347$	20.6212	1.10700	0.553501	−	0.832849i	$-0.313292\pi$
$347$	20.6212	1.10700	0.553501	+	0.832849i	$0.313292\pi$
$348$	−21.0042	−1.12595
$349$	3.59110	0.192227	0.0961137	−	0.995370i	$-0.469359\pi$
$349$	3.59110	0.192227	0.0961137	+	0.995370i	$0.469359\pi$
$350$	16.2215	0.867077
$351$	32.5677	1.73833
$352$	33.1908	1.76907
$353$	−22.2986	−1.18683	−0.593417	−	0.804895i	$-0.702221\pi$
$353$	−22.2986	−1.18683	−0.593417	+	0.804895i	$0.702221\pi$
$354$	−27.0061	−1.43536
$355$	−8.90648	−0.472707
$356$	4.70457	0.249342
$357$	2.54005	0.134434
$358$	0.0585980	0.00309700
$359$	34.5794	1.82503	0.912517	−	0.409039i	$-0.134136\pi$
$359$	34.5794	1.82503	0.912517	+	0.409039i	$0.134136\pi$
$360$	−22.4767	−1.18463
$361$	28.0512	1.47638
$362$	−69.1313	−3.63346
$363$	1.23763	0.0649588
$364$	67.7791	3.55259
$365$	−11.9418	−0.625062
$366$	20.7281	1.08348
$367$	−12.7030	−0.663092	−0.331546	−	0.943439i	$-0.607570\pi$
$367$	−12.7030	−0.663092	−0.331546	+	0.943439i	$0.607570\pi$
$368$	−50.6958	−2.64270
$369$	16.3455	0.850911
$370$	3.86459	0.200911
$371$	14.1843	0.736410
$372$	−6.51509	−0.337792
$373$	18.0801	0.936153	0.468076	−	0.883688i	$-0.344947\pi$
$373$	18.0801	0.936153	0.468076	+	0.883688i	$0.344947\pi$
$374$	−11.2437	−0.581400
$375$	−10.1839	−0.525895
$376$	42.0882	2.17053
$377$	33.0735	1.70337
$378$	−24.8374	−1.27750
$379$	5.37775	0.276237	0.138118	−	0.990416i	$-0.455895\pi$
$379$	5.37775	0.276237	0.138118	+	0.990416i	$0.455895\pi$
$380$	46.1566	2.36779
$381$	6.28718	0.322102
$382$	0.215359	0.0110187
$383$	−27.7188	−1.41636	−0.708182	−	0.706030i	$-0.750484\pi$
$383$	−27.7188	−1.41636	−0.708182	+	0.706030i	$0.750484\pi$
$384$	0.586842	0.0299472
$385$	8.71054	0.443930
$386$	3.96840	0.201986
$387$	4.57723	0.232674
$388$	92.8109	4.71176
$389$	−31.9372	−1.61928	−0.809641	−	0.586926i	$-0.800338\pi$
$389$	−31.9372	−1.61928	−0.809641	+	0.586926i	$0.800338\pi$
$390$	−22.8720	−1.15817
$391$	7.18070	0.363144
$392$	21.7281	1.09743
$393$	−9.93838	−0.501325
$394$	0.507576	0.0255713
$395$	−1.28171	−0.0644897
$396$	32.7033	1.64340
$397$	−3.66376	−0.183879	−0.0919395	−	0.995765i	$-0.529307\pi$
$397$	−3.66376	−0.183879	−0.0919395	+	0.995765i	$0.529307\pi$
$398$	−1.33988	−0.0671623
$399$	12.5848	0.630029
$400$	−30.0080	−1.50040
$401$	25.4575	1.27129	0.635644	−	0.771982i	$-0.280735\pi$
$401$	25.4575	1.27129	0.635644	+	0.771982i	$0.280735\pi$
$402$	−37.0053	−1.84566
$403$	10.2587	0.511024
$404$	−49.9145	−2.48334
$405$	−3.13196	−0.155628
$406$	−25.2231	−1.25180
$407$	−3.30120	−0.163634
$408$	−9.35589	−0.463186
$409$	17.5805	0.869300	0.434650	−	0.900599i	$-0.356872\pi$
$409$	17.5805	0.869300	0.434650	+	0.900599i	$0.356872\pi$
$410$	−27.3139	−1.34894
$411$	−16.0766	−0.793000
$412$	−24.8391	−1.22373
$413$	−22.9531	−1.12945
$414$	−29.5094	−1.45031
$415$	−16.8207	−0.825697
$416$	−74.0723	−3.63170
$417$	14.1834	0.694563
$418$	−55.7077	−2.72475
$419$	−0.920577	−0.0449731	−0.0224866	−	0.999747i	$-0.507158\pi$
$419$	−0.920577	−0.0449731	−0.0224866	+	0.999747i	$0.507158\pi$
$420$	12.3455	0.602401
$421$	−14.8444	−0.723470	−0.361735	−	0.932281i	$-0.617815\pi$
$421$	−14.8444	−0.723470	−0.361735	+	0.932281i	$0.617815\pi$
$422$	57.3992	2.79415
$423$	12.3042	0.598250
$424$	−52.2455	−2.53727
$425$	4.25043	0.206176
$426$	15.2353	0.738155
$427$	17.6173	0.852559
$428$	−46.7096	−2.25779
$429$	19.5377	0.943288
$430$	−7.64872	−0.368854
$431$	−14.8278	−0.714230	−0.357115	−	0.934060i	$-0.616240\pi$
$431$	−14.8278	−0.714230	−0.357115	+	0.934060i	$0.616240\pi$
$432$	45.9464	2.21060
$433$	3.69267	0.177458	0.0887291	−	0.996056i	$-0.471719\pi$
$433$	3.69267	0.177458	0.0887291	+	0.996056i	$0.471719\pi$
$434$	−7.82371	−0.375550
$435$	6.02413	0.288835
$436$	−76.0298	−3.64117
$437$	35.5771	1.70188
$438$	20.4275	0.976064
$439$	24.1807	1.15408	0.577040	−	0.816716i	$-0.304208\pi$
$439$	24.1807	1.15408	0.577040	+	0.816716i	$0.304208\pi$
$440$	−32.0839	−1.52954
$441$	6.35204	0.302478
$442$	25.0928	1.19354
$443$	26.5688	1.26232	0.631161	−	0.775652i	$-0.282579\pi$
$443$	26.5688	1.26232	0.631161	+	0.775652i	$0.282579\pi$
$444$	−4.67883	−0.222047
$445$	−1.34930	−0.0639628
$446$	26.5172	1.25562
$447$	4.08501	0.193214
$448$	17.0074	0.803524
$449$	−6.00090	−0.283200	−0.141600	−	0.989924i	$-0.545225\pi$
$449$	−6.00090	−0.283200	−0.141600	+	0.989924i	$0.545225\pi$
$450$	−17.4673	−0.823418
$451$	23.3320	1.09866
$452$	−65.2834	−3.07067
$453$	−18.2038	−0.855290
$454$	57.7654	2.71107
$455$	−19.4394	−0.911335
$456$	−46.3542	−2.17074
$457$	−29.1149	−1.36194	−0.680970	−	0.732312i	$-0.738441\pi$
$457$	−29.1149	−1.36194	−0.680970	+	0.732312i	$0.738441\pi$
$458$	−36.5021	−1.70563
$459$	−6.50798	−0.303767
$460$	34.9007	1.62725
$461$	10.4469	0.486561	0.243281	−	0.969956i	$-0.421776\pi$
$461$	10.4469	0.486561	0.243281	+	0.969956i	$0.421776\pi$
$462$	−14.9002	−0.693218
$463$	14.5473	0.676069	0.338035	−	0.941134i	$-0.390238\pi$
$463$	14.5473	0.676069	0.338035	+	0.941134i	$0.390238\pi$
$464$	46.6600	2.16614
$465$	1.86857	0.0866527
$466$	41.4738	1.92124
$467$	36.5180	1.68985	0.844927	−	0.534882i	$-0.179644\pi$
$467$	36.5180	1.68985	0.844927	+	0.534882i	$0.179644\pi$
$468$	−72.9845	−3.37371
$469$	−31.4516	−1.45230
$470$	−20.5608	−0.948398
$471$	−13.7541	−0.633755
$472$	84.5441	3.89146
$473$	6.53367	0.300419
$474$	2.19248	0.100704
$475$	21.0590	0.966251
$476$	−13.5443	−0.620800
$477$	−15.2736	−0.699330
$478$	41.2863	1.88839
$479$	26.2866	1.20107	0.600533	−	0.799600i	$-0.294955\pi$
$479$	26.2866	1.20107	0.600533	+	0.799600i	$0.294955\pi$
$480$	−13.4918	−0.615814
$481$	7.36734	0.335922
$482$	−20.3630	−0.927511
$483$	9.51583	0.432985
$484$	−6.59939	−0.299972
$485$	−26.6187	−1.20869
$486$	42.2496	1.91648
$487$	14.6439	0.663576	0.331788	−	0.943354i	$-0.392348\pi$
$487$	14.6439	0.663576	0.331788	+	0.943354i	$0.392348\pi$
$488$	−64.8905	−2.93745
$489$	10.5966	0.479197
$490$	−10.6145	−0.479515
$491$	21.7624	0.982122	0.491061	−	0.871125i	$-0.336609\pi$
$491$	21.7624	0.982122	0.491061	+	0.871125i	$0.336609\pi$
$492$	33.0687	1.49085
$493$	−6.60906	−0.297657
$494$	124.324	5.59359
$495$	−9.37950	−0.421577
$496$	14.4730	0.649857
$497$	12.9489	0.580836
$498$	28.7734	1.28937
$499$	44.0423	1.97160	0.985802	−	0.167914i	$-0.0537029\pi$
$499$	44.0423	1.97160	0.985802	+	0.167914i	$0.0537029\pi$
$500$	54.3034	2.42852
$501$	−15.4729	−0.691280
$502$	32.8094	1.46436
$503$	7.35324	0.327865	0.163932	−	0.986472i	$-0.447582\pi$
$503$	7.35324	0.327865	0.163932	+	0.986472i	$0.447582\pi$
$504$	32.6782	1.45560
$505$	14.3158	0.637043
$506$	−42.1226	−1.87258
$507$	−31.7936	−1.41200
$508$	−33.5250	−1.48743
$509$	18.9210	0.838660	0.419330	−	0.907834i	$-0.362265\pi$
$509$	18.9210	0.838660	0.419330	+	0.907834i	$0.362265\pi$
$510$	4.57050	0.202385
$511$	17.3618	0.768041
$512$	40.9284	1.80880
$513$	−32.2441	−1.42361
$514$	−25.6774	−1.13258
$515$	7.12399	0.313920
$516$	9.26025	0.407660
$517$	17.5634	0.772436
$518$	−5.61861	−0.246868
$519$	6.97422	0.306134
$520$	71.6022	3.13996
$521$	−8.65749	−0.379292	−0.189646	−	0.981853i	$-0.560734\pi$
$521$	−8.65749	−0.379292	−0.189646	+	0.981853i	$0.560734\pi$
$522$	27.1602	1.18877
$523$	−26.2733	−1.14885	−0.574425	−	0.818557i	$-0.694774\pi$
$523$	−26.2733	−1.14885	−0.574425	+	0.818557i	$0.694774\pi$
$524$	52.9942	2.31506
$525$	5.63265	0.245829
$526$	−50.7329	−2.21206
$527$	−2.05000	−0.0892994
$528$	27.5637	1.19956
$529$	3.90115	0.169615
$530$	25.5228	1.10864
$531$	24.7158	1.07258
$532$	−67.1057	−2.90940
$533$	−52.0704	−2.25542
$534$	2.30810	0.0998810
$535$	13.3966	0.579185
$536$	115.847	5.00384
$537$	0.0203472	0.000878045 0
$538$	−7.27108	−0.313478
$539$	9.06709	0.390547
$540$	−31.6311	−1.36118
$541$	18.6330	0.801095	0.400548	−	0.916276i	$-0.368820\pi$
$541$	18.6330	0.801095	0.400548	+	0.916276i	$0.368820\pi$
$542$	−10.0798	−0.432966
$543$	−24.0047	−1.03014
$544$	14.8018	0.634623
$545$	21.8058	0.934057
$546$	33.2529	1.42309
$547$	−33.6275	−1.43781	−0.718905	−	0.695108i	$-0.755356\pi$
$547$	−33.6275	−1.43781	−0.718905	+	0.695108i	$0.755356\pi$
$548$	85.7249	3.66199
$549$	−18.9703	−0.809631
$550$	−24.9334	−1.06316
$551$	−32.7449	−1.39498
$552$	−35.0501	−1.49183
$553$	1.86344	0.0792413
$554$	13.0545	0.554631
$555$	1.34191	0.0569611
$556$	−75.6297	−3.20742
$557$	−2.14991	−0.0910944	−0.0455472	−	0.998962i	$-0.514503\pi$
$557$	−2.14991	−0.0910944	−0.0455472	+	0.998962i	$0.514503\pi$
$558$	8.42456	0.356640
$559$	−14.5813	−0.616723
$560$	−27.4251	−1.15892
$561$	−3.90420	−0.164836
$562$	5.25600	0.221711
$563$	−13.5613	−0.571542	−0.285771	−	0.958298i	$-0.592250\pi$
$563$	−13.5613	−0.571542	−0.285771	+	0.958298i	$0.592250\pi$
$564$	24.8927	1.04817
$565$	18.7237	0.787710
$566$	25.9697	1.09159
$567$	4.55345	0.191227
$568$	−47.6951	−2.00124
$569$	−11.9369	−0.500420	−0.250210	−	0.968192i	$-0.580500\pi$
$569$	−11.9369	−0.500420	−0.250210	+	0.968192i	$0.580500\pi$
$570$	22.6448	0.948485
$571$	27.4802	1.15001	0.575005	−	0.818150i	$-0.305000\pi$
$571$	27.4802	1.15001	0.575005	+	0.818150i	$0.305000\pi$
$572$	−104.180	−4.35600
$573$	0.0747797	0.00312397
$574$	39.7109	1.65750
$575$	15.9234	0.664053
$576$	−18.3136	−0.763065
$577$	17.9876	0.748834	0.374417	−	0.927260i	$-0.377843\pi$
$577$	17.9876	0.748834	0.374417	+	0.927260i	$0.377843\pi$
$578$	39.4586	1.64126
$579$	1.37796	0.0572661
$580$	−32.1223	−1.33381
$581$	24.4551	1.01457
$582$	45.5337	1.88743
$583$	−21.8020	−0.902946
$584$	−63.9495	−2.64625
$585$	20.9324	0.865447
$586$	−24.9512	−1.03073
$587$	25.5882	1.05614	0.528069	−	0.849201i	$-0.322916\pi$
$587$	25.5882	1.05614	0.528069	+	0.849201i	$0.322916\pi$
$588$	12.8509	0.529962
$589$	−10.1568	−0.418504
$590$	−41.3011	−1.70034
$591$	0.176247	0.00724984
$592$	10.3938	0.427183
$593$	22.7669	0.934923	0.467462	−	0.884013i	$-0.345169\pi$
$593$	22.7669	0.934923	0.467462	+	0.884013i	$0.345169\pi$
$594$	38.1764	1.56640
$595$	3.88457	0.159252
$596$	−21.7824	−0.892241
$597$	−0.465252	−0.0190415
$598$	94.0056	3.84418
$599$	9.73393	0.397718	0.198859	−	0.980028i	$-0.436276\pi$
$599$	9.73393	0.397718	0.198859	+	0.980028i	$0.436276\pi$
$600$	−20.7470	−0.846993
$601$	−0.114948	−0.00468882	−0.00234441	−	0.999997i	$-0.500746\pi$
$601$	−0.114948	−0.00468882	−0.00234441	+	0.999997i	$0.500746\pi$
$602$	11.1202	0.453227
$603$	33.8671	1.37917
$604$	97.0678	3.94963
$605$	1.89274	0.0769509
$606$	−24.4884	−0.994774
$607$	−18.3099	−0.743178	−0.371589	−	0.928397i	$-0.621187\pi$
$607$	−18.3099	−0.743178	−0.371589	+	0.928397i	$0.621187\pi$
$608$	73.3364	2.97418
$609$	−8.75830	−0.354904
$610$	31.7000	1.28350
$611$	−39.1964	−1.58572
$612$	14.5845	0.589542
$613$	2.98660	0.120628	0.0603139	−	0.998179i	$-0.480790\pi$
$613$	2.98660	0.120628	0.0603139	+	0.998179i	$0.480790\pi$
$614$	58.3973	2.35672
$615$	−9.48430	−0.382444
$616$	46.6458	1.87941
$617$	22.8282	0.919029	0.459515	−	0.888170i	$-0.348023\pi$
$617$	22.8282	0.919029	0.459515	+	0.888170i	$0.348023\pi$
$618$	−12.1862	−0.490202
$619$	10.0532	0.404072	0.202036	−	0.979378i	$-0.435244\pi$
$619$	10.0532	0.404072	0.202036	+	0.979378i	$0.435244\pi$
$620$	−9.96371	−0.400152
$621$	−24.3809	−0.978374
$622$	−15.4324	−0.618783
$623$	1.96170	0.0785939
$624$	−61.5143	−2.46254
$625$	−0.224068	−0.00896272
$626$	28.4389	1.13665
$627$	−19.3436	−0.772507
$628$	73.3406	2.92661
$629$	−1.47221	−0.0587009
$630$	−15.9638	−0.636014
$631$	25.7628	1.02560	0.512800	−	0.858508i	$-0.328608\pi$
$631$	25.7628	1.02560	0.512800	+	0.858508i	$0.328608\pi$
$632$	−6.86368	−0.273022
$633$	19.9309	0.792182
$634$	43.4901	1.72721
$635$	9.61516	0.381566
$636$	−30.9002	−1.22527
$637$	−20.2352	−0.801747
$638$	38.7693	1.53489
$639$	−13.9433	−0.551589
$640$	0.897473	0.0354758
$641$	38.7003	1.52857	0.764285	−	0.644879i	$-0.223092\pi$
$641$	38.7003	1.52857	0.764285	+	0.644879i	$0.223092\pi$
$642$	−22.9161	−0.904425
$643$	40.8455	1.61079	0.805395	−	0.592738i	$-0.201953\pi$
$643$	40.8455	1.61079	0.805395	+	0.592738i	$0.201953\pi$
$644$	−50.7411	−1.99948
$645$	−2.65589	−0.104576
$646$	−24.8435	−0.977456
$647$	29.3855	1.15526	0.577631	−	0.816298i	$-0.303977\pi$
$647$	29.3855	1.15526	0.577631	+	0.816298i	$0.303977\pi$
$648$	−16.7719	−0.658864
$649$	35.2801	1.38487
$650$	55.6442	2.18255
$651$	−2.71665	−0.106474
$652$	−56.5042	−2.21288
$653$	22.4563	0.878784	0.439392	−	0.898295i	$-0.355194\pi$
$653$	22.4563	0.878784	0.439392	+	0.898295i	$0.355194\pi$
$654$	−37.3008	−1.45858
$655$	−15.1990	−0.593876
$656$	−73.4608	−2.86816
$657$	−18.6952	−0.729368
$658$	29.8927	1.16534
$659$	43.3610	1.68910	0.844552	−	0.535473i	$-0.179867\pi$
$659$	43.3610	1.68910	0.844552	+	0.535473i	$0.179867\pi$
$660$	−18.9758	−0.738631
$661$	40.6897	1.58265	0.791323	−	0.611398i	$-0.209393\pi$
$661$	40.6897	1.58265	0.791323	+	0.611398i	$0.209393\pi$
$662$	−39.1189	−1.52040
$663$	8.71307	0.338387
$664$	−90.0767	−3.49566
$665$	19.2463	0.746339
$666$	6.05011	0.234437
$667$	−24.7596	−0.958696
$668$	82.5060	3.19225
$669$	9.20764	0.355988
$670$	−56.5932	−2.18639
$671$	−27.0787	−1.04536
$672$	19.6153	0.756678
$673$	7.82055	0.301460	0.150730	−	0.988575i	$-0.451838\pi$
$673$	7.82055	0.301460	0.150730	+	0.988575i	$0.451838\pi$
$674$	35.3691	1.36237
$675$	−14.4317	−0.555475
$676$	169.532	6.52047
$677$	42.2837	1.62510	0.812548	−	0.582894i	$-0.198080\pi$
$677$	42.2837	1.62510	0.812548	+	0.582894i	$0.198080\pi$
$678$	−32.0285	−1.23005
$679$	38.7001	1.48517
$680$	−14.3082	−0.548695
$681$	20.0581	0.768627
$682$	12.0255	0.460479
$683$	15.0306	0.575131	0.287565	−	0.957761i	$-0.407154\pi$
$683$	15.0306	0.575131	0.287565	+	0.957761i	$0.407154\pi$
$684$	72.2594	2.76291
$685$	−24.5864	−0.939398
$686$	52.4182	2.00134
$687$	−12.6748	−0.483572
$688$	−20.5712	−0.784271
$689$	48.6558	1.85364
$690$	17.1225	0.651844
$691$	20.2573	0.770625	0.385312	−	0.922786i	$-0.374094\pi$
$691$	20.2573	0.770625	0.385312	+	0.922786i	$0.374094\pi$
$692$	−37.1885	−1.41369
$693$	13.6366	0.518010
$694$	−53.9460	−2.04776
$695$	21.6910	0.822788
$696$	32.2599	1.22281
$697$	10.4052	0.394125
$698$	−9.39452	−0.355588
$699$	14.4011	0.544699
$700$	−30.0349	−1.13521
$701$	10.7575	0.406305	0.203152	−	0.979147i	$-0.434881\pi$
$701$	10.7575	0.406305	0.203152	+	0.979147i	$0.434881\pi$
$702$	−85.1988	−3.21562
$703$	−7.29414	−0.275104
$704$	−26.1413	−0.985238
$705$	−7.13938	−0.268885
$706$	58.3343	2.19544
$707$	−20.8133	−0.782763
$708$	50.0029	1.87922
$709$	−48.9966	−1.84011	−0.920053	−	0.391795i	$-0.871854\pi$
$709$	−48.9966	−1.84011	−0.920053	+	0.391795i	$0.871854\pi$
$710$	23.2998	0.874427
$711$	−2.00655	−0.0752513
$712$	−7.22562	−0.270792
$713$	−7.67994	−0.287616
$714$	−6.64491	−0.248680
$715$	29.8795	1.11743
$716$	−0.108497	−0.00405471
$717$	14.3360	0.535387
$718$	−90.4617	−3.37600
$719$	−23.2652	−0.867647	−0.433823	−	0.900998i	$-0.642836\pi$
$719$	−23.2652	−0.867647	−0.433823	+	0.900998i	$0.642836\pi$
$720$	29.5313	1.10057
$721$	−10.3573	−0.385728
$722$	−73.3835	−2.73105
$723$	−7.07073	−0.262963
$724$	128.000	4.75706
$725$	−14.6558	−0.544303
$726$	−3.23771	−0.120163
$727$	22.4069	0.831026	0.415513	−	0.909587i	$-0.363602\pi$
$727$	22.4069	0.831026	0.415513	+	0.909587i	$0.363602\pi$
$728$	−104.100	−3.85821
$729$	7.90699	0.292852
$730$	31.2404	1.15626
$731$	2.91377	0.107770
$732$	−38.3790	−1.41853
$733$	−14.6584	−0.541419	−0.270709	−	0.962661i	$-0.587258\pi$
$733$	−14.6584	−0.541419	−0.270709	+	0.962661i	$0.587258\pi$
$734$	33.2318	1.22661
$735$	−3.68571	−0.135949
$736$	55.4523	2.04400
$737$	48.3429	1.78073
$738$	−42.7606	−1.57404
$739$	41.5741	1.52933	0.764663	−	0.644430i	$-0.222905\pi$
$739$	41.5741	1.52933	0.764663	+	0.644430i	$0.222905\pi$
$740$	−7.15546	−0.263040
$741$	43.1693	1.58586
$742$	−37.1068	−1.36223
$743$	35.0828	1.28706	0.643532	−	0.765419i	$-0.277468\pi$
$743$	35.0828	1.28706	0.643532	+	0.765419i	$0.277468\pi$
$744$	10.0064	0.366851
$745$	6.24731	0.228884
$746$	−47.2985	−1.73172
$747$	−26.3333	−0.963484
$748$	20.8183	0.761192
$749$	−19.4769	−0.711670
$750$	26.6417	0.972816
$751$	2.74070	0.100009	0.0500047	−	0.998749i	$-0.484076\pi$
$751$	2.74070	0.100009	0.0500047	+	0.998749i	$0.484076\pi$
$752$	−55.2982	−2.01652
$753$	11.3925	0.415166
$754$	−86.5221	−3.15095
$755$	−27.8396	−1.01319
$756$	45.9874	1.67255
$757$	−44.8032	−1.62840	−0.814200	−	0.580585i	$-0.802824\pi$
$757$	−44.8032	−1.62840	−0.814200	+	0.580585i	$0.802824\pi$
$758$	−14.0685	−0.510991
$759$	−14.6264	−0.530903
$760$	−70.8908	−2.57148
$761$	24.6446	0.893367	0.446683	−	0.894692i	$-0.352605\pi$
$761$	24.6446	0.893367	0.446683	+	0.894692i	$0.352605\pi$
$762$	−16.4476	−0.595834
$763$	−31.7027	−1.14772
$764$	−0.398746	−0.0144261
$765$	−4.18290	−0.151233
$766$	72.5138	2.62003
$767$	−78.7352	−2.84296
$768$	13.7631	0.496632
$769$	46.4915	1.67653	0.838263	−	0.545266i	$-0.183571\pi$
$769$	46.4915	1.67653	0.838263	+	0.545266i	$0.183571\pi$
$770$	−22.7872	−0.821195
$771$	−8.91605	−0.321104
$772$	−7.34767	−0.264448
$773$	−13.3099	−0.478724	−0.239362	−	0.970930i	$-0.576938\pi$
$773$	−13.3099	−0.478724	−0.239362	+	0.970930i	$0.576938\pi$
$774$	−11.9743	−0.430406
$775$	−4.54594	−0.163295
$776$	−142.546	−5.11710
$777$	−1.95097	−0.0699906
$778$	83.5495	2.99539
$779$	51.5531	1.84708
$780$	42.3485	1.51632
$781$	−19.9031	−0.712190
$782$	−18.7851	−0.671754
$783$	22.4400	0.801942
$784$	−28.5477	−1.01956
$785$	−21.0345	−0.750753
$786$	25.9993	0.927366
$787$	−6.05099	−0.215695	−0.107847	−	0.994167i	$-0.534396\pi$
$787$	−6.05099	−0.215695	−0.107847	+	0.994167i	$0.534396\pi$
$788$	−0.939799	−0.0334790
$789$	−17.6161	−0.627152
$790$	3.35302	0.119295
$791$	−27.2217	−0.967894
$792$	−50.2282	−1.78478
$793$	60.4320	2.14600
$794$	9.58460	0.340145
$795$	8.86235	0.314315
$796$	2.48085	0.0879315
$797$	−3.69842	−0.131005	−0.0655023	−	0.997852i	$-0.520865\pi$
$797$	−3.69842	−0.131005	−0.0655023	+	0.997852i	$0.520865\pi$
$798$	−32.9225	−1.16545
$799$	7.83260	0.277097
$800$	32.8236	1.16049
$801$	−2.11236	−0.0746365
$802$	−66.5983	−2.35167
$803$	−26.6860	−0.941730
$804$	68.5169	2.41640
$805$	14.5528	0.512920
$806$	−26.8374	−0.945308
$807$	−2.52476	−0.0888757
$808$	76.6624	2.69697
$809$	−38.3745	−1.34917	−0.674587	−	0.738195i	$-0.735678\pi$
$809$	−38.3745	−1.34917	−0.674587	+	0.738195i	$0.735678\pi$
$810$	8.19336	0.287885
$811$	−9.85553	−0.346075	−0.173037	−	0.984915i	$-0.555358\pi$
$811$	−9.85553	−0.346075	−0.173037	+	0.984915i	$0.555358\pi$
$812$	46.7017	1.63891
$813$	−3.50005	−0.122752
$814$	8.63611	0.302696
$815$	16.2057	0.567662
$816$	12.2924	0.430319
$817$	14.4364	0.505066
$818$	−45.9915	−1.60806
$819$	−30.4329	−1.06341
$820$	50.5729	1.76608
$821$	−7.13420	−0.248985	−0.124493	−	0.992221i	$-0.539730\pi$
$821$	−7.13420	−0.248985	−0.124493	+	0.992221i	$0.539730\pi$
$822$	42.0573	1.46692
$823$	−13.5620	−0.472742	−0.236371	−	0.971663i	$-0.575958\pi$
$823$	−13.5620	−0.472742	−0.236371	+	0.971663i	$0.575958\pi$
$824$	38.1497	1.32901
$825$	−8.65770	−0.301422
$826$	60.0464	2.08928
$827$	11.0103	0.382867	0.191433	−	0.981506i	$-0.438686\pi$
$827$	11.0103	0.382867	0.191433	+	0.981506i	$0.438686\pi$
$828$	54.6379	1.89880
$829$	21.3151	0.740306	0.370153	−	0.928971i	$-0.379305\pi$
$829$	21.3151	0.740306	0.370153	+	0.928971i	$0.379305\pi$
$830$	44.0039	1.52740
$831$	4.53294	0.157246
$832$	58.3400	2.02258
$833$	4.04358	0.140102
$834$	−37.1045	−1.28482
$835$	−23.6632	−0.818898
$836$	103.145	3.56735
$837$	6.96045	0.240588
$838$	2.40828	0.0831926
$839$	−29.9935	−1.03549	−0.517746	−	0.855534i	$-0.673229\pi$
$839$	−29.9935	−1.03549	−0.517746	+	0.855534i	$0.673229\pi$
$840$	−18.9612	−0.654223
$841$	−6.21143	−0.214187
$842$	38.8337	1.33830
$843$	1.82506	0.0628584
$844$	−106.277	−3.65821
$845$	−48.6228	−1.67267
$846$	−32.1884	−1.10666
$847$	−2.75180	−0.0945530
$848$	68.6435	2.35723
$849$	9.01753	0.309481
$850$	−11.1194	−0.381391
$851$	−5.51536	−0.189064
$852$	−28.2089	−0.966421
$853$	17.8596	0.611500	0.305750	−	0.952112i	$-0.401093\pi$
$853$	17.8596	0.611500	0.305750	+	0.952112i	$0.401093\pi$
$854$	−46.0877	−1.57709
$855$	−20.7244	−0.708759
$856$	71.7401	2.45203
$857$	48.9085	1.67068	0.835342	−	0.549731i	$-0.185270\pi$
$857$	48.9085	1.67068	0.835342	+	0.549731i	$0.185270\pi$
$858$	−51.1116	−1.74492
$859$	54.8883	1.87276	0.936382	−	0.350982i	$-0.114152\pi$
$859$	54.8883	1.87276	0.936382	+	0.350982i	$0.114152\pi$
$860$	14.1619	0.482918
$861$	13.7889	0.469925
$862$	38.7903	1.32120
$863$	−10.9087	−0.371336	−0.185668	−	0.982613i	$-0.559445\pi$
$863$	−10.9087	−0.371336	−0.185668	+	0.982613i	$0.559445\pi$
$864$	−50.2573	−1.70979
$865$	10.6659	0.362650
$866$	−9.66021	−0.328267
$867$	13.7013	0.465322
$868$	14.4859	0.491685
$869$	−2.86420	−0.0971614
$870$	−15.7595	−0.534296
$871$	−107.888	−3.65563
$872$	116.772	3.95440
$873$	−41.6722	−1.41039
$874$	−93.0717	−3.14820
$875$	22.6433	0.765484
$876$	−37.8224	−1.27790
$877$	−50.4513	−1.70362	−0.851809	−	0.523852i	$-0.824494\pi$
$877$	−50.4513	−1.70362	−0.851809	+	0.523852i	$0.824494\pi$
$878$	−63.2579	−2.13485
$879$	−8.66389	−0.292226
$880$	42.1539	1.42101
$881$	−42.9642	−1.44750	−0.723750	−	0.690062i	$-0.757583\pi$
$881$	−42.9642	−1.44750	−0.723750	+	0.690062i	$0.757583\pi$
$882$	−16.6173	−0.559533
$883$	9.51782	0.320300	0.160150	−	0.987093i	$-0.448802\pi$
$883$	9.51782	0.320300	0.160150	+	0.987093i	$0.448802\pi$
$884$	−46.4605	−1.56264
$885$	−14.3411	−0.482071
$886$	−69.5054	−2.33508
$887$	−15.6890	−0.526784	−0.263392	−	0.964689i	$-0.584841\pi$
$887$	−15.6890	−0.526784	−0.263392	+	0.964689i	$0.584841\pi$
$888$	7.18609	0.241149
$889$	−13.9792	−0.468847
$890$	3.52983	0.118320
$891$	−6.99891	−0.234472
$892$	−49.0977	−1.64391
$893$	38.8070	1.29863
$894$	−10.6866	−0.357413
$895$	0.0311175	0.00104014
$896$	−1.30481	−0.0435906
$897$	32.6419	1.08988
$898$	15.6987	0.523871
$899$	7.06856	0.235750
$900$	32.3415	1.07805
$901$	−9.72286	−0.323916
$902$	−61.0378	−2.03234
$903$	3.86132	0.128497
$904$	100.267	3.33483
$905$	−36.7110	−1.22031
$906$	47.6222	1.58214
$907$	−30.7043	−1.01952	−0.509759	−	0.860317i	$-0.670266\pi$
$907$	−30.7043	−1.01952	−0.509759	+	0.860317i	$0.670266\pi$
$908$	−106.955	−3.54943
$909$	22.4117	0.743349
$910$	50.8546	1.68581
$911$	16.3353	0.541211	0.270606	−	0.962690i	$-0.412776\pi$
$911$	16.3353	0.541211	0.270606	+	0.962690i	$0.412776\pi$
$912$	60.9031	2.01670
$913$	−37.5889	−1.24401
$914$	76.1662	2.51935
$915$	11.0073	0.363890
$916$	67.5853	2.23308
$917$	22.0974	0.729721
$918$	17.0252	0.561916
$919$	−16.8723	−0.556565	−0.278283	−	0.960499i	$-0.589765\pi$
$919$	−16.8723	−0.556565	−0.278283	+	0.960499i	$0.589765\pi$
$920$	−53.6031	−1.76724
$921$	20.2775	0.668166
$922$	−27.3297	−0.900056
$923$	44.4181	1.46204
$924$	27.5883	0.907589
$925$	−3.26468	−0.107342
$926$	−38.0565	−1.25061
$927$	11.1528	0.366306
$928$	−51.0379	−1.67540
$929$	48.0874	1.57770	0.788848	−	0.614588i	$-0.210678\pi$
$929$	48.0874	1.57770	0.788848	+	0.614588i	$0.210678\pi$
$930$	−4.88827	−0.160293
$931$	20.0341	0.656592
$932$	−76.7906	−2.51536
$933$	−5.35864	−0.175434
$934$	−95.5331	−3.12594
$935$	−5.97080	−0.195266
$936$	112.095	3.66394
$937$	37.8188	1.23549	0.617743	−	0.786380i	$-0.288047\pi$
$937$	37.8188	1.23549	0.617743	+	0.786380i	$0.288047\pi$
$938$	82.2791	2.68651
$939$	9.87491	0.322256
$940$	38.0692	1.24168
$941$	9.47965	0.309028	0.154514	−	0.987991i	$-0.450619\pi$
$941$	9.47965	0.309028	0.154514	+	0.987991i	$0.450619\pi$
$942$	35.9814	1.17234
$943$	38.9811	1.26940
$944$	−111.079	−3.61532
$945$	−13.1895	−0.429053
$946$	−17.0924	−0.555723
$947$	59.4509	1.93189	0.965947	−	0.258741i	$-0.0833076\pi$
$947$	59.4509	1.93189	0.965947	+	0.258741i	$0.0833076\pi$
$948$	−4.05947	−0.131845
$949$	59.5556	1.93326
$950$	−55.0914	−1.78740
$951$	15.1012	0.489690
$952$	20.8023	0.674206
$953$	−38.3368	−1.24185	−0.620925	−	0.783870i	$-0.713243\pi$
$953$	−38.3368	−1.24185	−0.620925	+	0.783870i	$0.713243\pi$
$954$	39.9565	1.29364
$955$	0.114363	0.00370069
$956$	−76.4434	−2.47236
$957$	13.4620	0.435164
$958$	−68.7672	−2.22177
$959$	35.7454	1.15428
$960$	10.6263	0.342961
$961$	−28.8075	−0.929273
$962$	−19.2733	−0.621398
$963$	20.9727	0.675835
$964$	37.7031	1.21433
$965$	2.10735	0.0678381
$966$	−24.8939	−0.800949
$967$	−43.2908	−1.39214	−0.696068	−	0.717975i	$-0.745069\pi$
$967$	−43.2908	−1.39214	−0.696068	+	0.717975i	$0.745069\pi$
$968$	10.1358	0.325778
$969$	−8.62650	−0.277123
$970$	69.6359	2.23588
$971$	−5.69144	−0.182647	−0.0913235	−	0.995821i	$-0.529110\pi$
$971$	−5.69144	−0.182647	−0.0913235	+	0.995821i	$0.529110\pi$
$972$	−78.2269	−2.50913
$973$	−31.5359	−1.01100
$974$	−38.3091	−1.22750
$975$	19.3215	0.618784
$976$	85.2572	2.72902
$977$	3.27115	0.104654	0.0523268	−	0.998630i	$-0.483336\pi$
$977$	3.27115	0.104654	0.0523268	+	0.998630i	$0.483336\pi$
$978$	−27.7214	−0.886432
$979$	−3.01524	−0.0963676
$980$	19.6532	0.627799
$981$	34.1375	1.08993
$982$	−56.9315	−1.81676
$983$	53.5632	1.70840	0.854201	−	0.519943i	$-0.174047\pi$
$983$	53.5632	1.70840	0.854201	+	0.519943i	$0.174047\pi$
$984$	−50.7894	−1.61911
$985$	0.269540	0.00858825
$986$	17.2897	0.550615
$987$	10.3797	0.330390
$988$	−230.191	−7.32334
$989$	10.9159	0.347105
$990$	24.5373	0.779846
$991$	14.2315	0.452078	0.226039	−	0.974118i	$-0.427422\pi$
$991$	14.2315	0.452078	0.226039	+	0.974118i	$0.427422\pi$
$992$	−15.8309	−0.502633
$993$	−13.5834	−0.431056
$994$	−33.8749	−1.07445
$995$	−0.711523	−0.0225568
$996$	−53.2752	−1.68809
$997$	−33.2822	−1.05406	−0.527029	−	0.849847i	$-0.676694\pi$
$997$	−33.2822	−1.05406	−0.527029	+	0.849847i	$0.676694\pi$
$998$	−115.217	−3.64713
$999$	4.99866	0.158151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.14	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.14	✓	275	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)

\(f(q)\)	\(=\)	\(q-2.61605 q^{2} -0.908380 q^{3} +4.84374 q^{4} -1.38921 q^{5} +2.37637 q^{6} +2.01973 q^{7} -7.43937 q^{8} -2.17484 q^{9} +O(q^{10})\)	\(q-2.61605 q^{2} -0.908380 q^{3} +4.84374 q^{4} -1.38921 q^{5} +2.37637 q^{6} +2.01973 q^{7} -7.43937 q^{8} -2.17484 q^{9} +3.63425 q^{10} -3.10444 q^{11} -4.39996 q^{12} +6.92822 q^{13} -5.28372 q^{14} +1.26193 q^{15} +9.77431 q^{16} -1.38446 q^{17} +5.68951 q^{18} -6.85939 q^{19} -6.72897 q^{20} -1.83468 q^{21} +8.12138 q^{22} -5.18663 q^{23} +6.75778 q^{24} -3.07009 q^{25} -18.1246 q^{26} +4.70073 q^{27} +9.78305 q^{28} +4.77374 q^{29} -3.30128 q^{30} +1.48072 q^{31} -10.6914 q^{32} +2.82001 q^{33} +3.62183 q^{34} -2.80583 q^{35} -10.5344 q^{36} +1.06338 q^{37} +17.9445 q^{38} -6.29346 q^{39} +10.3349 q^{40} -7.51569 q^{41} +4.79963 q^{42} -2.10462 q^{43} -15.0371 q^{44} +3.02132 q^{45} +13.5685 q^{46} -5.65750 q^{47} -8.87880 q^{48} -2.92069 q^{49} +8.03153 q^{50} +1.25762 q^{51} +33.5585 q^{52} +7.02284 q^{53} -12.2974 q^{54} +4.31272 q^{55} -15.0255 q^{56} +6.23093 q^{57} -12.4884 q^{58} -11.3644 q^{59} +6.11247 q^{60} +8.72258 q^{61} -3.87364 q^{62} -4.39260 q^{63} +8.42063 q^{64} -9.62476 q^{65} -7.37730 q^{66} -15.5722 q^{67} -6.70597 q^{68} +4.71143 q^{69} +7.34021 q^{70} +6.41118 q^{71} +16.1795 q^{72} +8.59609 q^{73} -2.78186 q^{74} +2.78881 q^{75} -33.2251 q^{76} -6.27013 q^{77} +16.4640 q^{78} +0.922615 q^{79} -13.5786 q^{80} +2.25449 q^{81} +19.6615 q^{82} +12.1081 q^{83} -8.88673 q^{84} +1.92331 q^{85} +5.50580 q^{86} -4.33637 q^{87} +23.0951 q^{88} +0.971268 q^{89} -7.90393 q^{90} +13.9931 q^{91} -25.1227 q^{92} -1.34506 q^{93} +14.8003 q^{94} +9.52914 q^{95} +9.71185 q^{96} +19.1610 q^{97} +7.64067 q^{98} +6.75167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

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