LMFDB - Embedded newform 2013.4.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.31511 q^{2} -3.00000 q^{3} +10.6201 q^{4} +3.60789 q^{5} +12.9453 q^{6} -12.6536 q^{7} -11.3062 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.31511 q^{2} -3.00000 q^{3} +10.6201 q^{4} +3.60789 q^{5} +12.9453 q^{6} -12.6536 q^{7} -11.3062 q^{8} +9.00000 q^{9} -15.5684 q^{10} +11.0000 q^{11} -31.8604 q^{12} -30.2273 q^{13} +54.6018 q^{14} -10.8237 q^{15} -36.1737 q^{16} -105.291 q^{17} -38.8360 q^{18} -93.4142 q^{19} +38.3163 q^{20} +37.9609 q^{21} -47.4662 q^{22} -34.1989 q^{23} +33.9186 q^{24} -111.983 q^{25} +130.434 q^{26} -27.0000 q^{27} -134.383 q^{28} -203.863 q^{29} +46.7053 q^{30} -235.480 q^{31} +246.543 q^{32} -33.0000 q^{33} +454.341 q^{34} -45.6529 q^{35} +95.5813 q^{36} +165.903 q^{37} +403.092 q^{38} +90.6820 q^{39} -40.7915 q^{40} +83.6688 q^{41} -163.805 q^{42} -300.651 q^{43} +116.822 q^{44} +32.4710 q^{45} +147.572 q^{46} -337.904 q^{47} +108.521 q^{48} -182.886 q^{49} +483.219 q^{50} +315.873 q^{51} -321.019 q^{52} -23.5137 q^{53} +116.508 q^{54} +39.6868 q^{55} +143.064 q^{56} +280.243 q^{57} +879.691 q^{58} -131.274 q^{59} -114.949 q^{60} +61.0000 q^{61} +1016.12 q^{62} -113.883 q^{63} -774.469 q^{64} -109.057 q^{65} +142.399 q^{66} -313.901 q^{67} -1118.20 q^{68} +102.597 q^{69} +196.997 q^{70} -583.968 q^{71} -101.756 q^{72} +525.284 q^{73} -715.891 q^{74} +335.949 q^{75} -992.072 q^{76} -139.190 q^{77} -391.302 q^{78} +1176.16 q^{79} -130.511 q^{80} +81.0000 q^{81} -361.040 q^{82} +1019.03 q^{83} +403.150 q^{84} -379.878 q^{85} +1297.34 q^{86} +611.589 q^{87} -124.368 q^{88} -1581.35 q^{89} -140.116 q^{90} +382.486 q^{91} -363.197 q^{92} +706.440 q^{93} +1458.09 q^{94} -337.028 q^{95} -739.629 q^{96} -803.064 q^{97} +789.171 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * 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 $

$2$	−4.31511	−1.52562	−0.762810	−	0.646622i	$-0.776181\pi$
$2$	−4.31511	−1.52562	−0.762810	+	0.646622i	$0.776181\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	10.6201	1.32752
$5$	3.60789	0.322699	0.161350	−	0.986897i	$-0.448415\pi$
$5$	3.60789	0.322699	0.161350	+	0.986897i	$0.448415\pi$
$6$	12.9453	0.880817
$7$	−12.6536	−0.683232	−0.341616	−	0.939840i	$-0.610974\pi$
$7$	−12.6536	−0.683232	−0.341616	+	0.939840i	$0.610974\pi$
$8$	−11.3062	−0.499668
$9$	9.00000	0.333333
$10$	−15.5684	−0.492317
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−31.8604	−0.766443
$13$	−30.2273	−0.644889	−0.322444	−	0.946588i	$-0.604505\pi$
$13$	−30.2273	−0.644889	−0.322444	+	0.946588i	$0.604505\pi$
$14$	54.6018	1.04235
$15$	−10.8237	−0.186311
$16$	−36.1737	−0.565215
$17$	−105.291	−1.50216	−0.751082	−	0.660209i	$-0.770468\pi$
$17$	−105.291	−1.50216	−0.751082	+	0.660209i	$0.770468\pi$
$18$	−38.8360	−0.508540
$19$	−93.4142	−1.12793	−0.563965	−	0.825798i	$-0.690725\pi$
$19$	−93.4142	−1.12793	−0.563965	+	0.825798i	$0.690725\pi$
$20$	38.3163	0.428389
$21$	37.9609	0.394464
$22$	−47.4662	−0.459992
$23$	−34.1989	−0.310042	−0.155021	−	0.987911i	$-0.549545\pi$
$23$	−34.1989	−0.310042	−0.155021	+	0.987911i	$0.549545\pi$
$24$	33.9186	0.288483
$25$	−111.983	−0.895865
$26$	130.434	0.983855
$27$	−27.0000	−0.192450
$28$	−134.383	−0.907002
$29$	−203.863	−1.30539	−0.652697	−	0.757619i	$-0.726362\pi$
$29$	−203.863	−1.30539	−0.652697	+	0.757619i	$0.726362\pi$
$30$	46.7053	0.284239
$31$	−235.480	−1.36431	−0.682153	−	0.731210i	$-0.738956\pi$
$31$	−235.480	−1.36431	−0.682153	+	0.731210i	$0.738956\pi$
$32$	246.543	1.36197
$33$	−33.0000	−0.174078
$34$	454.341	2.29173
$35$	−45.6529	−0.220479
$36$	95.5813	0.442506
$37$	165.903	0.737145	0.368572	−	0.929599i	$-0.379847\pi$
$37$	165.903	0.737145	0.368572	+	0.929599i	$0.379847\pi$
$38$	403.092	1.72079
$39$	90.6820	0.372327
$40$	−40.7915	−0.161242
$41$	83.6688	0.318704	0.159352	−	0.987222i	$-0.449059\pi$
$41$	83.6688	0.318704	0.159352	+	0.987222i	$0.449059\pi$
$42$	−163.805	−0.601803
$43$	−300.651	−1.06625	−0.533126	−	0.846036i	$-0.678983\pi$
$43$	−300.651	−1.06625	−0.533126	+	0.846036i	$0.678983\pi$
$44$	116.822	0.400262
$45$	32.4710	0.107566
$46$	147.572	0.473007
$47$	−337.904	−1.04869	−0.524344	−	0.851507i	$-0.675689\pi$
$47$	−337.904	−1.04869	−0.524344	+	0.851507i	$0.675689\pi$
$48$	108.521	0.326327
$49$	−182.886	−0.533194
$50$	483.219	1.36675
$51$	315.873	0.867275
$52$	−321.019	−0.856101
$53$	−23.5137	−0.0609406	−0.0304703	−	0.999536i	$-0.509700\pi$
$53$	−23.5137	−0.0609406	−0.0304703	+	0.999536i	$0.509700\pi$
$54$	116.508	0.293606
$55$	39.6868	0.0972975
$56$	143.064	0.341389
$57$	280.243	0.651211
$58$	879.691	1.99154
$59$	−131.274	−0.289668	−0.144834	−	0.989456i	$-0.546265\pi$
$59$	−131.274	−0.289668	−0.144834	+	0.989456i	$0.546265\pi$
$60$	−114.949	−0.247331
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	1016.12	2.08141
$63$	−113.883	−0.227744
$64$	−774.469	−1.51264
$65$	−109.057	−0.208105
$66$	142.399	0.265576
$67$	−313.901	−0.572374	−0.286187	−	0.958174i	$-0.592388\pi$
$67$	−313.901	−0.572374	−0.286187	+	0.958174i	$0.592388\pi$
$68$	−1118.20	−1.99415
$69$	102.597	0.179003
$70$	196.997	0.336367
$71$	−583.968	−0.976117	−0.488058	−	0.872811i	$-0.662295\pi$
$71$	−583.968	−0.976117	−0.488058	+	0.872811i	$0.662295\pi$
$72$	−101.756	−0.166556
$73$	525.284	0.842189	0.421094	−	0.907017i	$-0.361646\pi$
$73$	525.284	0.842189	0.421094	+	0.907017i	$0.361646\pi$
$74$	−715.891	−1.12460
$75$	335.949	0.517228
$76$	−992.072	−1.49735
$77$	−139.190	−0.206002
$78$	−391.302	−0.568029
$79$	1176.16	1.67504	0.837518	−	0.546410i	$-0.184006\pi$
$79$	1176.16	1.67504	0.837518	+	0.546410i	$0.184006\pi$
$80$	−130.511	−0.182394
$81$	81.0000	0.111111
$82$	−361.040	−0.486222
$83$	1019.03	1.34763	0.673816	−	0.738899i	$-0.264654\pi$
$83$	1019.03	1.34763	0.673816	+	0.738899i	$0.264654\pi$
$84$	403.150	0.523658
$85$	−379.878	−0.484747
$86$	1297.34	1.62669
$87$	611.589	0.753669
$88$	−124.368	−0.150655
$89$	−1581.35	−1.88340	−0.941702	−	0.336447i	$-0.890775\pi$
$89$	−1581.35	−1.88340	−0.941702	+	0.336447i	$0.890775\pi$
$90$	−140.116	−0.164106
$91$	382.486	0.440609
$92$	−363.197	−0.411586
$93$	706.440	0.787682
$94$	1458.09	1.59990
$95$	−337.028	−0.363983
$96$	−739.629	−0.786334
$97$	−803.064	−0.840606	−0.420303	−	0.907384i	$-0.638076\pi$
$97$	−803.064	−0.840606	−0.420303	+	0.907384i	$0.638076\pi$
$98$	789.171	0.813452
$99$	99.0000	0.100504
$100$	−1189.28	−1.18928
$101$	−791.716	−0.779987	−0.389994	−	0.920818i	$-0.627523\pi$
$101$	−791.716	−0.779987	−0.389994	+	0.920818i	$0.627523\pi$
$102$	−1363.02	−1.32313
$103$	−972.635	−0.930452	−0.465226	−	0.885192i	$-0.654027\pi$
$103$	−972.635	−0.930452	−0.465226	+	0.885192i	$0.654027\pi$
$104$	341.756	0.322230
$105$	136.959	0.127293
$106$	101.464	0.0929722
$107$	318.524	0.287784	0.143892	−	0.989593i	$-0.454038\pi$
$107$	318.524	0.287784	0.143892	+	0.989593i	$0.454038\pi$
$108$	−286.744	−0.255481
$109$	1355.35	1.19100	0.595500	−	0.803355i	$-0.296954\pi$
$109$	1355.35	1.19100	0.595500	+	0.803355i	$0.296954\pi$
$110$	−171.253	−0.148439
$111$	−497.710	−0.425591
$112$	457.729	0.386173
$113$	437.762	0.364435	0.182218	−	0.983258i	$-0.441672\pi$
$113$	437.762	0.364435	0.182218	+	0.983258i	$0.441672\pi$
$114$	−1209.28	−0.993501
$115$	−123.386	−0.100050
$116$	−2165.05	−1.73293
$117$	−272.046	−0.214963
$118$	566.461	0.441923
$119$	1332.31	1.02633
$120$	122.374	0.0930934
$121$	121.000	0.0909091
$122$	−263.221	−0.195336
$123$	−251.006	−0.184004
$124$	−2500.83	−1.81114
$125$	−855.009	−0.611795
$126$	491.416	0.347451
$127$	811.845	0.567241	0.283620	−	0.958937i	$-0.408464\pi$
$127$	811.845	0.567241	0.283620	+	0.958937i	$0.408464\pi$
$128$	1369.57	0.945737
$129$	901.952	0.615601
$130$	470.592	0.317490
$131$	1482.65	0.988856	0.494428	−	0.869219i	$-0.335378\pi$
$131$	1482.65	0.988856	0.494428	+	0.869219i	$0.335378\pi$
$132$	−350.465	−0.231091
$133$	1182.03	0.770638
$134$	1354.51	0.873226
$135$	−97.4130	−0.0621035
$136$	1190.44	0.750582
$137$	−574.776	−0.358441	−0.179221	−	0.983809i	$-0.557358\pi$
$137$	−574.776	−0.358441	−0.179221	+	0.983809i	$0.557358\pi$
$138$	−442.716	−0.273091
$139$	−1252.60	−0.764346	−0.382173	−	0.924091i	$-0.624824\pi$
$139$	−1252.60	−0.764346	−0.382173	+	0.924091i	$0.624824\pi$
$140$	−484.840	−0.292689
$141$	1013.71	0.605460
$142$	2519.89	1.48918
$143$	−332.501	−0.194441
$144$	−325.564	−0.188405
$145$	−735.515	−0.421250
$146$	−2266.65	−1.28486
$147$	548.657	0.307840
$148$	1761.92	0.978573
$149$	−3498.78	−1.92370	−0.961851	−	0.273574i	$-0.911794\pi$
$149$	−3498.78	−1.92370	−0.961851	+	0.273574i	$0.911794\pi$
$150$	−1449.66	−0.789093
$151$	−821.026	−0.442478	−0.221239	−	0.975220i	$-0.571010\pi$
$151$	−821.026	−0.442478	−0.221239	+	0.975220i	$0.571010\pi$
$152$	1056.16	0.563590
$153$	−947.618	−0.500721
$154$	600.619	0.314281
$155$	−849.586	−0.440261
$156$	963.056	0.494270
$157$	185.177	0.0941321	0.0470661	−	0.998892i	$-0.485013\pi$
$157$	185.177	0.0941321	0.0470661	+	0.998892i	$0.485013\pi$
$158$	−5075.23	−2.55547
$159$	70.5410	0.0351841
$160$	889.500	0.439507
$161$	432.741	0.211831
$162$	−349.524	−0.169513
$163$	−653.657	−0.314100	−0.157050	−	0.987591i	$-0.550198\pi$
$163$	−653.657	−0.314100	−0.157050	+	0.987591i	$0.550198\pi$
$164$	888.575	0.423086
$165$	−119.060	−0.0561748
$166$	−4397.24	−2.05597
$167$	−388.276	−0.179915	−0.0899573	−	0.995946i	$-0.528673\pi$
$167$	−388.276	−0.179915	−0.0899573	+	0.995946i	$0.528673\pi$
$168$	−429.193	−0.197101
$169$	−1283.31	−0.584119
$170$	1639.21	0.739540
$171$	−840.728	−0.375977
$172$	−3192.95	−1.41547
$173$	−1950.22	−0.857064	−0.428532	−	0.903527i	$-0.640969\pi$
$173$	−1950.22	−0.857064	−0.428532	+	0.903527i	$0.640969\pi$
$174$	−2639.07	−1.14981
$175$	1416.99	0.612084
$176$	−397.911	−0.170419
$177$	393.822	0.167240
$178$	6823.70	2.87336
$179$	−3402.41	−1.42072	−0.710358	−	0.703840i	$-0.751467\pi$
$179$	−3402.41	−1.42072	−0.710358	+	0.703840i	$0.751467\pi$
$180$	344.847	0.142796
$181$	−865.656	−0.355490	−0.177745	−	0.984077i	$-0.556880\pi$
$181$	−865.656	−0.355490	−0.177745	+	0.984077i	$0.556880\pi$
$182$	−1650.47	−0.672201
$183$	−183.000	−0.0739221
$184$	386.659	0.154918
$185$	598.561	0.237876
$186$	−3048.37	−1.20170
$187$	−1158.20	−0.452919
$188$	−3588.59	−1.39215
$189$	341.648	0.131488
$190$	1454.31	0.555299
$191$	−1310.54	−0.496477	−0.248238	−	0.968699i	$-0.579852\pi$
$191$	−1310.54	−0.496477	−0.248238	+	0.968699i	$0.579852\pi$
$192$	2323.41	0.873320
$193$	−1218.47	−0.454443	−0.227221	−	0.973843i	$-0.572964\pi$
$193$	−1218.47	−0.454443	−0.227221	+	0.973843i	$0.572964\pi$
$194$	3465.30	1.28245
$195$	327.171	0.120150
$196$	−1942.27	−0.707825
$197$	−2747.02	−0.993488	−0.496744	−	0.867897i	$-0.665471\pi$
$197$	−2747.02	−0.993488	−0.496744	+	0.867897i	$0.665471\pi$
$198$	−427.196	−0.153331
$199$	5264.24	1.87524	0.937619	−	0.347666i	$-0.113026\pi$
$199$	5264.24	1.87524	0.937619	+	0.347666i	$0.113026\pi$
$200$	1266.10	0.447635
$201$	941.702	0.330460
$202$	3416.34	1.18996
$203$	2579.61	0.891887
$204$	3354.61	1.15132
$205$	301.868	0.102846
$206$	4197.02	1.41952
$207$	−307.790	−0.103347
$208$	1093.44	0.364501
$209$	−1027.56	−0.340084
$210$	−590.991	−0.194201
$211$	−3380.00	−1.10279	−0.551396	−	0.834244i	$-0.685905\pi$
$211$	−3380.00	−1.10279	−0.551396	+	0.834244i	$0.685905\pi$
$212$	−249.718	−0.0808997
$213$	1751.91	0.563561
$214$	−1374.46	−0.439049
$215$	−1084.71	−0.344079
$216$	305.267	0.0961611
$217$	2979.68	0.932137
$218$	−5848.48	−1.81702
$219$	−1575.85	−0.486238
$220$	421.479	0.129164
$221$	3182.66	0.968728
$222$	2147.67	0.649290
$223$	3291.17	0.988311	0.494155	−	0.869374i	$-0.335477\pi$
$223$	3291.17	0.988311	0.494155	+	0.869374i	$0.335477\pi$
$224$	−3119.66	−0.930542
$225$	−1007.85	−0.298622
$226$	−1888.99	−0.555990
$227$	4340.55	1.26913	0.634565	−	0.772869i	$-0.281179\pi$
$227$	4340.55	1.26913	0.634565	+	0.772869i	$0.281179\pi$
$228$	2976.22	0.864494
$229$	−1342.76	−0.387476	−0.193738	−	0.981053i	$-0.562061\pi$
$229$	−1342.76	−0.387476	−0.193738	+	0.981053i	$0.562061\pi$
$230$	532.424	0.152639
$231$	417.570	0.118935
$232$	2304.91	0.652263
$233$	−2225.79	−0.625822	−0.312911	−	0.949783i	$-0.601304\pi$
$233$	−2225.79	−0.625822	−0.312911	+	0.949783i	$0.601304\pi$
$234$	1173.91	0.327952
$235$	−1219.12	−0.338411
$236$	−1394.15	−0.384539
$237$	−3528.47	−0.967082
$238$	−5749.07	−1.56578
$239$	−3430.53	−0.928463	−0.464231	−	0.885714i	$-0.653669\pi$
$239$	−3430.53	−0.928463	−0.464231	+	0.885714i	$0.653669\pi$
$240$	391.533	0.105305
$241$	3057.60	0.817252	0.408626	−	0.912702i	$-0.366008\pi$
$241$	3057.60	0.817252	0.408626	+	0.912702i	$0.366008\pi$
$242$	−522.128	−0.138693
$243$	−243.000	−0.0641500
$244$	647.829	0.169971
$245$	−659.831	−0.172061
$246$	1083.12	0.280720
$247$	2823.66	0.727390
$248$	2662.38	0.681699
$249$	−3057.10	−0.778056
$250$	3689.45	0.933366
$251$	−5203.13	−1.30844	−0.654220	−	0.756304i	$-0.727003\pi$
$251$	−5203.13	−1.30844	−0.654220	+	0.756304i	$0.727003\pi$
$252$	−1209.45	−0.302334
$253$	−376.188	−0.0934812
$254$	−3503.20	−0.865394
$255$	1139.63	0.279869
$256$	285.900	0.0697999
$257$	1180.02	0.286411	0.143205	−	0.989693i	$-0.454259\pi$
$257$	1180.02	0.286411	0.143205	+	0.989693i	$0.454259\pi$
$258$	−3892.02	−0.939173
$259$	−2099.28	−0.503641
$260$	−1158.20	−0.276263
$261$	−1834.77	−0.435131
$262$	−6397.81	−1.50862
$263$	−2035.67	−0.477281	−0.238641	−	0.971108i	$-0.576702\pi$
$263$	−2035.67	−0.477281	−0.238641	+	0.971108i	$0.576702\pi$
$264$	373.104	0.0869810
$265$	−84.8347	−0.0196655
$266$	−5100.58	−1.17570
$267$	4744.06	1.08738
$268$	−3333.67	−0.759837
$269$	−6871.21	−1.55742	−0.778708	−	0.627387i	$-0.784125\pi$
$269$	−6871.21	−1.55742	−0.778708	+	0.627387i	$0.784125\pi$
$270$	420.348	0.0947464
$271$	−958.623	−0.214879	−0.107439	−	0.994212i	$-0.534265\pi$
$271$	−958.623	−0.214879	−0.107439	+	0.994212i	$0.534265\pi$
$272$	3808.76	0.849045
$273$	−1147.46	−0.254385
$274$	2480.22	0.546845
$275$	−1231.81	−0.270113
$276$	1089.59	0.237630
$277$	3188.22	0.691557	0.345779	−	0.938316i	$-0.387615\pi$
$277$	3188.22	0.691557	0.345779	+	0.938316i	$0.387615\pi$
$278$	5405.10	1.16610
$279$	−2119.32	−0.454769
$280$	516.160	0.110166
$281$	5335.08	1.13261	0.566306	−	0.824195i	$-0.308372\pi$
$281$	5335.08	1.13261	0.566306	+	0.824195i	$0.308372\pi$
$282$	−4374.27	−0.923702
$283$	−3798.14	−0.797795	−0.398897	−	0.916996i	$-0.630607\pi$
$283$	−3798.14	−0.797795	−0.398897	+	0.916996i	$0.630607\pi$
$284$	−6201.83	−1.29581
$285$	1011.08	0.210145
$286$	1434.78	0.296644
$287$	−1058.71	−0.217749
$288$	2218.89	0.453990
$289$	6173.16	1.25650
$290$	3173.83	0.642667
$291$	2409.19	0.485324
$292$	5578.59	1.11802
$293$	6509.14	1.29784	0.648921	−	0.760855i	$-0.275220\pi$
$293$	6509.14	1.29784	0.648921	+	0.760855i	$0.275220\pi$
$294$	−2367.51	−0.469647
$295$	−473.622	−0.0934757
$296$	−1875.74	−0.368327
$297$	−297.000	−0.0580259
$298$	15097.6	2.93484
$299$	1033.74	0.199943
$300$	3567.83	0.686629
$301$	3804.32	0.728497
$302$	3542.81	0.675053
$303$	2375.15	0.450326
$304$	3379.14	0.637523
$305$	220.081	0.0413174
$306$	4089.07	0.763910
$307$	−3027.79	−0.562884	−0.281442	−	0.959578i	$-0.590813\pi$
$307$	−3027.79	−0.562884	−0.281442	+	0.959578i	$0.590813\pi$
$308$	−1478.22	−0.273472
$309$	2917.90	0.537197
$310$	3666.05	0.671671
$311$	−5069.64	−0.924350	−0.462175	−	0.886789i	$-0.652931\pi$
$311$	−5069.64	−0.924350	−0.462175	+	0.886789i	$0.652931\pi$
$312$	−1025.27	−0.186040
$313$	2166.44	0.391227	0.195614	−	0.980681i	$-0.437330\pi$
$313$	2166.44	0.391227	0.195614	+	0.980681i	$0.437330\pi$
$314$	−799.059	−0.143610
$315$	−410.876	−0.0734929
$316$	12490.9	2.22364
$317$	−5561.08	−0.985305	−0.492652	−	0.870226i	$-0.663973\pi$
$317$	−5561.08	−0.985305	−0.492652	+	0.870226i	$0.663973\pi$
$318$	−304.392	−0.0536775
$319$	−2242.49	−0.393591
$320$	−2794.20	−0.488127
$321$	−955.572	−0.166152
$322$	−1867.32	−0.323173
$323$	9835.66	1.69434
$324$	860.231	0.147502
$325$	3384.95	0.577733
$326$	2820.60	0.479198
$327$	−4066.05	−0.687625
$328$	−945.975	−0.159246
$329$	4275.71	0.716497
$330$	513.758	0.0857014
$331$	−2349.22	−0.390105	−0.195052	−	0.980793i	$-0.562488\pi$
$331$	−2349.22	−0.390105	−0.195052	+	0.980793i	$0.562488\pi$
$332$	10822.3	1.78900
$333$	1493.13	0.245715
$334$	1675.45	0.274481
$335$	−1132.52	−0.184705
$336$	−1373.19	−0.222957
$337$	11048.6	1.78592	0.892959	−	0.450139i	$-0.148626\pi$
$337$	11048.6	1.78592	0.892959	+	0.450139i	$0.148626\pi$
$338$	5537.61	0.891143
$339$	−1313.29	−0.210407
$340$	−4034.36	−0.643511
$341$	−2590.28	−0.411354
$342$	3627.83	0.573598
$343$	6654.36	1.04753
$344$	3399.21	0.532771
$345$	370.158	0.0577641
$346$	8415.39	1.30755
$347$	−1593.29	−0.246491	−0.123245	−	0.992376i	$-0.539330\pi$
$347$	−1593.29	−0.246491	−0.123245	+	0.992376i	$0.539330\pi$
$348$	6495.16	1.00051
$349$	11702.1	1.79484	0.897418	−	0.441181i	$-0.145440\pi$
$349$	11702.1	1.79484	0.897418	+	0.441181i	$0.145440\pi$
$350$	−6114.48	−0.933807
$351$	816.138	0.124109
$352$	2711.97	0.410650
$353$	2677.95	0.403776	0.201888	−	0.979409i	$-0.435292\pi$
$353$	2677.95	0.403776	0.201888	+	0.979409i	$0.435292\pi$
$354$	−1699.38	−0.255145
$355$	−2106.89	−0.314992
$356$	−16794.2	−2.50025
$357$	−3996.93	−0.592550
$358$	14681.8	2.16747
$359$	−842.881	−0.123915	−0.0619576	−	0.998079i	$-0.519734\pi$
$359$	−842.881	−0.123915	−0.0619576	+	0.998079i	$0.519734\pi$
$360$	−367.123	−0.0537475
$361$	1867.21	0.272227
$362$	3735.40	0.542343
$363$	−363.000	−0.0524864
$364$	4062.05	0.584916
$365$	1895.17	0.271774
$366$	789.664	0.112777
$367$	11925.8	1.69625	0.848123	−	0.529799i	$-0.177733\pi$
$367$	11925.8	1.69625	0.848123	+	0.529799i	$0.177733\pi$
$368$	1237.10	0.175240
$369$	753.019	0.106235
$370$	−2582.86	−0.362909
$371$	297.533	0.0416365
$372$	7502.50	1.04566
$373$	−5204.93	−0.722523	−0.361262	−	0.932465i	$-0.617654\pi$
$373$	−5204.93	−0.722523	−0.361262	+	0.932465i	$0.617654\pi$
$374$	4997.75	0.690983
$375$	2565.03	0.353220
$376$	3820.40	0.523995
$377$	6162.24	0.841834
$378$	−1474.25	−0.200601
$379$	4370.01	0.592275	0.296137	−	0.955145i	$-0.404301\pi$
$379$	4370.01	0.592275	0.296137	+	0.955145i	$0.404301\pi$
$380$	−3579.29	−0.483193
$381$	−2435.53	−0.327497
$382$	5655.10	0.757435
$383$	12384.2	1.65223	0.826114	−	0.563503i	$-0.190547\pi$
$383$	12384.2	1.65223	0.826114	+	0.563503i	$0.190547\pi$
$384$	−4108.72	−0.546021
$385$	−502.182	−0.0664768
$386$	5257.83	0.693307
$387$	−2705.86	−0.355417
$388$	−8528.65	−1.11592
$389$	3405.77	0.443905	0.221953	−	0.975057i	$-0.428757\pi$
$389$	3405.77	0.443905	0.221953	+	0.975057i	$0.428757\pi$
$390$	−1411.78	−0.183303
$391$	3600.83	0.465734
$392$	2067.74	0.266420
$393$	−4447.96	−0.570916
$394$	11853.7	1.51569
$395$	4243.44	0.540533
$396$	1051.39	0.133421
$397$	−6477.52	−0.818885	−0.409442	−	0.912336i	$-0.634277\pi$
$397$	−6477.52	−0.818885	−0.409442	+	0.912336i	$0.634277\pi$
$398$	−22715.8	−2.86090
$399$	−3546.09	−0.444928
$400$	4050.85	0.506356
$401$	2841.69	0.353884	0.176942	−	0.984221i	$-0.443380\pi$
$401$	2841.69	0.353884	0.176942	+	0.984221i	$0.443380\pi$
$402$	−4063.54	−0.504157
$403$	7117.94	0.879825
$404$	−8408.14	−1.03545
$405$	292.239	0.0358555
$406$	−11131.3	−1.36068
$407$	1824.94	0.222258
$408$	−3571.31	−0.433349
$409$	5444.92	0.658273	0.329137	−	0.944282i	$-0.393242\pi$
$409$	5444.92	0.658273	0.329137	+	0.944282i	$0.393242\pi$
$410$	−1302.59	−0.156903
$411$	1724.33	0.206946
$412$	−10329.5	−1.23519
$413$	1661.09	0.197910
$414$	1328.15	0.157669
$415$	3676.56	0.434880
$416$	−7452.34	−0.878319
$417$	3757.80	0.441295
$418$	4434.01	0.518839
$419$	−1574.06	−0.183527	−0.0917633	−	0.995781i	$-0.529250\pi$
$419$	−1574.06	−0.183527	−0.0917633	+	0.995781i	$0.529250\pi$
$420$	1454.52	0.168984
$421$	2071.71	0.239831	0.119915	−	0.992784i	$-0.461738\pi$
$421$	2071.71	0.239831	0.119915	+	0.992784i	$0.461738\pi$
$422$	14585.1	1.68244
$423$	−3041.13	−0.349563
$424$	265.850	0.0304500
$425$	11790.8	1.34574
$426$	−7559.66	−0.859781
$427$	−771.872	−0.0874789
$428$	3382.77	0.382038
$429$	997.502	0.112261
$430$	4680.66	0.524934
$431$	−8574.93	−0.958329	−0.479164	−	0.877725i	$-0.659060\pi$
$431$	−8574.93	−0.958329	−0.479164	+	0.877725i	$0.659060\pi$
$432$	976.691	0.108776
$433$	−3197.86	−0.354918	−0.177459	−	0.984128i	$-0.556788\pi$
$433$	−3197.86	−0.354918	−0.177459	+	0.984128i	$0.556788\pi$
$434$	−12857.6	−1.42209
$435$	2206.55	0.243209
$436$	14394.0	1.58107
$437$	3194.66	0.349706
$438$	6799.96	0.741815
$439$	3256.85	0.354080	0.177040	−	0.984204i	$-0.443348\pi$
$439$	3256.85	0.354080	0.177040	+	0.984204i	$0.443348\pi$
$440$	−448.706	−0.0486164
$441$	−1645.97	−0.177731
$442$	−13733.5	−1.47791
$443$	14827.7	1.59026	0.795128	−	0.606442i	$-0.207404\pi$
$443$	14827.7	1.59026	0.795128	+	0.606442i	$0.207404\pi$
$444$	−5285.75	−0.564979
$445$	−5705.34	−0.607774
$446$	−14201.8	−1.50779
$447$	10496.4	1.11065
$448$	9799.85	1.03348
$449$	−10522.5	−1.10599	−0.552993	−	0.833186i	$-0.686514\pi$
$449$	−10522.5	−1.10599	−0.552993	+	0.833186i	$0.686514\pi$
$450$	4348.97	0.455583
$451$	920.357	0.0960930
$452$	4649.10	0.483794
$453$	2463.08	0.255465
$454$	−18729.9	−1.93621
$455$	1379.97	0.142184
$456$	−3168.47	−0.325389
$457$	−10598.7	−1.08488	−0.542438	−	0.840096i	$-0.682499\pi$
$457$	−10598.7	−1.08488	−0.542438	+	0.840096i	$0.682499\pi$
$458$	5794.15	0.591141
$459$	2842.85	0.289092
$460$	−1310.38	−0.132819
$461$	10229.6	1.03349	0.516744	−	0.856140i	$-0.327144\pi$
$461$	10229.6	1.03349	0.516744	+	0.856140i	$0.327144\pi$
$462$	−1801.86	−0.181450
$463$	−1936.49	−0.194376	−0.0971881	−	0.995266i	$-0.530985\pi$
$463$	−1936.49	−0.194376	−0.0971881	+	0.995266i	$0.530985\pi$
$464$	7374.49	0.737828
$465$	2548.76	0.254185
$466$	9604.53	0.954766
$467$	4532.06	0.449077	0.224538	−	0.974465i	$-0.427913\pi$
$467$	4532.06	0.449077	0.224538	+	0.974465i	$0.427913\pi$
$468$	−2889.17	−0.285367
$469$	3971.98	0.391064
$470$	5260.63	0.516287
$471$	−555.531	−0.0543472
$472$	1484.21	0.144738
$473$	−3307.16	−0.321487
$474$	15225.7	1.47540
$475$	10460.8	1.01047
$476$	14149.3	1.36247
$477$	−211.623	−0.0203135
$478$	14803.1	1.41648
$479$	−9941.84	−0.948339	−0.474169	−	0.880434i	$-0.657252\pi$
$479$	−9941.84	−0.948339	−0.474169	+	0.880434i	$0.657252\pi$
$480$	−2668.50	−0.253750
$481$	−5014.82	−0.475376
$482$	−13193.9	−1.24682
$483$	−1298.22	−0.122301
$484$	1285.04	0.120683
$485$	−2897.36	−0.271263
$486$	1048.57	0.0978686
$487$	−4433.19	−0.412499	−0.206250	−	0.978499i	$-0.566126\pi$
$487$	−4433.19	−0.412499	−0.206250	+	0.978499i	$0.566126\pi$
$488$	−689.677	−0.0639759
$489$	1960.97	0.181346
$490$	2847.24	0.262500
$491$	−6912.49	−0.635349	−0.317675	−	0.948200i	$-0.602902\pi$
$491$	−6912.49	−0.635349	−0.317675	+	0.948200i	$0.602902\pi$
$492$	−2665.72	−0.244269
$493$	21464.9	1.96091
$494$	−12184.4	−1.10972
$495$	357.181	0.0324325
$496$	8518.20	0.771126
$497$	7389.32	0.666914
$498$	13191.7	1.18702
$499$	−8191.42	−0.734866	−0.367433	−	0.930050i	$-0.619763\pi$
$499$	−8191.42	−0.734866	−0.367433	+	0.930050i	$0.619763\pi$
$500$	−9080.32	−0.812168
$501$	1164.83	0.103874
$502$	22452.0	1.99618
$503$	−9255.92	−0.820479	−0.410240	−	0.911978i	$-0.634555\pi$
$503$	−9255.92	−0.820479	−0.410240	+	0.911978i	$0.634555\pi$
$504$	1287.58	0.113796
$505$	−2856.42	−0.251701
$506$	1623.29	0.142617
$507$	3849.93	0.337241
$508$	8621.91	0.753022
$509$	−12971.8	−1.12960	−0.564800	−	0.825228i	$-0.691047\pi$
$509$	−12971.8	−1.12960	−0.564800	+	0.825228i	$0.691047\pi$
$510$	−4917.64	−0.426974
$511$	−6646.75	−0.575410
$512$	−12190.3	−1.05223
$513$	2522.18	0.217070
$514$	−5091.91	−0.436954
$515$	−3509.16	−0.300256
$516$	9578.86	0.817221
$517$	−3716.94	−0.316191
$518$	9058.62	0.768365
$519$	5850.65	0.494826
$520$	1233.02	0.103983
$521$	−7143.28	−0.600677	−0.300339	−	0.953833i	$-0.597100\pi$
$521$	−7143.28	−0.600677	−0.300339	+	0.953833i	$0.597100\pi$
$522$	7917.22	0.663845
$523$	−4815.01	−0.402573	−0.201287	−	0.979532i	$-0.564512\pi$
$523$	−4815.01	−0.402573	−0.201287	+	0.979532i	$0.564512\pi$
$524$	15746.0	1.31272
$525$	−4250.98	−0.353387
$526$	8784.14	0.728150
$527$	24793.9	2.04941
$528$	1193.73	0.0983912
$529$	−10997.4	−0.903874
$530$	366.071	0.0300021
$531$	−1181.47	−0.0965560
$532$	12553.3	1.02304
$533$	−2529.09	−0.205529
$534$	−20471.1	−1.65894
$535$	1149.20	0.0928677
$536$	3549.02	0.285997
$537$	10207.2	0.820251
$538$	29650.0	2.37603
$539$	−2011.74	−0.160764
$540$	−1034.54	−0.0824435
$541$	−6460.72	−0.513434	−0.256717	−	0.966487i	$-0.582641\pi$
$541$	−6460.72	−0.513434	−0.256717	+	0.966487i	$0.582641\pi$
$542$	4136.56	0.327824
$543$	2596.97	0.205242
$544$	−25958.7	−2.04590
$545$	4889.96	0.384335
$546$	4951.40	0.388096
$547$	7900.33	0.617539	0.308770	−	0.951137i	$-0.400083\pi$
$547$	7900.33	0.617539	0.308770	+	0.951137i	$0.400083\pi$
$548$	−6104.21	−0.475837
$549$	549.000	0.0426790
$550$	5315.41	0.412091
$551$	19043.7	1.47239
$552$	−1159.98	−0.0894420
$553$	−14882.6	−1.14444
$554$	−13757.5	−1.05505
$555$	−1795.68	−0.137338
$556$	−13302.8	−1.01468
$557$	6515.89	0.495668	0.247834	−	0.968802i	$-0.420281\pi$
$557$	6515.89	0.495668	0.247834	+	0.968802i	$0.420281\pi$
$558$	9145.10	0.693804
$559$	9087.87	0.687613
$560$	1651.44	0.124618
$561$	3474.60	0.261493
$562$	−23021.4	−1.72794
$563$	3038.72	0.227472	0.113736	−	0.993511i	$-0.463718\pi$
$563$	3038.72	0.227472	0.113736	+	0.993511i	$0.463718\pi$
$564$	10765.8	0.803759
$565$	1579.40	0.117603
$566$	16389.4	1.21713
$567$	−1024.94	−0.0759147
$568$	6602.46	0.487734
$569$	−5904.56	−0.435030	−0.217515	−	0.976057i	$-0.569795\pi$
$569$	−5904.56	−0.435030	−0.217515	+	0.976057i	$0.569795\pi$
$570$	−4362.94	−0.320602
$571$	−8991.80	−0.659011	−0.329505	−	0.944154i	$-0.606882\pi$
$571$	−8991.80	−0.659011	−0.329505	+	0.944154i	$0.606882\pi$
$572$	−3531.20	−0.258124
$573$	3931.61	0.286641
$574$	4568.47	0.332202
$575$	3829.70	0.277756
$576$	−6970.22	−0.504212
$577$	−9719.70	−0.701276	−0.350638	−	0.936511i	$-0.614035\pi$
$577$	−9719.70	−0.701276	−0.350638	+	0.936511i	$0.614035\pi$
$578$	−26637.8	−1.91693
$579$	3655.41	0.262373
$580$	−7811.28	−0.559217
$581$	−12894.5	−0.920745
$582$	−10395.9	−0.740420
$583$	−258.650	−0.0183743
$584$	−5938.95	−0.420814
$585$	−981.512	−0.0693684
$586$	−28087.6	−1.98002
$587$	4304.16	0.302643	0.151322	−	0.988485i	$-0.451647\pi$
$587$	4304.16	0.302643	0.151322	+	0.988485i	$0.451647\pi$
$588$	5826.81	0.408663
$589$	21997.2	1.53884
$590$	2043.73	0.142608
$591$	8241.06	0.573590
$592$	−6001.35	−0.416645
$593$	−15277.0	−1.05793	−0.528965	−	0.848644i	$-0.677420\pi$
$593$	−15277.0	−1.05793	−0.528965	+	0.848644i	$0.677420\pi$
$594$	1281.59	0.0885255
$595$	4806.83	0.331195
$596$	−37157.6	−2.55375
$597$	−15792.7	−1.08267
$598$	−4460.71	−0.305037
$599$	22551.0	1.53824	0.769121	−	0.639103i	$-0.220694\pi$
$599$	22551.0	1.53824	0.769121	+	0.639103i	$0.220694\pi$
$600$	−3798.31	−0.258442
$601$	21171.4	1.43694	0.718470	−	0.695558i	$-0.244843\pi$
$601$	21171.4	1.43694	0.718470	+	0.695558i	$0.244843\pi$
$602$	−16416.1	−1.11141
$603$	−2825.11	−0.190791
$604$	−8719.41	−0.587397
$605$	436.555	0.0293363
$606$	−10249.0	−0.687026
$607$	−5002.36	−0.334497	−0.167248	−	0.985915i	$-0.553488\pi$
$607$	−5002.36	−0.334497	−0.167248	+	0.985915i	$0.553488\pi$
$608$	−23030.6	−1.53621
$609$	−7738.82	−0.514931
$610$	−949.674	−0.0630347
$611$	10213.9	0.676287
$612$	−10063.8	−0.664716
$613$	7060.47	0.465203	0.232602	−	0.972572i	$-0.425276\pi$
$613$	7060.47	0.465203	0.232602	+	0.972572i	$0.425276\pi$
$614$	13065.3	0.858747
$615$	−905.604	−0.0593780
$616$	1573.71	0.102933
$617$	−23003.4	−1.50094	−0.750470	−	0.660904i	$-0.770173\pi$
$617$	−23003.4	−1.50094	−0.750470	+	0.660904i	$0.770173\pi$
$618$	−12591.1	−0.819558
$619$	−12547.0	−0.814709	−0.407355	−	0.913270i	$-0.633549\pi$
$619$	−12547.0	−0.814709	−0.407355	+	0.913270i	$0.633549\pi$
$620$	−9022.73	−0.584454
$621$	923.371	0.0596676
$622$	21876.0	1.41021
$623$	20009.9	1.28680
$624$	−3280.31	−0.210444
$625$	10913.1	0.698439
$626$	−9348.40	−0.596864
$627$	3082.67	0.196348
$628$	1966.61	0.124962
$629$	−17468.1	−1.10731
$630$	1772.97	0.112122
$631$	−9083.20	−0.573053	−0.286527	−	0.958072i	$-0.592501\pi$
$631$	−9083.20	−0.573053	−0.286527	+	0.958072i	$0.592501\pi$
$632$	−13297.8	−0.836961
$633$	10140.0	0.636697
$634$	23996.7	1.50320
$635$	2929.05	0.183048
$636$	749.155	0.0467075
$637$	5528.14	0.343851
$638$	9676.60	0.600470
$639$	−5255.72	−0.325372
$640$	4941.27	0.305189
$641$	8537.40	0.526064	0.263032	−	0.964787i	$-0.415278\pi$
$641$	8537.40	0.526064	0.263032	+	0.964787i	$0.415278\pi$
$642$	4123.39	0.253485
$643$	27911.0	1.71182	0.855912	−	0.517122i	$-0.172997\pi$
$643$	27911.0	1.71182	0.855912	+	0.517122i	$0.172997\pi$
$644$	4595.77	0.281209
$645$	3254.14	0.198654
$646$	−42441.9	−2.58491
$647$	−4186.94	−0.254414	−0.127207	−	0.991876i	$-0.540601\pi$
$647$	−4186.94	−0.254414	−0.127207	+	0.991876i	$0.540601\pi$
$648$	−915.801	−0.0555186
$649$	−1444.01	−0.0873382
$650$	−14606.4	−0.881402
$651$	−8939.04	−0.538170
$652$	−6941.93	−0.416974
$653$	−613.514	−0.0367667	−0.0183833	−	0.999831i	$-0.505852\pi$
$653$	−613.514	−0.0367667	−0.0183833	+	0.999831i	$0.505852\pi$
$654$	17545.5	1.04905
$655$	5349.25	0.319103
$656$	−3026.61	−0.180136
$657$	4727.55	0.280730
$658$	−18450.1	−1.09310
$659$	12644.9	0.747461	0.373730	−	0.927537i	$-0.378078\pi$
$659$	12644.9	0.747461	0.373730	+	0.927537i	$0.378078\pi$
$660$	−1264.44	−0.0745730
$661$	10426.2	0.613514	0.306757	−	0.951788i	$-0.400756\pi$
$661$	10426.2	0.613514	0.306757	+	0.951788i	$0.400756\pi$
$662$	10137.1	0.595152
$663$	−9547.98	−0.559296
$664$	−11521.4	−0.673368
$665$	4264.63	0.248685
$666$	−6443.02	−0.374868
$667$	6971.90	0.404727
$668$	−4123.55	−0.238840
$669$	−9873.52	−0.570601
$670$	4886.94	0.281789
$671$	671.000	0.0386046
$672$	9358.99	0.537249
$673$	4189.51	0.239961	0.119981	−	0.992776i	$-0.461717\pi$
$673$	4189.51	0.239961	0.119981	+	0.992776i	$0.461717\pi$
$674$	−47675.8	−2.72463
$675$	3023.54	0.172409
$676$	−13628.9	−0.775428
$677$	−18725.3	−1.06303	−0.531516	−	0.847049i	$-0.678377\pi$
$677$	−18725.3	−1.06303	−0.531516	+	0.847049i	$0.678377\pi$
$678$	5666.97	0.321001
$679$	10161.7	0.574329
$680$	4294.97	0.242213
$681$	−13021.7	−0.732733
$682$	11177.3	0.627570
$683$	15122.2	0.847198	0.423599	−	0.905850i	$-0.360767\pi$
$683$	15122.2	0.847198	0.423599	+	0.905850i	$0.360767\pi$
$684$	−8928.65	−0.499116
$685$	−2073.73	−0.115669
$686$	−28714.3	−1.59813
$687$	4028.28	0.223709
$688$	10875.7	0.602661
$689$	710.755	0.0392999
$690$	−1597.27	−0.0881262
$691$	−16158.0	−0.889552	−0.444776	−	0.895642i	$-0.646717\pi$
$691$	−16158.0	−0.889552	−0.444776	+	0.895642i	$0.646717\pi$
$692$	−20711.6	−1.13777
$693$	−1252.71	−0.0686674
$694$	6875.21	0.376051
$695$	−4519.24	−0.246654
$696$	−6914.74	−0.376584
$697$	−8809.56	−0.478746
$698$	−50495.7	−2.73824
$699$	6677.37	0.361318
$700$	15048.7	0.812552
$701$	10654.9	0.574080	0.287040	−	0.957919i	$-0.407329\pi$
$701$	10654.9	0.574080	0.287040	+	0.957919i	$0.407329\pi$
$702$	−3521.72	−0.189343
$703$	−15497.7	−0.831448
$704$	−8519.16	−0.456077
$705$	3657.36	0.195382
$706$	−11555.7	−0.616009
$707$	10018.1	0.532912
$708$	4182.44	0.222014
$709$	−4192.66	−0.222085	−0.111043	−	0.993816i	$-0.535419\pi$
$709$	−4192.66	−0.222085	−0.111043	+	0.993816i	$0.535419\pi$
$710$	9091.47	0.480559
$711$	10585.4	0.558345
$712$	17879.1	0.941076
$713$	8053.17	0.422992
$714$	17247.2	0.904006
$715$	−1199.63	−0.0627461
$716$	−36134.1	−1.88603
$717$	10291.6	0.536048
$718$	3637.12	0.189048
$719$	21931.7	1.13757	0.568786	−	0.822485i	$-0.307413\pi$
$719$	21931.7	1.13757	0.568786	+	0.822485i	$0.307413\pi$
$720$	−1174.60	−0.0607981
$721$	12307.4	0.635715
$722$	−8057.20	−0.415316
$723$	−9172.81	−0.471840
$724$	−9193.38	−0.471919
$725$	22829.2	1.16946
$726$	1566.38	0.0800743
$727$	−23836.5	−1.21602	−0.608011	−	0.793929i	$-0.708032\pi$
$727$	−23836.5	−1.21602	−0.608011	+	0.793929i	$0.708032\pi$
$728$	−4324.45	−0.220158
$729$	729.000	0.0370370
$730$	−8177.84	−0.414624
$731$	31655.8	1.60168
$732$	−1943.49	−0.0981329
$733$	26286.5	1.32458	0.662288	−	0.749249i	$-0.269586\pi$
$733$	26286.5	1.32458	0.662288	+	0.749249i	$0.269586\pi$
$734$	−51461.1	−2.58783
$735$	1979.49	0.0993397
$736$	−8431.51	−0.422268
$737$	−3452.91	−0.172577
$738$	−3249.36	−0.162074
$739$	1342.89	0.0668460	0.0334230	−	0.999441i	$-0.489359\pi$
$739$	1342.89	0.0668460	0.0334230	+	0.999441i	$0.489359\pi$
$740$	6356.81	0.315785
$741$	−8470.98	−0.419959
$742$	−1283.89	−0.0635216
$743$	−32928.4	−1.62588	−0.812938	−	0.582350i	$-0.802133\pi$
$743$	−32928.4	−1.62588	−0.812938	+	0.582350i	$0.802133\pi$
$744$	−7987.15	−0.393579
$745$	−12623.2	−0.620777
$746$	22459.8	1.10230
$747$	9171.30	0.449211
$748$	−12300.2	−0.601258
$749$	−4030.48	−0.196623
$750$	−11068.4	−0.538879
$751$	−18120.2	−0.880447	−0.440224	−	0.897888i	$-0.645101\pi$
$751$	−18120.2	−0.880447	−0.440224	+	0.897888i	$0.645101\pi$
$752$	12223.2	0.592734
$753$	15609.4	0.755428
$754$	−26590.7	−1.28432
$755$	−2962.17	−0.142787
$756$	3628.35	0.174553
$757$	22768.1	1.09316	0.546579	−	0.837408i	$-0.315930\pi$
$757$	22768.1	1.09316	0.546579	+	0.837408i	$0.315930\pi$
$758$	−18857.0	−0.903586
$759$	1128.56	0.0539714
$760$	3810.50	0.181870
$761$	−24495.1	−1.16682	−0.583408	−	0.812179i	$-0.698281\pi$
$761$	−24495.1	−1.16682	−0.583408	+	0.812179i	$0.698281\pi$
$762$	10509.6	0.499636
$763$	−17150.1	−0.813730
$764$	−13918.1	−0.659082
$765$	−3418.90	−0.161582
$766$	−53439.2	−2.52067
$767$	3968.06	0.186804
$768$	−857.701	−0.0402990
$769$	−13881.0	−0.650926	−0.325463	−	0.945555i	$-0.605520\pi$
$769$	−13881.0	−0.650926	−0.325463	+	0.945555i	$0.605520\pi$
$770$	2166.97	0.101418
$771$	−3540.06	−0.165359
$772$	−12940.3	−0.603281
$773$	−16265.4	−0.756826	−0.378413	−	0.925637i	$-0.623530\pi$
$773$	−16265.4	−0.756826	−0.378413	+	0.925637i	$0.623530\pi$
$774$	11676.1	0.542232
$775$	26369.8	1.22223
$776$	9079.59	0.420023
$777$	6297.84	0.290777
$778$	−14696.2	−0.677231
$779$	−7815.85	−0.359476
$780$	3474.60	0.159501
$781$	−6423.65	−0.294310
$782$	−15538.0	−0.710533
$783$	5504.30	0.251223
$784$	6615.65	0.301369
$785$	668.099	0.0303764
$786$	19193.4	0.871002
$787$	−10621.9	−0.481107	−0.240553	−	0.970636i	$-0.577329\pi$
$787$	−10621.9	−0.481107	−0.240553	+	0.970636i	$0.577329\pi$
$788$	−29173.7	−1.31887
$789$	6107.02	0.275558
$790$	−18310.9	−0.824648
$791$	−5539.28	−0.248994
$792$	−1119.31	−0.0502185
$793$	−1843.87	−0.0825695
$794$	27951.2	1.24931
$795$	254.504	0.0113539
$796$	55907.0	2.48941
$797$	14025.2	0.623336	0.311668	−	0.950191i	$-0.399112\pi$
$797$	14025.2	0.623336	0.311668	+	0.950191i	$0.399112\pi$
$798$	15301.7	0.678792
$799$	35578.2	1.57530
$800$	−27608.7	−1.22014
$801$	−14232.2	−0.627802
$802$	−12262.2	−0.539893
$803$	5778.12	0.253930
$804$	10001.0	0.438692
$805$	1561.28	0.0683577
$806$	−30714.6	−1.34228
$807$	20613.6	0.899174
$808$	8951.29	0.389734
$809$	−5556.81	−0.241492	−0.120746	−	0.992683i	$-0.538529\pi$
$809$	−5556.81	−0.241492	−0.120746	+	0.992683i	$0.538529\pi$
$810$	−1261.04	−0.0547019
$811$	2388.02	0.103397	0.0516985	−	0.998663i	$-0.483537\pi$
$811$	2388.02	0.103397	0.0516985	+	0.998663i	$0.483537\pi$
$812$	27395.8	1.18400
$813$	2875.87	0.124060
$814$	−7874.80	−0.339081
$815$	−2358.32	−0.101360
$816$	−11426.3	−0.490196
$817$	28085.0	1.20266
$818$	−23495.4	−1.00428
$819$	3442.37	0.146870
$820$	3205.88	0.136529
$821$	−3002.07	−0.127616	−0.0638082	−	0.997962i	$-0.520325\pi$
$821$	−3002.07	−0.127616	−0.0638082	+	0.997962i	$0.520325\pi$
$822$	−7440.66	−0.315721
$823$	−1210.15	−0.0512552	−0.0256276	−	0.999672i	$-0.508158\pi$
$823$	−1210.15	−0.0512552	−0.0256276	+	0.999672i	$0.508158\pi$
$824$	10996.8	0.464917
$825$	3695.44	0.155950
$826$	−7167.79	−0.301936
$827$	−7937.56	−0.333756	−0.166878	−	0.985978i	$-0.553369\pi$
$827$	−7937.56	−0.333756	−0.166878	+	0.985978i	$0.553369\pi$
$828$	−3268.78	−0.137195
$829$	−32691.8	−1.36964	−0.684821	−	0.728711i	$-0.740120\pi$
$829$	−32691.8	−1.36964	−0.684821	+	0.728711i	$0.740120\pi$
$830$	−15864.7	−0.663462
$831$	−9564.65	−0.399271
$832$	23410.1	0.975481
$833$	19256.2	0.800945
$834$	−16215.3	−0.673249
$835$	−1400.86	−0.0580583
$836$	−10912.8	−0.451467
$837$	6357.96	0.262561
$838$	6792.22	0.279992
$839$	−2997.82	−0.123356	−0.0616782	−	0.998096i	$-0.519645\pi$
$839$	−2997.82	−0.123356	−0.0616782	+	0.998096i	$0.519645\pi$
$840$	−1548.48	−0.0636044
$841$	17171.1	0.704053
$842$	−8939.63	−0.365891
$843$	−16005.2	−0.653914
$844$	−35896.1	−1.46398
$845$	−4630.04	−0.188495
$846$	13122.8	0.533300
$847$	−1531.09	−0.0621120
$848$	850.577	0.0344445
$849$	11394.4	0.460607
$850$	−50878.5	−2.05308
$851$	−5673.72	−0.228546
$852$	18605.5	0.748138
$853$	−2298.08	−0.0922447	−0.0461224	−	0.998936i	$-0.514686\pi$
$853$	−2298.08	−0.0922447	−0.0461224	+	0.998936i	$0.514686\pi$
$854$	3330.71	0.133460
$855$	−3033.25	−0.121328
$856$	−3601.29	−0.143796
$857$	−3704.47	−0.147657	−0.0738286	−	0.997271i	$-0.523522\pi$
$857$	−3704.47	−0.147657	−0.0738286	+	0.997271i	$0.523522\pi$
$858$	−4304.33	−0.171267
$859$	11015.0	0.437517	0.218759	−	0.975779i	$-0.429799\pi$
$859$	11015.0	0.437517	0.218759	+	0.975779i	$0.429799\pi$
$860$	−11519.8	−0.456771
$861$	3176.14	0.125717
$862$	37001.7	1.46205
$863$	43147.9	1.70194	0.850968	−	0.525217i	$-0.176016\pi$
$863$	43147.9	1.70194	0.850968	+	0.525217i	$0.176016\pi$
$864$	−6656.66	−0.262111
$865$	−7036.16	−0.276574
$866$	13799.1	0.541470
$867$	−18519.5	−0.725438
$868$	31644.6	1.23743
$869$	12937.7	0.505042
$870$	−9521.48	−0.371044
$871$	9488.38	0.369118
$872$	−15323.9	−0.595105
$873$	−7227.57	−0.280202
$874$	−13785.3	−0.533519
$875$	10819.0	0.417998
$876$	−16735.8	−0.645490
$877$	−23982.5	−0.923410	−0.461705	−	0.887034i	$-0.652762\pi$
$877$	−23982.5	−0.923410	−0.461705	+	0.887034i	$0.652762\pi$
$878$	−14053.7	−0.540191
$879$	−19527.4	−0.749310
$880$	−1435.62	−0.0549940
$881$	45005.3	1.72107	0.860537	−	0.509388i	$-0.170128\pi$
$881$	45005.3	1.72107	0.860537	+	0.509388i	$0.170128\pi$
$882$	7102.54	0.271151
$883$	25047.4	0.954602	0.477301	−	0.878740i	$-0.341615\pi$
$883$	25047.4	0.954602	0.477301	+	0.878740i	$0.341615\pi$
$884$	33800.3	1.28600
$885$	1420.87	0.0539682
$886$	−63982.9	−2.42613
$887$	45321.3	1.71560	0.857802	−	0.513979i	$-0.171829\pi$
$887$	45321.3	1.71560	0.857802	+	0.513979i	$0.171829\pi$
$888$	5627.21	0.212654
$889$	−10272.8	−0.387557
$890$	24619.2	0.927232
$891$	891.000	0.0335013
$892$	34952.7	1.31200
$893$	31565.0	1.18285
$894$	−45292.9	−1.69443
$895$	−12275.5	−0.458464
$896$	−17330.1	−0.646158
$897$	−3101.23	−0.115437
$898$	45405.7	1.68731
$899$	48005.7	1.78096
$900$	−10703.5	−0.396426
$901$	2475.77	0.0915427
$902$	−3971.44	−0.146601
$903$	−11413.0	−0.420598
$904$	−4949.42	−0.182097
$905$	−3123.19	−0.114716
$906$	−10628.4	−0.389742
$907$	−36434.5	−1.33383	−0.666916	−	0.745133i	$-0.732386\pi$
$907$	−36434.5	−1.33383	−0.666916	+	0.745133i	$0.732386\pi$
$908$	46097.3	1.68479
$909$	−7125.44	−0.259996
$910$	−5954.70	−0.216919
$911$	−9498.84	−0.345456	−0.172728	−	0.984970i	$-0.555258\pi$
$911$	−9498.84	−0.345456	−0.172728	+	0.984970i	$0.555258\pi$
$912$	−10137.4	−0.368074
$913$	11209.4	0.406326
$914$	45734.7	1.65511
$915$	−660.244	−0.0238546
$916$	−14260.3	−0.514381
$917$	−18761.0	−0.675618
$918$	−12267.2	−0.441044
$919$	9424.82	0.338298	0.169149	−	0.985590i	$-0.445898\pi$
$919$	9424.82	0.338298	0.169149	+	0.985590i	$0.445898\pi$
$920$	1395.02	0.0499920
$921$	9083.38	0.324981
$922$	−44141.6	−1.57671
$923$	17651.8	0.629487
$924$	4434.65	0.157889
$925$	−18578.4	−0.660382
$926$	8356.15	0.296544
$927$	−8753.71	−0.310151
$928$	−50261.0	−1.77791
$929$	−53315.7	−1.88292	−0.941459	−	0.337128i	$-0.890544\pi$
$929$	−53315.7	−1.88292	−0.941459	+	0.337128i	$0.890544\pi$
$930$	−10998.2	−0.387789
$931$	17084.1	0.601406
$932$	−23638.2	−0.830789
$933$	15208.9	0.533674
$934$	−19556.3	−0.685120
$935$	−4178.66	−0.146157
$936$	3075.80	0.107410
$937$	−48316.0	−1.68454	−0.842270	−	0.539056i	$-0.818781\pi$
$937$	−48316.0	−1.68454	−0.842270	+	0.539056i	$0.818781\pi$
$938$	−17139.5	−0.596616
$939$	−6499.31	−0.225875
$940$	−12947.2	−0.449247
$941$	−28486.2	−0.986849	−0.493424	−	0.869789i	$-0.664255\pi$
$941$	−28486.2	−0.986849	−0.493424	+	0.869789i	$0.664255\pi$
$942$	2397.18	0.0829132
$943$	−2861.38	−0.0988118
$944$	4748.67	0.163725
$945$	1232.63	0.0424311
$946$	14270.7	0.490467
$947$	−47076.0	−1.61538	−0.807689	−	0.589608i	$-0.799282\pi$
$947$	−47076.0	−1.61538	−0.807689	+	0.589608i	$0.799282\pi$
$948$	−37472.8	−1.28382
$949$	−15877.9	−0.543118
$950$	−45139.5	−1.54160
$951$	16683.3	0.568866
$952$	−15063.4	−0.512822
$953$	16684.5	0.567118	0.283559	−	0.958955i	$-0.408485\pi$
$953$	16684.5	0.567118	0.283559	+	0.958955i	$0.408485\pi$
$954$	913.176	0.0309907
$955$	−4728.27	−0.160213
$956$	−36432.7	−1.23255
$957$	6727.48	0.227240
$958$	42900.1	1.44681
$959$	7273.01	0.244899
$960$	8382.60	0.281820
$961$	25659.9	0.861330
$962$	21639.5	0.725244
$963$	2866.71	0.0959279
$964$	32472.2	1.08492
$965$	−4396.11	−0.146648
$966$	5601.97	0.186584
$967$	−1388.51	−0.0461753	−0.0230876	−	0.999733i	$-0.507350\pi$
$967$	−1388.51	−0.0461753	−0.0230876	+	0.999733i	$0.507350\pi$
$968$	−1368.05	−0.0454243
$969$	−29507.0	−0.978225
$970$	12502.4	0.413844
$971$	11771.6	0.389053	0.194526	−	0.980897i	$-0.437683\pi$
$971$	11771.6	0.389053	0.194526	+	0.980897i	$0.437683\pi$
$972$	−2580.69	−0.0851603
$973$	15849.9	0.522226
$974$	19129.7	0.629317
$975$	−10154.9	−0.333554
$976$	−2206.60	−0.0723683
$977$	−23554.1	−0.771303	−0.385652	−	0.922644i	$-0.626023\pi$
$977$	−23554.1	−0.771303	−0.385652	+	0.922644i	$0.626023\pi$
$978$	−8461.79	−0.276665
$979$	−17394.9	−0.567868
$980$	−7007.50	−0.228415
$981$	12198.2	0.397000
$982$	29828.1	0.969302
$983$	36568.3	1.18652	0.593259	−	0.805011i	$-0.297841\pi$
$983$	36568.3	1.18652	0.593259	+	0.805011i	$0.297841\pi$
$984$	2837.93	0.0919408
$985$	−9910.95	−0.320598
$986$	−92623.4	−2.99161
$987$	−12827.1	−0.413670
$988$	29987.7	0.965623
$989$	10281.9	0.330583
$990$	−1541.27	−0.0494797
$991$	29525.0	0.946411	0.473205	−	0.880952i	$-0.343097\pi$
$991$	29525.0	0.946411	0.473205	+	0.880952i	$0.343097\pi$
$992$	−58056.0	−1.85814
$993$	7047.65	0.225227
$994$	−31885.7	−1.01746
$995$	18992.8	0.605138
$996$	−32466.8	−1.03288
$997$	31163.2	0.989917	0.494958	−	0.868917i	$-0.335183\pi$
$997$	31163.2	0.989917	0.494958	+	0.868917i	$0.335183\pi$
$998$	35346.8	1.12113
$999$	−4479.39	−0.141864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.7	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.7	✓	39	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-4.31511 q^{2} -3.00000 q^{3} +10.6201 q^{4} +3.60789 q^{5} +12.9453 q^{6} -12.6536 q^{7} -11.3062 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.31511 q^{2} -3.00000 q^{3} +10.6201 q^{4} +3.60789 q^{5} +12.9453 q^{6} -12.6536 q^{7} -11.3062 q^{8} +9.00000 q^{9} -15.5684 q^{10} +11.0000 q^{11} -31.8604 q^{12} -30.2273 q^{13} +54.6018 q^{14} -10.8237 q^{15} -36.1737 q^{16} -105.291 q^{17} -38.8360 q^{18} -93.4142 q^{19} +38.3163 q^{20} +37.9609 q^{21} -47.4662 q^{22} -34.1989 q^{23} +33.9186 q^{24} -111.983 q^{25} +130.434 q^{26} -27.0000 q^{27} -134.383 q^{28} -203.863 q^{29} +46.7053 q^{30} -235.480 q^{31} +246.543 q^{32} -33.0000 q^{33} +454.341 q^{34} -45.6529 q^{35} +95.5813 q^{36} +165.903 q^{37} +403.092 q^{38} +90.6820 q^{39} -40.7915 q^{40} +83.6688 q^{41} -163.805 q^{42} -300.651 q^{43} +116.822 q^{44} +32.4710 q^{45} +147.572 q^{46} -337.904 q^{47} +108.521 q^{48} -182.886 q^{49} +483.219 q^{50} +315.873 q^{51} -321.019 q^{52} -23.5137 q^{53} +116.508 q^{54} +39.6868 q^{55} +143.064 q^{56} +280.243 q^{57} +879.691 q^{58} -131.274 q^{59} -114.949 q^{60} +61.0000 q^{61} +1016.12 q^{62} -113.883 q^{63} -774.469 q^{64} -109.057 q^{65} +142.399 q^{66} -313.901 q^{67} -1118.20 q^{68} +102.597 q^{69} +196.997 q^{70} -583.968 q^{71} -101.756 q^{72} +525.284 q^{73} -715.891 q^{74} +335.949 q^{75} -992.072 q^{76} -139.190 q^{77} -391.302 q^{78} +1176.16 q^{79} -130.511 q^{80} +81.0000 q^{81} -361.040 q^{82} +1019.03 q^{83} +403.150 q^{84} -379.878 q^{85} +1297.34 q^{86} +611.589 q^{87} -124.368 q^{88} -1581.35 q^{89} -140.116 q^{90} +382.486 q^{91} -363.197 q^{92} +706.440 q^{93} +1458.09 q^{94} -337.028 q^{95} -739.629 q^{96} -803.064 q^{97} +789.171 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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