LMFDB - Embedded newform 1849.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.24346 q^{2} -0.263601 q^{3} +19.4939 q^{4} +17.3447 q^{5} +1.38218 q^{6} -21.1320 q^{7} -60.2678 q^{8} -26.9305 q^{9} +O(q^{10})$	\(q-5.24346 q^{2} -0.263601 q^{3} +19.4939 q^{4} +17.3447 q^{5} +1.38218 q^{6} -21.1320 q^{7} -60.2678 q^{8} -26.9305 q^{9} -90.9462 q^{10} +36.3168 q^{11} -5.13861 q^{12} -33.3499 q^{13} +110.805 q^{14} -4.57208 q^{15} +160.061 q^{16} -97.2404 q^{17} +141.209 q^{18} +102.339 q^{19} +338.115 q^{20} +5.57043 q^{21} -190.426 q^{22} -45.3534 q^{23} +15.8867 q^{24} +175.838 q^{25} +174.869 q^{26} +14.2161 q^{27} -411.945 q^{28} +39.2707 q^{29} +23.9735 q^{30} -95.4669 q^{31} -357.130 q^{32} -9.57314 q^{33} +509.876 q^{34} -366.528 q^{35} -524.980 q^{36} -253.143 q^{37} -536.611 q^{38} +8.79106 q^{39} -1045.33 q^{40} -119.918 q^{41} -29.2083 q^{42} +707.955 q^{44} -467.101 q^{45} +237.809 q^{46} -303.993 q^{47} -42.1922 q^{48} +103.562 q^{49} -922.000 q^{50} +25.6327 q^{51} -650.119 q^{52} +617.683 q^{53} -74.5418 q^{54} +629.903 q^{55} +1273.58 q^{56} -26.9767 q^{57} -205.914 q^{58} -507.907 q^{59} -89.1276 q^{60} +372.772 q^{61} +500.577 q^{62} +569.096 q^{63} +592.110 q^{64} -578.443 q^{65} +50.1964 q^{66} -386.618 q^{67} -1895.59 q^{68} +11.9552 q^{69} +1921.88 q^{70} -69.4996 q^{71} +1623.04 q^{72} +856.812 q^{73} +1327.35 q^{74} -46.3511 q^{75} +1994.99 q^{76} -767.447 q^{77} -46.0956 q^{78} +700.782 q^{79} +2776.20 q^{80} +723.376 q^{81} +628.787 q^{82} -774.745 q^{83} +108.589 q^{84} -1686.60 q^{85} -10.3518 q^{87} -2188.73 q^{88} +720.027 q^{89} +2449.23 q^{90} +704.750 q^{91} -884.113 q^{92} +25.1652 q^{93} +1593.97 q^{94} +1775.04 q^{95} +94.1398 q^{96} +797.619 q^{97} -543.025 q^{98} -978.029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * 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 $

$2$	−5.24346	−1.85384	−0.926922	−	0.375255i	$-0.877555\pi$
$2$	−5.24346	−1.85384	−0.926922	+	0.375255i	$0.877555\pi$
$3$	−0.263601	−0.0507301	−0.0253650	−	0.999678i	$-0.508075\pi$
$3$	−0.263601	−0.0507301	−0.0253650	+	0.999678i	$0.508075\pi$
$4$	19.4939	2.43674
$5$	17.3447	1.55136	0.775678	−	0.631129i	$-0.217408\pi$
$5$	17.3447	1.55136	0.775678	+	0.631129i	$0.217408\pi$
$6$	1.38218	0.0940456
$7$	−21.1320	−1.14102	−0.570511	−	0.821290i	$-0.693255\pi$
$7$	−21.1320	−1.14102	−0.570511	+	0.821290i	$0.693255\pi$
$8$	−60.2678	−2.66348
$9$	−26.9305	−0.997426
$10$	−90.9462	−2.87597
$11$	36.3168	0.995447	0.497724	−	0.867336i	$-0.334169\pi$
$11$	36.3168	0.995447	0.497724	+	0.867336i	$0.334169\pi$
$12$	−5.13861	−0.123616
$13$	−33.3499	−0.711507	−0.355753	−	0.934580i	$-0.615776\pi$
$13$	−33.3499	−0.711507	−0.355753	+	0.934580i	$0.615776\pi$
$14$	110.805	2.11528
$15$	−4.57208	−0.0787004
$16$	160.061	2.50095
$17$	−97.2404	−1.38731	−0.693654	−	0.720308i	$-0.744000\pi$
$17$	−97.2404	−1.38731	−0.693654	+	0.720308i	$0.744000\pi$
$18$	141.209	1.84907
$19$	102.339	1.23570	0.617848	−	0.786298i	$-0.288005\pi$
$19$	102.339	1.23570	0.617848	+	0.786298i	$0.288005\pi$
$20$	338.115	3.78024
$21$	5.57043	0.0578841
$22$	−190.426	−1.84540
$23$	−45.3534	−0.411167	−0.205583	−	0.978640i	$-0.565909\pi$
$23$	−45.3534	−0.411167	−0.205583	+	0.978640i	$0.565909\pi$
$24$	15.8867	0.135119
$25$	175.838	1.40670
$26$	174.869	1.31902
$27$	14.2161	0.101330
$28$	−411.945	−2.78037
$29$	39.2707	0.251462	0.125731	−	0.992064i	$-0.459872\pi$
$29$	39.2707	0.251462	0.125731	+	0.992064i	$0.459872\pi$
$30$	23.9735	0.145898
$31$	−95.4669	−0.553108	−0.276554	−	0.960998i	$-0.589193\pi$
$31$	−95.4669	−0.553108	−0.276554	+	0.960998i	$0.589193\pi$
$32$	−357.130	−1.97288
$33$	−9.57314	−0.0504991
$34$	509.876	2.57185
$35$	−366.528	−1.77013
$36$	−524.980	−2.43047
$37$	−253.143	−1.12477	−0.562384	−	0.826876i	$-0.690116\pi$
$37$	−253.143	−1.12477	−0.562384	+	0.826876i	$0.690116\pi$
$38$	−536.611	−2.29079
$39$	8.79106	0.0360948
$40$	−1045.33	−4.13201
$41$	−119.918	−0.456783	−0.228391	−	0.973569i	$-0.573347\pi$
$41$	−119.918	−0.456783	−0.228391	+	0.973569i	$0.573347\pi$
$42$	−29.2083	−0.107308
$43$	0	0
$43$	0	0
$44$	707.955	2.42564
$45$	−467.101	−1.54736
$46$	237.809	0.762238
$47$	−303.993	−0.943444	−0.471722	−	0.881747i	$-0.656367\pi$
$47$	−303.993	−0.943444	−0.471722	+	0.881747i	$0.656367\pi$
$48$	−42.1922	−0.126873
$49$	103.562	0.301931
$50$	−922.000	−2.60781
$51$	25.6327	0.0703783
$52$	−650.119	−1.73375
$53$	617.683	1.60086	0.800428	−	0.599429i	$-0.204606\pi$
$53$	617.683	1.60086	0.800428	+	0.599429i	$0.204606\pi$
$54$	−74.5418	−0.187849
$55$	629.903	1.54429
$56$	1273.58	3.03909
$57$	−26.9767	−0.0626869
$58$	−205.914	−0.466170
$59$	−507.907	−1.12074	−0.560372	−	0.828241i	$-0.689342\pi$
$59$	−507.907	−1.12074	−0.560372	+	0.828241i	$0.689342\pi$
$60$	−89.1276	−0.191772
$61$	372.772	0.782435	0.391217	−	0.920298i	$-0.372054\pi$
$61$	372.772	0.782435	0.391217	+	0.920298i	$0.372054\pi$
$62$	500.577	1.02538
$63$	569.096	1.13809
$64$	592.110	1.15647
$65$	−578.443	−1.10380
$66$	50.1964	0.0936174
$67$	−386.618	−0.704969	−0.352485	−	0.935818i	$-0.614663\pi$
$67$	−386.618	−0.704969	−0.352485	+	0.935818i	$0.614663\pi$
$68$	−1895.59	−3.38051
$69$	11.9552	0.0208585
$70$	1921.88	3.28155
$71$	−69.4996	−0.116170	−0.0580851	−	0.998312i	$-0.518499\pi$
$71$	−69.4996	−0.116170	−0.0580851	+	0.998312i	$0.518499\pi$
$72$	1623.04	2.65663
$73$	856.812	1.37373	0.686864	−	0.726785i	$-0.258987\pi$
$73$	856.812	1.37373	0.686864	+	0.726785i	$0.258987\pi$
$74$	1327.35	2.08515
$75$	−46.3511	−0.0713622
$76$	1994.99	3.01106
$77$	−767.447	−1.13583
$78$	−46.0956	−0.0669141
$79$	700.782	0.998027	0.499014	−	0.866594i	$-0.333696\pi$
$79$	700.782	0.998027	0.499014	+	0.866594i	$0.333696\pi$
$80$	2776.20	3.87986
$81$	723.376	0.992286
$82$	628.787	0.846804
$83$	−774.745	−1.02457	−0.512285	−	0.858815i	$-0.671201\pi$
$83$	−774.745	−1.02457	−0.512285	+	0.858815i	$0.671201\pi$
$84$	108.589	0.141048
$85$	−1686.60	−2.15221
$86$	0	0
$87$	−10.3518	−0.0127567
$88$	−2188.73	−2.65136
$89$	720.027	0.857558	0.428779	−	0.903409i	$-0.358944\pi$
$89$	720.027	0.857558	0.428779	+	0.903409i	$0.358944\pi$
$90$	2449.23	2.86857
$91$	704.750	0.811845
$92$	−884.113	−1.00190
$93$	25.1652	0.0280592
$94$	1593.97	1.74900
$95$	1775.04	1.91700
$96$	94.1398	0.100084
$97$	797.619	0.834907	0.417454	−	0.908698i	$-0.362923\pi$
$97$	797.619	0.834907	0.417454	+	0.908698i	$0.362923\pi$
$98$	−543.025	−0.559733
$99$	−978.029	−0.992885
$100$	3427.77	3.42777
$101$	918.843	0.905231	0.452615	−	0.891706i	$-0.350491\pi$
$101$	918.843	0.905231	0.452615	+	0.891706i	$0.350491\pi$
$102$	−134.404	−0.130470
$103$	853.738	0.816712	0.408356	−	0.912823i	$-0.366102\pi$
$103$	853.738	0.816712	0.408356	+	0.912823i	$0.366102\pi$
$104$	2009.92	1.89509
$105$	96.6173	0.0897989
$106$	−3238.80	−2.96774
$107$	−1295.90	−1.17083	−0.585417	−	0.810732i	$-0.699069\pi$
$107$	−1295.90	−1.17083	−0.585417	+	0.810732i	$0.699069\pi$
$108$	277.128	0.246913
$109$	−699.409	−0.614598	−0.307299	−	0.951613i	$-0.599425\pi$
$109$	−699.409	−0.614598	−0.307299	+	0.951613i	$0.599425\pi$
$110$	−3302.87	−2.86288
$111$	66.7288	0.0570596
$112$	−3382.40	−2.85364
$113$	1001.50	0.833748	0.416874	−	0.908964i	$-0.363126\pi$
$113$	1001.50	0.833748	0.416874	+	0.908964i	$0.363126\pi$
$114$	141.451	0.116212
$115$	−786.640	−0.637866
$116$	765.539	0.612746
$117$	898.129	0.709676
$118$	2663.19	2.07768
$119$	2054.89	1.58295
$120$	275.549	0.209617
$121$	−12.0919	−0.00908482
$122$	−1954.61	−1.45051
$123$	31.6106	0.0231726
$124$	−1861.02	−1.34778
$125$	881.771	0.630944
$126$	−2984.03	−2.10983
$127$	−146.087	−0.102072	−0.0510359	−	0.998697i	$-0.516252\pi$
$127$	−146.087	−0.102072	−0.0510359	+	0.998697i	$0.516252\pi$
$128$	−247.671	−0.171025
$129$	0	0
$130$	3033.04	2.04627
$131$	964.255	0.643109	0.321555	−	0.946891i	$-0.395795\pi$
$131$	964.255	0.643109	0.321555	+	0.946891i	$0.395795\pi$
$132$	−186.618	−0.123053
$133$	−2162.63	−1.40996
$134$	2027.22	1.30690
$135$	246.575	0.157198
$136$	5860.46	3.69508
$137$	−1714.68	−1.06930	−0.534652	−	0.845072i	$-0.679557\pi$
$137$	−1714.68	−1.06930	−0.534652	+	0.845072i	$0.679557\pi$
$138$	−62.6866	−0.0386684
$139$	2374.12	1.44871	0.724354	−	0.689428i	$-0.242138\pi$
$139$	2374.12	1.44871	0.724354	+	0.689428i	$0.242138\pi$
$140$	−7145.06	−4.31334
$141$	80.1328	0.0478610
$142$	364.418	0.215361
$143$	−1211.16	−0.708268
$144$	−4310.51	−2.49451
$145$	681.138	0.390106
$146$	−4492.66	−2.54668
$147$	−27.2992	−0.0153170
$148$	−4934.74	−2.74077
$149$	1191.49	0.655103	0.327552	−	0.944833i	$-0.393776\pi$
$149$	1191.49	0.655103	0.327552	+	0.944833i	$0.393776\pi$
$150$	243.040	0.132294
$151$	1723.48	0.928842	0.464421	−	0.885614i	$-0.346262\pi$
$151$	1723.48	0.928842	0.464421	+	0.885614i	$0.346262\pi$
$152$	−6167.75	−3.29125
$153$	2618.73	1.38374
$154$	4024.08	2.10565
$155$	−1655.84	−0.858068
$156$	171.372	0.0879535
$157$	−2681.58	−1.36314	−0.681570	−	0.731753i	$-0.738703\pi$
$157$	−2681.58	−1.36314	−0.681570	+	0.731753i	$0.738703\pi$
$158$	−3674.53	−1.85019
$159$	−162.822	−0.0812115
$160$	−6194.30	−3.06064
$161$	958.408	0.469150
$162$	−3793.00	−1.83954
$163$	1996.74	0.959487	0.479744	−	0.877409i	$-0.340730\pi$
$163$	1996.74	0.959487	0.479744	+	0.877409i	$0.340730\pi$
$164$	−2337.68	−1.11306
$165$	−166.043	−0.0783421
$166$	4062.35	1.89939
$167$	−685.126	−0.317465	−0.158732	−	0.987322i	$-0.550741\pi$
$167$	−685.126	−0.317465	−0.158732	+	0.987322i	$0.550741\pi$
$168$	−335.717	−0.154173
$169$	−1084.79	−0.493758
$170$	8843.64	3.98986
$171$	−2756.05	−1.23251
$172$	0	0
$173$	−1233.93	−0.542278	−0.271139	−	0.962540i	$-0.587400\pi$
$173$	−1233.93	−0.542278	−0.271139	+	0.962540i	$0.587400\pi$
$174$	54.2793	0.0236489
$175$	−3715.81	−1.60508
$176$	5812.89	2.48956
$177$	133.885	0.0568554
$178$	−3775.43	−1.58978
$179$	−946.070	−0.395042	−0.197521	−	0.980299i	$-0.563289\pi$
$179$	−946.070	−0.395042	−0.197521	+	0.980299i	$0.563289\pi$
$180$	−9105.62	−3.77052
$181$	−1088.54	−0.447019	−0.223510	−	0.974702i	$-0.571751\pi$
$181$	−1088.54	−0.447019	−0.223510	+	0.974702i	$0.571751\pi$
$182$	−3695.33	−1.50503
$183$	−98.2630	−0.0396930
$184$	2733.35	1.09514
$185$	−4390.69	−1.74492
$186$	−131.953	−0.0520174
$187$	−3531.46	−1.38099
$188$	−5926.00	−2.29892
$189$	−300.416	−0.115619
$190$	−9307.35	−3.55382
$191$	−260.032	−0.0985094	−0.0492547	−	0.998786i	$-0.515685\pi$
$191$	−260.032	−0.0985094	−0.0492547	+	0.998786i	$0.515685\pi$
$192$	−156.081	−0.0586676
$193$	4207.27	1.56915	0.784575	−	0.620033i	$-0.212881\pi$
$193$	4207.27	1.56915	0.784575	+	0.620033i	$0.212881\pi$
$194$	−4182.29	−1.54779
$195$	152.478	0.0559959
$196$	2018.83	0.735727
$197$	662.600	0.239636	0.119818	−	0.992796i	$-0.461769\pi$
$197$	662.600	0.239636	0.119818	+	0.992796i	$0.461769\pi$
$198$	5128.26	1.84065
$199$	−3359.63	−1.19677	−0.598387	−	0.801207i	$-0.704191\pi$
$199$	−3359.63	−1.19677	−0.598387	+	0.801207i	$0.704191\pi$
$200$	−10597.4	−3.74674
$201$	101.913	0.0357631
$202$	−4817.92	−1.67816
$203$	−829.869	−0.286923
$204$	499.680	0.171493
$205$	−2079.95	−0.708633
$206$	−4476.54	−1.51406
$207$	1221.39	0.410108
$208$	−5338.00	−1.77944
$209$	3716.63	1.23007
$210$	−506.609	−0.166473
$211$	4043.95	1.31942	0.659708	−	0.751522i	$-0.270680\pi$
$211$	4043.95	1.31942	0.659708	+	0.751522i	$0.270680\pi$
$212$	12041.0	3.90086
$213$	18.3202	0.00589332
$214$	6795.00	2.17054
$215$	0	0
$216$	−856.775	−0.269890
$217$	2017.41	0.631109
$218$	3667.32	1.13937
$219$	−225.857	−0.0696894
$220$	12279.3	3.76303
$221$	3242.95	0.987080
$222$	−349.890	−0.105780
$223$	−296.002	−0.0888869	−0.0444435	−	0.999012i	$-0.514151\pi$
$223$	−296.002	−0.0888869	−0.0444435	+	0.999012i	$0.514151\pi$
$224$	7546.87	2.25110
$225$	−4735.41	−1.40308
$226$	−5251.34	−1.54564
$227$	1851.46	0.541347	0.270674	−	0.962671i	$-0.412754\pi$
$227$	1851.46	0.541347	0.270674	+	0.962671i	$0.412754\pi$
$228$	−525.881	−0.152751
$229$	−2320.62	−0.669656	−0.334828	−	0.942279i	$-0.608678\pi$
$229$	−2320.62	−0.669656	−0.334828	+	0.942279i	$0.608678\pi$
$230$	4124.72	1.18250
$231$	202.300	0.0576206
$232$	−2366.76	−0.669764
$233$	6543.25	1.83975	0.919876	−	0.392208i	$-0.128289\pi$
$233$	6543.25	1.83975	0.919876	+	0.392208i	$0.128289\pi$
$234$	−4709.31	−1.31563
$235$	−5272.65	−1.46362
$236$	−9901.09	−2.73096
$237$	−184.727	−0.0506300
$238$	−10774.7	−2.93454
$239$	6225.87	1.68501	0.842506	−	0.538687i	$-0.181079\pi$
$239$	6225.87	1.68501	0.842506	+	0.538687i	$0.181079\pi$
$240$	−731.810	−0.196826
$241$	−1357.58	−0.362862	−0.181431	−	0.983404i	$-0.558073\pi$
$241$	−1357.58	−0.362862	−0.181431	+	0.983404i	$0.558073\pi$
$242$	63.4034	0.0168418
$243$	−574.519	−0.151668
$244$	7266.77	1.90659
$245$	1796.26	0.468403
$246$	−165.749	−0.0429584
$247$	−3413.00	−0.879206
$248$	5753.58	1.47320
$249$	204.224	0.0519765
$250$	−4623.53	−1.16967
$251$	−808.999	−0.203440	−0.101720	−	0.994813i	$-0.532435\pi$
$251$	−808.999	−0.203440	−0.101720	+	0.994813i	$0.532435\pi$
$252$	11093.9	2.77321
$253$	−1647.09	−0.409295
$254$	766.001	0.189225
$255$	444.591	0.109182
$256$	−3438.23	−0.839412
$257$	2783.54	0.675612	0.337806	−	0.941216i	$-0.390315\pi$
$257$	2783.54	0.675612	0.337806	+	0.941216i	$0.390315\pi$
$258$	0	0
$259$	5349.42	1.28339
$260$	−11276.1	−2.68967
$261$	−1057.58	−0.250814
$262$	−5056.03	−1.19222
$263$	717.814	0.168298	0.0841488	−	0.996453i	$-0.473183\pi$
$263$	717.814	0.168298	0.0841488	+	0.996453i	$0.473183\pi$
$264$	576.952	0.134504
$265$	10713.5	2.48350
$266$	11339.7	2.61384
$267$	−189.800	−0.0435040
$268$	−7536.70	−1.71782
$269$	−63.3056	−0.0143487	−0.00717437	−	0.999974i	$-0.502284\pi$
$269$	−63.3056	−0.0143487	−0.00717437	+	0.999974i	$0.502284\pi$
$270$	−1292.90	−0.291421
$271$	1613.82	0.361745	0.180872	−	0.983507i	$-0.442108\pi$
$271$	1613.82	0.361745	0.180872	+	0.983507i	$0.442108\pi$
$272$	−15564.4	−3.46959
$273$	−185.773	−0.0411850
$274$	8990.84	1.98232
$275$	6385.87	1.40030
$276$	233.053	0.0508267
$277$	−3900.82	−0.846128	−0.423064	−	0.906100i	$-0.639045\pi$
$277$	−3900.82	−0.846128	−0.423064	+	0.906100i	$0.639045\pi$
$278$	−12448.6	−2.68568
$279$	2570.97	0.551685
$280$	22089.8	4.71472
$281$	6601.81	1.40153	0.700766	−	0.713391i	$-0.252842\pi$
$281$	6601.81	1.40153	0.700766	+	0.713391i	$0.252842\pi$
$282$	−420.173	−0.0887268
$283$	−784.085	−0.164696	−0.0823481	−	0.996604i	$-0.526242\pi$
$283$	−784.085	−0.164696	−0.0823481	+	0.996604i	$0.526242\pi$
$284$	−1354.82	−0.283076
$285$	−467.903	−0.0972497
$286$	6350.67	1.31302
$287$	2534.12	0.521199
$288$	9617.68	1.96780
$289$	4542.69	0.924626
$290$	−3571.52	−0.723196
$291$	−210.253	−0.0423549
$292$	16702.6	3.34742
$293$	6862.21	1.36824	0.684120	−	0.729369i	$-0.260186\pi$
$293$	6862.21	1.36824	0.684120	+	0.729369i	$0.260186\pi$
$294$	143.142	0.0283953
$295$	−8809.50	−1.73867
$296$	15256.4	2.99580
$297$	516.285	0.100868
$298$	−6247.51	−1.21446
$299$	1512.53	0.292548
$300$	−903.564	−0.173891
$301$	0	0
$302$	−9037.03	−1.72193
$303$	−242.208	−0.0459224
$304$	16380.5	3.09041
$305$	6465.61	1.21383
$306$	−13731.2	−2.56523
$307$	2420.09	0.449908	0.224954	−	0.974369i	$-0.427777\pi$
$307$	2420.09	0.449908	0.224954	+	0.974369i	$0.427777\pi$
$308$	−14960.5	−2.76771
$309$	−225.046	−0.0414318
$310$	8682.35	1.59072
$311$	8914.06	1.62530	0.812652	−	0.582749i	$-0.198023\pi$
$311$	8914.06	1.62530	0.812652	+	0.582749i	$0.198023\pi$
$312$	−529.818	−0.0961379
$313$	−3386.93	−0.611632	−0.305816	−	0.952091i	$-0.598929\pi$
$313$	−3386.93	−0.611632	−0.305816	+	0.952091i	$0.598929\pi$
$314$	14060.7	2.52705
$315$	9870.79	1.76558
$316$	13661.0	2.43193
$317$	−8460.23	−1.49897	−0.749486	−	0.662020i	$-0.769699\pi$
$317$	−8460.23	−1.49897	−0.749486	+	0.662020i	$0.769699\pi$
$318$	853.751	0.150553
$319$	1426.19	0.250317
$320$	10270.0	1.79409
$321$	341.601	0.0593965
$322$	−5025.38	−0.869731
$323$	−9951.49	−1.71429
$324$	14101.4	2.41794
$325$	−5864.18	−1.00088
$326$	−10469.8	−1.77874
$327$	184.365	0.0311786
$328$	7227.21	1.21663
$329$	6423.98	1.07649
$330$	870.641	0.145234
$331$	−2691.35	−0.446919	−0.223459	−	0.974713i	$-0.571735\pi$
$331$	−2691.35	−0.446919	−0.223459	+	0.974713i	$0.571735\pi$
$332$	−15102.8	−2.49661
$333$	6817.27	1.12187
$334$	3592.43	0.588530
$335$	−6705.77	−1.09366
$336$	891.606	0.144765
$337$	−2370.03	−0.383098	−0.191549	−	0.981483i	$-0.561351\pi$
$337$	−2370.03	−0.383098	−0.191549	+	0.981483i	$0.561351\pi$
$338$	5688.04	0.915350
$339$	−263.997	−0.0422961
$340$	−32878.5	−5.24437
$341$	−3467.05	−0.550590
$342$	14451.2	2.28489
$343$	5059.80	0.796512
$344$	0	0
$345$	207.359	0.0323590
$346$	6470.07	1.00530
$347$	4030.27	0.623505	0.311752	−	0.950163i	$-0.399084\pi$
$347$	4030.27	0.623505	0.311752	+	0.950163i	$0.399084\pi$
$348$	−201.797	−0.0310846
$349$	−8845.92	−1.35677	−0.678383	−	0.734708i	$-0.737319\pi$
$349$	−8845.92	−1.35677	−0.678383	+	0.734708i	$0.737319\pi$
$350$	19483.7	2.97557
$351$	−474.107	−0.0720967
$352$	−12969.8	−1.96390
$353$	3480.43	0.524772	0.262386	−	0.964963i	$-0.415491\pi$
$353$	3480.43	0.524772	0.262386	+	0.964963i	$0.415491\pi$
$354$	−702.021	−0.105401
$355$	−1205.45	−0.180221
$356$	14036.1	2.08964
$357$	−541.670	−0.0803032
$358$	4960.68	0.732347
$359$	1957.76	0.287817	0.143909	−	0.989591i	$-0.454033\pi$
$359$	1957.76	0.287817	0.143909	+	0.989591i	$0.454033\pi$
$360$	28151.2	4.12138
$361$	3614.30	0.526942
$362$	5707.71	0.828703
$363$	3.18744	0.000460874 0
$364$	13738.3	1.97825
$365$	14861.1	2.13114
$366$	515.238	0.0735845
$367$	8421.02	1.19775	0.598874	−	0.800843i	$-0.295615\pi$
$367$	8421.02	1.19775	0.598874	+	0.800843i	$0.295615\pi$
$368$	−7259.29	−1.02831
$369$	3229.46	0.455607
$370$	23022.4	3.23480
$371$	−13052.9	−1.82661
$372$	490.567	0.0683729
$373$	3156.93	0.438230	0.219115	−	0.975699i	$-0.429683\pi$
$373$	3156.93	0.438230	0.219115	+	0.975699i	$0.429683\pi$
$374$	18517.1	2.56014
$375$	−232.436	−0.0320078
$376$	18321.0	2.51285
$377$	−1309.67	−0.178917
$378$	1575.22	0.214340
$379$	−14495.4	−1.96458	−0.982291	−	0.187360i	$-0.940007\pi$
$379$	−14495.4	−1.96458	−0.982291	+	0.187360i	$0.940007\pi$
$380$	34602.4	4.67123
$381$	38.5087	0.00517811
$382$	1363.47	0.182621
$383$	−7817.26	−1.04293	−0.521467	−	0.853272i	$-0.674615\pi$
$383$	−7817.26	−1.04293	−0.521467	+	0.853272i	$0.674615\pi$
$384$	65.2863	0.00867611
$385$	−13311.1	−1.76207
$386$	−22060.7	−2.90896
$387$	0	0
$388$	15548.7	2.03445
$389$	−1394.45	−0.181752	−0.0908761	−	0.995862i	$-0.528967\pi$
$389$	−1394.45	−0.181752	−0.0908761	+	0.995862i	$0.528967\pi$
$390$	−799.514	−0.103808
$391$	4410.18	0.570415
$392$	−6241.47	−0.804189
$393$	−254.179	−0.0326250
$394$	−3474.32	−0.444248
$395$	12154.8	1.54830
$396$	−19065.6	−2.41940
$397$	−1061.24	−0.134161	−0.0670806	−	0.997748i	$-0.521368\pi$
$397$	−1061.24	−0.134161	−0.0670806	+	0.997748i	$0.521368\pi$
$398$	17616.1	2.21863
$399$	570.073	0.0715271
$400$	28144.8	3.51809
$401$	1869.08	0.232762	0.116381	−	0.993205i	$-0.462871\pi$
$401$	1869.08	0.232762	0.116381	+	0.993205i	$0.462871\pi$
$402$	−534.377	−0.0662993
$403$	3183.81	0.393540
$404$	17911.8	2.20581
$405$	12546.7	1.53939
$406$	4351.39	0.531911
$407$	−9193.34	−1.11965
$408$	−1544.82	−0.187451
$409$	−8954.10	−1.08252	−0.541261	−	0.840855i	$-0.682053\pi$
$409$	−8954.10	−1.08252	−0.541261	+	0.840855i	$0.682053\pi$
$410$	10906.1	1.31369
$411$	451.990	0.0542459
$412$	16642.7	1.99011
$413$	10733.1	1.27879
$414$	−6404.31	−0.760277
$415$	−13437.7	−1.58947
$416$	11910.2	1.40372
$417$	−625.822	−0.0734931
$418$	−19488.0	−2.28036
$419$	−13510.0	−1.57520	−0.787599	−	0.616188i	$-0.788676\pi$
$419$	−13510.0	−1.57520	−0.787599	+	0.616188i	$0.788676\pi$
$420$	1883.45	0.218816
$421$	13011.1	1.50623	0.753113	−	0.657891i	$-0.228551\pi$
$421$	13011.1	1.50623	0.753113	+	0.657891i	$0.228551\pi$
$422$	−21204.3	−2.44599
$423$	8186.67	0.941016
$424$	−37226.4	−4.26385
$425$	−17098.6	−1.95153
$426$	−96.0611	−0.0109253
$427$	−7877.42	−0.892775
$428$	−25262.1	−2.85302
$429$	319.263	0.0359305
$430$	0	0
$431$	4471.08	0.499685	0.249842	−	0.968287i	$-0.419621\pi$
$431$	4471.08	0.499685	0.249842	+	0.968287i	$0.419621\pi$
$432$	2275.45	0.253420
$433$	−7935.01	−0.880675	−0.440337	−	0.897832i	$-0.645141\pi$
$433$	−7935.01	−0.880675	−0.440337	+	0.897832i	$0.645141\pi$
$434$	−10578.2	−1.16998
$435$	−179.549	−0.0197901
$436$	−13634.2	−1.49761
$437$	−4641.42	−0.508076
$438$	1184.27	0.129193
$439$	7465.62	0.811650	0.405825	−	0.913951i	$-0.366984\pi$
$439$	7465.62	0.811650	0.405825	+	0.913951i	$0.366984\pi$
$440$	−37962.8	−4.11320
$441$	−2788.99	−0.301154
$442$	−17004.3	−1.82989
$443$	−991.443	−0.106332	−0.0531658	−	0.998586i	$-0.516931\pi$
$443$	−991.443	−0.106332	−0.0531658	+	0.998586i	$0.516931\pi$
$444$	1300.80	0.139039
$445$	12488.6	1.33038
$446$	1552.08	0.164782
$447$	−314.077	−0.0332334
$448$	−12512.5	−1.31955
$449$	10504.4	1.10408	0.552042	−	0.833817i	$-0.313849\pi$
$449$	10504.4	1.10408	0.552042	+	0.833817i	$0.313849\pi$
$450$	24829.9	2.60110
$451$	−4355.05	−0.454703
$452$	19523.2	2.03162
$453$	−454.313	−0.0471202
$454$	−9708.07	−1.00357
$455$	12223.7	1.25946
$456$	1625.83	0.166966
$457$	−14707.7	−1.50546	−0.752731	−	0.658329i	$-0.771264\pi$
$457$	−14707.7	−1.50546	−0.752731	+	0.658329i	$0.771264\pi$
$458$	12168.1	1.24144
$459$	−1382.38	−0.140575
$460$	−15334.7	−1.55431
$461$	13281.1	1.34179	0.670893	−	0.741554i	$-0.265911\pi$
$461$	13281.1	1.34179	0.670893	+	0.741554i	$0.265911\pi$
$462$	−1060.75	−0.106820
$463$	11026.5	1.10680	0.553398	−	0.832917i	$-0.313331\pi$
$463$	11026.5	1.10680	0.553398	+	0.832917i	$0.313331\pi$
$464$	6285.69	0.628892
$465$	436.482	0.0435298
$466$	−34309.3	−3.41061
$467$	280.075	0.0277523	0.0138761	−	0.999904i	$-0.495583\pi$
$467$	280.075	0.0277523	0.0138761	+	0.999904i	$0.495583\pi$
$468$	17508.0	1.72929
$469$	8170.03	0.804386
$470$	27647.0	2.71332
$471$	706.867	0.0691522
$472$	30610.5	2.98509
$473$	0	0
$474$	968.609	0.0938601
$475$	17995.1	1.73826
$476$	40057.7	3.85723
$477$	−16634.5	−1.59674
$478$	−32645.1	−3.12375
$479$	5514.63	0.526034	0.263017	−	0.964791i	$-0.415283\pi$
$479$	5514.63	0.526034	0.263017	+	0.964791i	$0.415283\pi$
$480$	1632.82	0.155266
$481$	8442.29	0.800281
$482$	7118.44	0.672689
$483$	−252.638	−0.0238000
$484$	−235.718	−0.0221373
$485$	13834.5	1.29524
$486$	3012.47	0.281169
$487$	−2316.89	−0.215581	−0.107791	−	0.994174i	$-0.534378\pi$
$487$	−2316.89	−0.215581	−0.107791	+	0.994174i	$0.534378\pi$
$488$	−22466.1	−2.08400
$489$	−526.342	−0.0486749
$490$	−9418.60	−0.868345
$491$	−12410.0	−1.14064	−0.570322	−	0.821421i	$-0.693182\pi$
$491$	−12410.0	−1.14064	−0.570322	+	0.821421i	$0.693182\pi$
$492$	616.214	0.0564656
$493$	−3818.70	−0.348855
$494$	17895.9	1.62991
$495$	−16963.6	−1.54032
$496$	−15280.5	−1.38329
$497$	1468.67	0.132553
$498$	−1070.84	−0.0963563
$499$	−1649.51	−0.147980	−0.0739901	−	0.997259i	$-0.523573\pi$
$499$	−1649.51	−0.147980	−0.0739901	+	0.997259i	$0.523573\pi$
$500$	17189.1	1.53744
$501$	180.600	0.0161050
$502$	4241.95	0.377147
$503$	18128.1	1.60694	0.803469	−	0.595346i	$-0.202985\pi$
$503$	18128.1	1.60694	0.803469	+	0.595346i	$0.202985\pi$
$504$	−34298.2	−3.03127
$505$	15937.0	1.40434
$506$	8636.44	0.758768
$507$	285.951	0.0250484
$508$	−2847.80	−0.248722
$509$	−5830.73	−0.507746	−0.253873	−	0.967238i	$-0.581704\pi$
$509$	−5830.73	−0.507746	−0.253873	+	0.967238i	$0.581704\pi$
$510$	−2331.19	−0.202406
$511$	−18106.2	−1.56745
$512$	20009.6	1.72716
$513$	1454.87	0.125212
$514$	−14595.4	−1.25248
$515$	14807.8	1.26701
$516$	0	0
$517$	−11040.0	−0.939149
$518$	−28049.5	−2.37920
$519$	325.266	0.0275098
$520$	34861.5	2.93995
$521$	12723.2	1.06989	0.534946	−	0.844886i	$-0.320332\pi$
$521$	12723.2	1.06989	0.534946	+	0.844886i	$0.320332\pi$
$522$	5545.38	0.464971
$523$	−13066.1	−1.09243	−0.546215	−	0.837645i	$-0.683932\pi$
$523$	−13066.1	−1.09243	−0.546215	+	0.837645i	$0.683932\pi$
$524$	18797.1	1.56709
$525$	979.493	0.0814259
$526$	−3763.83	−0.311998
$527$	9283.23	0.767332
$528$	−1532.28	−0.126296
$529$	−10110.1	−0.830942
$530$	−56175.9	−4.60401
$531$	13678.2	1.11786
$532$	−42158.1	−3.43569
$533$	3999.26	0.325004
$534$	995.208	0.0806496
$535$	−22477.0	−1.81638
$536$	23300.6	1.87767
$537$	249.385	0.0200405
$538$	331.940	0.0266003
$539$	3761.05	0.300557
$540$	4806.70	0.383051
$541$	5388.28	0.428207	0.214104	−	0.976811i	$-0.431317\pi$
$541$	5388.28	0.428207	0.214104	+	0.976811i	$0.431317\pi$
$542$	−8462.03	−0.670619
$543$	286.940	0.0226773
$544$	34727.4	2.73700
$545$	−12131.0	−0.953461
$546$	974.093	0.0763505
$547$	16337.2	1.27702	0.638509	−	0.769614i	$-0.279551\pi$
$547$	16337.2	1.27702	0.638509	+	0.769614i	$0.279551\pi$
$548$	−33425.7	−2.60561
$549$	−10038.9	−0.780421
$550$	−33484.1	−2.59594
$551$	4018.93	0.310730
$552$	−720.513	−0.0555563
$553$	−14808.9	−1.13877
$554$	20453.8	1.56859
$555$	1157.39	0.0885197
$556$	46280.9	3.53012
$557$	21829.0	1.66055	0.830274	−	0.557355i	$-0.188184\pi$
$557$	21829.0	1.66055	0.830274	+	0.557355i	$0.188184\pi$
$558$	−13480.8	−1.02274
$559$	0	0
$560$	−58666.7	−4.42700
$561$	930.896	0.0700579
$562$	−34616.3	−2.59822
$563$	−878.803	−0.0657853	−0.0328927	−	0.999459i	$-0.510472\pi$
$563$	−878.803	−0.0657853	−0.0328927	+	0.999459i	$0.510472\pi$
$564$	1562.10	0.116625
$565$	17370.8	1.29344
$566$	4111.32	0.305321
$567$	−15286.4	−1.13222
$568$	4188.58	0.309417
$569$	−17405.9	−1.28241	−0.641207	−	0.767368i	$-0.721566\pi$
$569$	−17405.9	−1.28241	−0.641207	+	0.767368i	$0.721566\pi$
$570$	2453.43	0.180286
$571$	26498.5	1.94208	0.971042	−	0.238911i	$-0.0767903\pi$
$571$	26498.5	1.94208	0.971042	+	0.238911i	$0.0767903\pi$
$572$	−23610.2	−1.72586
$573$	68.5449	0.00499739
$574$	−13287.5	−0.966222
$575$	−7974.85	−0.578390
$576$	−15945.8	−1.15349
$577$	12626.9	0.911028	0.455514	−	0.890229i	$-0.349455\pi$
$577$	12626.9	0.911028	0.455514	+	0.890229i	$0.349455\pi$
$578$	−23819.4	−1.71411
$579$	−1109.04	−0.0796031
$580$	13278.0	0.950586
$581$	16371.9	1.16906
$582$	1102.46	0.0785193
$583$	22432.3	1.59357
$584$	−51638.1	−3.65891
$585$	15577.8	1.10096
$586$	−35981.7	−2.53650
$587$	23661.9	1.66377	0.831885	−	0.554949i	$-0.187262\pi$
$587$	23661.9	1.66377	0.831885	+	0.554949i	$0.187262\pi$
$588$	−532.167	−0.0373235
$589$	−9770.00	−0.683473
$590$	46192.2	3.22323
$591$	−174.662	−0.0121567
$592$	−40518.2	−2.81299
$593$	7718.20	0.534483	0.267241	−	0.963630i	$-0.413888\pi$
$593$	7718.20	0.534483	0.267241	+	0.963630i	$0.413888\pi$
$594$	−2707.12	−0.186994
$595$	35641.3	2.45572
$596$	23226.7	1.59631
$597$	885.603	0.0607124
$598$	−7930.89	−0.542338
$599$	−21718.8	−1.48148	−0.740739	−	0.671793i	$-0.765524\pi$
$599$	−21718.8	−1.48148	−0.740739	+	0.671793i	$0.765524\pi$
$600$	2793.48	0.190072
$601$	−9546.80	−0.647957	−0.323978	−	0.946065i	$-0.605020\pi$
$601$	−9546.80	−0.647957	−0.323978	+	0.946065i	$0.605020\pi$
$602$	0	0
$603$	10411.8	0.703155
$604$	33597.4	2.26334
$605$	−209.730	−0.0140938
$606$	1270.01	0.0851330
$607$	14707.9	0.983485	0.491743	−	0.870741i	$-0.336360\pi$
$607$	14707.9	0.983485	0.491743	+	0.870741i	$0.336360\pi$
$608$	−36548.3	−2.43788
$609$	218.755	0.0145556
$610$	−33902.2	−2.25026
$611$	10138.1	0.671267
$612$	51049.3	3.37181
$613$	−27607.3	−1.81900	−0.909502	−	0.415699i	$-0.863537\pi$
$613$	−27607.3	−1.81900	−0.909502	+	0.415699i	$0.863537\pi$
$614$	−12689.6	−0.834058
$615$	548.276	0.0359490
$616$	46252.3	3.02526
$617$	24017.4	1.56711	0.783553	−	0.621325i	$-0.213405\pi$
$617$	24017.4	1.56711	0.783553	+	0.621325i	$0.213405\pi$
$618$	1180.02	0.0768081
$619$	9536.64	0.619241	0.309620	−	0.950860i	$-0.399798\pi$
$619$	9536.64	0.619241	0.309620	+	0.950860i	$0.399798\pi$
$620$	−32278.8	−2.09088
$621$	−644.750	−0.0416633
$622$	−46740.5	−3.01306
$623$	−15215.6	−0.978493
$624$	1407.10	0.0902712
$625$	−6685.73	−0.427887
$626$	17759.2	1.13387
$627$	−979.707	−0.0624015
$628$	−52274.3	−3.32161
$629$	24615.7	1.56040
$630$	−51757.1	−3.27310
$631$	−14631.7	−0.923103	−0.461552	−	0.887113i	$-0.652707\pi$
$631$	−14631.7	−0.923103	−0.461552	+	0.887113i	$0.652707\pi$
$632$	−42234.6	−2.65823
$633$	−1065.99	−0.0669341
$634$	44360.9	2.77886
$635$	−2533.83	−0.158350
$636$	−3174.03	−0.197891
$637$	−3453.79	−0.214826
$638$	−7478.15	−0.464048
$639$	1871.66	0.115871
$640$	−4295.77	−0.265321
$641$	23349.8	1.43878	0.719391	−	0.694605i	$-0.244421\pi$
$641$	23349.8	1.43878	0.719391	+	0.694605i	$0.244421\pi$
$642$	−1791.17	−0.110112
$643$	24399.8	1.49648	0.748238	−	0.663430i	$-0.230900\pi$
$643$	24399.8	1.49648	0.748238	+	0.663430i	$0.230900\pi$
$644$	18683.1	1.14319
$645$	0	0
$646$	52180.3	3.17803
$647$	25788.3	1.56699	0.783496	−	0.621396i	$-0.213434\pi$
$647$	25788.3	1.56699	0.783496	+	0.621396i	$0.213434\pi$
$648$	−43596.3	−2.64294
$649$	−18445.6	−1.11564
$650$	30748.6	1.85548
$651$	−531.791	−0.0320162
$652$	38924.2	2.33802
$653$	11442.0	0.685699	0.342850	−	0.939390i	$-0.388608\pi$
$653$	11442.0	0.685699	0.342850	+	0.939390i	$0.388608\pi$
$654$	−966.711	−0.0578003
$655$	16724.7	0.997691
$656$	−19194.2	−1.14239
$657$	−23074.4	−1.37019
$658$	−33683.9	−1.99564
$659$	4523.57	0.267395	0.133697	−	0.991022i	$-0.457315\pi$
$659$	4523.57	0.267395	0.133697	+	0.991022i	$0.457315\pi$
$660$	−3236.83	−0.190899
$661$	25793.6	1.51778	0.758890	−	0.651219i	$-0.225742\pi$
$661$	25793.6	1.51778	0.758890	+	0.651219i	$0.225742\pi$
$662$	14112.0	0.828517
$663$	−854.846	−0.0500746
$664$	46692.2	2.72893
$665$	−37510.2	−2.18734
$666$	−35746.1	−2.07978
$667$	−1781.06	−0.103393
$668$	−13355.8	−0.773578
$669$	78.0266	0.00450924
$670$	35161.5	2.02747
$671$	13537.9	0.778872
$672$	−1989.36	−0.114198
$673$	−1315.10	−0.0753247	−0.0376624	−	0.999291i	$-0.511991\pi$
$673$	−1315.10	−0.0753247	−0.0376624	+	0.999291i	$0.511991\pi$
$674$	12427.2	0.710203
$675$	2499.74	0.142541
$676$	−21146.7	−1.20316
$677$	9826.65	0.557856	0.278928	−	0.960312i	$-0.410021\pi$
$677$	9826.65	0.557856	0.278928	+	0.960312i	$0.410021\pi$
$678$	1384.26	0.0784103
$679$	−16855.3	−0.952647
$680$	101648.	5.73238
$681$	−488.048	−0.0274626
$682$	18179.3	1.02071
$683$	5626.63	0.315222	0.157611	−	0.987501i	$-0.449621\pi$
$683$	5626.63	0.315222	0.157611	+	0.987501i	$0.449621\pi$
$684$	−53726.0	−3.00331
$685$	−29740.5	−1.65887
$686$	−26530.9	−1.47661
$687$	611.719	0.0339717
$688$	0	0
$689$	−20599.7	−1.13902
$690$	−1087.28	−0.0599885
$691$	16628.4	0.915445	0.457723	−	0.889095i	$-0.348665\pi$
$691$	16628.4	0.915445	0.457723	+	0.889095i	$0.348665\pi$
$692$	−24054.1	−1.32139
$693$	20667.7	1.13290
$694$	−21132.6	−1.15588
$695$	41178.4	2.24746
$696$	623.880	0.0339772
$697$	11660.9	0.633699
$698$	46383.2	2.51523
$699$	−1724.81	−0.0933308
$700$	−72435.7	−3.91116
$701$	−21557.9	−1.16153	−0.580763	−	0.814073i	$-0.697246\pi$
$701$	−21557.9	−1.16153	−0.580763	+	0.814073i	$0.697246\pi$
$702$	2485.96	0.133656
$703$	−25906.4	−1.38987
$704$	21503.5	1.15120
$705$	1389.88	0.0742494
$706$	−18249.5	−0.972846
$707$	−19417.0	−1.03289
$708$	2609.94	0.138542
$709$	−9112.17	−0.482672	−0.241336	−	0.970442i	$-0.577586\pi$
$709$	−9112.17	−0.482672	−0.241336	+	0.970442i	$0.577586\pi$
$710$	6320.72	0.334102
$711$	−18872.4	−0.995459
$712$	−43394.4	−2.28409
$713$	4329.74	0.227420
$714$	2840.23	0.148869
$715$	−21007.2	−1.09877
$716$	−18442.6	−0.962614
$717$	−1641.15	−0.0854808
$718$	−10265.4	−0.533568
$719$	20421.4	1.05924	0.529619	−	0.848236i	$-0.322335\pi$
$719$	20421.4	1.05924	0.529619	+	0.848236i	$0.322335\pi$
$720$	−74764.5	−3.86987
$721$	−18041.2	−0.931886
$722$	−18951.4	−0.976868
$723$	357.861	0.0184080
$724$	−21219.9	−1.08927
$725$	6905.28	0.353732
$726$	−16.7132	−0.000854388 0
$727$	7868.82	0.401428	0.200714	−	0.979650i	$-0.435674\pi$
$727$	7868.82	0.401428	0.200714	+	0.979650i	$0.435674\pi$
$728$	−42473.7	−2.16234
$729$	−19379.7	−0.984592
$730$	−77923.8	−3.95080
$731$	0	0
$732$	−1915.53	−0.0967213
$733$	−5935.63	−0.299096	−0.149548	−	0.988754i	$-0.547782\pi$
$733$	−5935.63	−0.299096	−0.149548	+	0.988754i	$0.547782\pi$
$734$	−44155.3	−2.22044
$735$	−473.495	−0.0237621
$736$	16197.0	0.811183
$737$	−14040.7	−0.701760
$738$	−16933.6	−0.844625
$739$	−11556.0	−0.575230	−0.287615	−	0.957746i	$-0.592862\pi$
$739$	−11556.0	−0.575230	−0.287615	+	0.957746i	$0.592862\pi$
$740$	−85591.5	−4.25190
$741$	899.670	0.0446022
$742$	68442.4	3.38625
$743$	15163.6	0.748719	0.374360	−	0.927284i	$-0.377863\pi$
$743$	15163.6	0.748719	0.374360	+	0.927284i	$0.377863\pi$
$744$	−1516.65	−0.0747353
$745$	20666.0	1.01630
$746$	−16553.3	−0.812410
$747$	20864.3	1.02193
$748$	−68841.8	−3.36512
$749$	27385.0	1.33595
$750$	1218.77	0.0593375
$751$	22378.4	1.08735	0.543675	−	0.839296i	$-0.317032\pi$
$751$	22378.4	1.08735	0.543675	+	0.839296i	$0.317032\pi$
$752$	−48657.2	−2.35950
$753$	213.253	0.0103205
$754$	6867.22	0.331683
$755$	29893.3	1.44096
$756$	−5856.28	−0.281734
$757$	−13521.9	−0.649222	−0.324611	−	0.945848i	$-0.605233\pi$
$757$	−13521.9	−0.649222	−0.324611	+	0.945848i	$0.605233\pi$
$758$	76005.9	3.64203
$759$	434.174	0.0207635
$760$	−106978.	−5.10591
$761$	6937.39	0.330460	0.165230	−	0.986255i	$-0.447163\pi$
$761$	6937.39	0.330460	0.165230	+	0.986255i	$0.447163\pi$
$762$	−201.919	−0.00959940
$763$	14779.9	0.701270
$764$	−5069.04	−0.240041
$765$	45421.1	2.14667
$766$	40989.5	1.93344
$767$	16938.6	0.797417
$768$	906.321	0.0425834
$769$	14517.5	0.680773	0.340387	−	0.940286i	$-0.389442\pi$
$769$	14517.5	0.680773	0.340387	+	0.940286i	$0.389442\pi$
$770$	69796.4	3.26661
$771$	−733.744	−0.0342739
$772$	82016.1	3.82361
$773$	19825.3	0.922467	0.461233	−	0.887279i	$-0.347407\pi$
$773$	19825.3	0.922467	0.461233	+	0.887279i	$0.347407\pi$
$774$	0	0
$775$	−16786.7	−0.778060
$776$	−48070.7	−2.22376
$777$	−1410.11	−0.0651063
$778$	7311.77	0.336940
$779$	−12272.3	−0.564444
$780$	2972.39	0.136447
$781$	−2524.00	−0.115641
$782$	−23124.6	−1.05746
$783$	558.278	0.0254805
$784$	16576.3	0.755114
$785$	−46511.1	−2.11472
$786$	1332.78	0.0604816
$787$	−37668.5	−1.70614	−0.853072	−	0.521793i	$-0.825263\pi$
$787$	−37668.5	−1.70614	−0.853072	+	0.521793i	$0.825263\pi$
$788$	12916.6	0.583930
$789$	−189.216	−0.00853775
$790$	−63733.5	−2.87030
$791$	−21163.8	−0.951325
$792$	58943.7	2.64453
$793$	−12431.9	−0.556708
$794$	5564.56	0.248714
$795$	−2824.10	−0.125988
$796$	−65492.3	−2.91622
$797$	39167.1	1.74074	0.870370	−	0.492398i	$-0.163879\pi$
$797$	39167.1	1.74074	0.870370	+	0.492398i	$0.163879\pi$
$798$	−2989.15	−0.132600
$799$	29560.3	1.30885
$800$	−62797.0	−2.77526
$801$	−19390.7	−0.855351
$802$	−9800.46	−0.431504
$803$	31116.6	1.36747
$804$	1986.68	0.0871454
$805$	16623.3	0.727819
$806$	−16694.2	−0.729562
$807$	16.6874	0.000727912 0
$808$	−55376.6	−2.41107
$809$	−20934.7	−0.909796	−0.454898	−	0.890544i	$-0.650324\pi$
$809$	−20934.7	−0.909796	−0.454898	+	0.890544i	$0.650324\pi$
$810$	−65788.3	−2.85379
$811$	12410.4	0.537348	0.268674	−	0.963231i	$-0.413415\pi$
$811$	12410.4	0.537348	0.268674	+	0.963231i	$0.413415\pi$
$812$	−16177.4	−0.699156
$813$	−425.406	−0.0183513
$814$	48204.9	2.07565
$815$	34632.8	1.48851
$816$	4102.78	0.176012
$817$	0	0
$818$	46950.5	2.00683
$819$	−18979.3	−0.809756
$820$	−40546.2	−1.72675
$821$	−14654.5	−0.622956	−0.311478	−	0.950253i	$-0.600824\pi$
$821$	−14654.5	−0.622956	−0.311478	+	0.950253i	$0.600824\pi$
$822$	−2369.99	−0.100563
$823$	37214.9	1.57622	0.788111	−	0.615533i	$-0.211059\pi$
$823$	37214.9	1.57622	0.788111	+	0.615533i	$0.211059\pi$
$824$	−51452.9	−2.17530
$825$	−1683.32	−0.0710373
$826$	−56278.7	−2.37068
$827$	−6749.98	−0.283821	−0.141910	−	0.989880i	$-0.545324\pi$
$827$	−6749.98	−0.283821	−0.141910	+	0.989880i	$0.545324\pi$
$828$	23809.6	0.999326
$829$	40197.8	1.68411	0.842056	−	0.539391i	$-0.181345\pi$
$829$	40197.8	1.68411	0.842056	+	0.539391i	$0.181345\pi$
$830$	70460.1	2.94663
$831$	1028.26	0.0429241
$832$	−19746.8	−0.822833
$833$	−10070.4	−0.418872
$834$	3281.47	0.136245
$835$	−11883.3	−0.492501
$836$	72451.5	2.99735
$837$	−1357.17	−0.0560462
$838$	70839.3	2.92017
$839$	−20925.3	−0.861049	−0.430524	−	0.902579i	$-0.641671\pi$
$839$	−20925.3	−0.861049	−0.430524	+	0.902579i	$0.641671\pi$
$840$	−5822.91	−0.239178
$841$	−22846.8	−0.936767
$842$	−68223.1	−2.79231
$843$	−1740.24	−0.0710999
$844$	78832.3	3.21507
$845$	−18815.3	−0.765994
$846$	−42926.5	−1.74450
$847$	255.526	0.0103660
$848$	98866.8	4.00365
$849$	206.686	0.00835505
$850$	89655.6	3.61784
$851$	11480.9	0.462467
$852$	357.131	0.0143605
$853$	−8942.48	−0.358951	−0.179475	−	0.983762i	$-0.557440\pi$
$853$	−8942.48	−0.358951	−0.179475	+	0.983762i	$0.557440\pi$
$854$	41304.9	1.65507
$855$	−47802.7	−1.91207
$856$	78101.0	3.11850
$857$	−36974.1	−1.47376	−0.736878	−	0.676025i	$-0.763701\pi$
$857$	−36974.1	−1.47376	−0.736878	+	0.676025i	$0.763701\pi$
$858$	−1674.04	−0.0666095
$859$	5890.03	0.233953	0.116976	−	0.993135i	$-0.462680\pi$
$859$	5890.03	0.233953	0.116976	+	0.993135i	$0.462680\pi$
$860$	0	0
$861$	−667.996	−0.0264405
$862$	−23443.9	−0.926338
$863$	39948.5	1.57574	0.787870	−	0.615842i	$-0.211184\pi$
$863$	39948.5	1.57574	0.787870	+	0.615842i	$0.211184\pi$
$864$	−5077.01	−0.199911
$865$	−21402.2	−0.841266
$866$	41606.9	1.63263
$867$	−1197.46	−0.0469063
$868$	39327.1	1.53785
$869$	25450.2	0.993484
$870$	941.457	0.0366878
$871$	12893.7	0.501591
$872$	42151.8	1.63697
$873$	−21480.3	−0.832758
$874$	24337.1	0.941894
$875$	−18633.6	−0.719921
$876$	−4402.82	−0.169815
$877$	12620.7	0.485941	0.242971	−	0.970034i	$-0.421878\pi$
$877$	12620.7	0.485941	0.242971	+	0.970034i	$0.421878\pi$
$878$	−39145.7	−1.50467
$879$	−1808.89	−0.0694109
$880$	100823.	3.86219
$881$	51822.2	1.98176	0.990882	−	0.134732i	$-0.0430174\pi$
$881$	51822.2	1.98176	0.990882	+	0.134732i	$0.0430174\pi$
$882$	14624.0	0.558293
$883$	−19085.4	−0.727377	−0.363688	−	0.931521i	$-0.618483\pi$
$883$	−19085.4	−0.727377	−0.363688	+	0.931521i	$0.618483\pi$
$884$	63217.8	2.40525
$885$	2322.19	0.0882030
$886$	5198.59	0.197122
$887$	28069.6	1.06255	0.531276	−	0.847199i	$-0.321713\pi$
$887$	28069.6	1.06255	0.531276	+	0.847199i	$0.321713\pi$
$888$	−4021.60	−0.151977
$889$	3087.11	0.116466
$890$	−65483.7	−2.46631
$891$	26270.7	0.987768
$892$	−5770.24	−0.216594
$893$	−31110.3	−1.16581
$894$	1646.85	0.0616096
$895$	−16409.3	−0.612851
$896$	5233.78	0.195143
$897$	−398.704	−0.0148410
$898$	−55079.4	−2.04680
$899$	−3749.05	−0.139085
$900$	−92311.6	−3.41895
$901$	−60063.7	−2.22088
$902$	22835.5	0.842949
$903$	0	0
$904$	−60358.4	−2.22067
$905$	−18880.4	−0.693486
$906$	2382.17	0.0873535
$907$	44592.6	1.63249	0.816247	−	0.577703i	$-0.196051\pi$
$907$	44592.6	1.63249	0.816247	+	0.577703i	$0.196051\pi$
$908$	36092.2	1.31912
$909$	−24744.9	−0.902901
$910$	−64094.3	−2.33484
$911$	42010.9	1.52786	0.763931	−	0.645298i	$-0.223267\pi$
$911$	42010.9	1.52786	0.763931	+	0.645298i	$0.223267\pi$
$912$	−4317.91	−0.156777
$913$	−28136.2	−1.01991
$914$	77119.1	2.79089
$915$	−1704.34	−0.0615779
$916$	−45238.0	−1.63177
$917$	−20376.7	−0.733802
$918$	7248.47	0.260605
$919$	−4232.68	−0.151930	−0.0759648	−	0.997110i	$-0.524204\pi$
$919$	−4232.68	−0.151930	−0.0759648	+	0.997110i	$0.524204\pi$
$920$	47409.0	1.69894
$921$	−637.938	−0.0228238
$922$	−69639.0	−2.48746
$923$	2317.80	0.0826559
$924$	3943.61	0.140406
$925$	−44512.2	−1.58222
$926$	−57817.2	−2.05183
$927$	−22991.6	−0.814610
$928$	−14024.7	−0.496104
$929$	−18923.3	−0.668304	−0.334152	−	0.942519i	$-0.608450\pi$
$929$	−18923.3	−0.668304	−0.334152	+	0.942519i	$0.608450\pi$
$930$	−2288.68	−0.0806975
$931$	10598.5	0.373095
$932$	127553.	4.48299
$933$	−2349.76	−0.0824518
$934$	−1468.56	−0.0514484
$935$	−61252.0	−2.14241
$936$	−54128.2	−1.89021
$937$	−36496.5	−1.27245	−0.636226	−	0.771503i	$-0.719506\pi$
$937$	−36496.5	−1.27245	−0.636226	+	0.771503i	$0.719506\pi$
$938$	−42839.2	−1.49121
$939$	892.799	0.0310281
$940$	−102785.	−3.56645
$941$	−32815.4	−1.13682	−0.568412	−	0.822744i	$-0.692442\pi$
$941$	−32815.4	−1.13682	−0.568412	+	0.822744i	$0.692442\pi$
$942$	−3706.43	−0.128197
$943$	5438.70	0.187814
$944$	−81296.0	−2.80292
$945$	−5210.62	−0.179367
$946$	0	0
$947$	27175.4	0.932503	0.466252	−	0.884652i	$-0.345604\pi$
$947$	27175.4	0.932503	0.466252	+	0.884652i	$0.345604\pi$
$948$	−3601.05	−0.123372
$949$	−28574.6	−0.977418
$950$	−94356.7	−3.22246
$951$	2230.13	0.0760429
$952$	−123843.	−4.21616
$953$	16536.5	0.562089	0.281044	−	0.959695i	$-0.409319\pi$
$953$	16536.5	0.562089	0.281044	+	0.959695i	$0.409319\pi$
$954$	87222.5	2.96010
$955$	−4510.18	−0.152823
$956$	121366.	4.10593
$957$	−375.944	−0.0126986
$958$	−28915.8	−0.975184
$959$	36234.6	1.22010
$960$	−2707.17	−0.0910143
$961$	−20677.1	−0.694071
$962$	−44266.8	−1.48360
$963$	34899.2	1.16782
$964$	−26464.6	−0.884199
$965$	72973.8	2.43431
$966$	1324.70	0.0441215
$967$	2156.59	0.0717180	0.0358590	−	0.999357i	$-0.488583\pi$
$967$	2156.59	0.0717180	0.0358590	+	0.999357i	$0.488583\pi$
$968$	728.752	0.0241973
$969$	2623.23	0.0869661
$970$	−72540.4	−2.40117
$971$	−39773.2	−1.31450	−0.657251	−	0.753672i	$-0.728281\pi$
$971$	−39773.2	−1.31450	−0.657251	+	0.753672i	$0.728281\pi$
$972$	−11199.6	−0.369576
$973$	−50170.0	−1.65301
$974$	12148.5	0.399654
$975$	1545.80	0.0507747
$976$	59666.1	1.95683
$977$	−25493.5	−0.834810	−0.417405	−	0.908721i	$-0.637060\pi$
$977$	−25493.5	−0.834810	−0.417405	+	0.908721i	$0.637060\pi$
$978$	2759.85	0.0902356
$979$	26149.0	0.853654
$980$	35016.0	1.14137
$981$	18835.4	0.613017
$982$	65071.5	2.11458
$983$	1511.54	0.0490443	0.0245222	−	0.999699i	$-0.492194\pi$
$983$	1511.54	0.0490443	0.0245222	+	0.999699i	$0.492194\pi$
$984$	−1905.10	−0.0617199
$985$	11492.6	0.371761
$986$	20023.2	0.646722
$987$	−1693.37	−0.0546104
$988$	−66532.6	−2.14239
$989$	0	0
$990$	88948.0	2.85551
$991$	27879.7	0.893670	0.446835	−	0.894616i	$-0.352551\pi$
$991$	27879.7	0.893670	0.446835	+	0.894616i	$0.352551\pi$
$992$	34094.0	1.09122
$993$	709.443	0.0226722
$994$	−7700.90	−0.245732
$995$	−58271.8	−1.85662
$996$	3981.12	0.126653
$997$	−45827.6	−1.45574	−0.727871	−	0.685714i	$-0.759490\pi$
$997$	−45827.6	−1.45574	−0.727871	+	0.685714i	$0.759490\pi$
$998$	8649.13	0.274332
$999$	−3598.72	−0.113972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.h.1.1		30
43.16	even	7		43.4.e.a.41.10	yes	60
43.35	even	7		43.4.e.a.21.10	✓	60
43.42	odd	2		1849.4.a.g.1.30		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.10	✓	60	43.35	even	7
43.4.e.a.41.10	yes	60	43.16	even	7
1849.4.a.g.1.30		30	43.42	odd	2
1849.4.a.h.1.1		30	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-5.24346 q^{2} -0.263601 q^{3} +19.4939 q^{4} +17.3447 q^{5} +1.38218 q^{6} -21.1320 q^{7} -60.2678 q^{8} -26.9305 q^{9} +O(q^{10})\)	\(q-5.24346 q^{2} -0.263601 q^{3} +19.4939 q^{4} +17.3447 q^{5} +1.38218 q^{6} -21.1320 q^{7} -60.2678 q^{8} -26.9305 q^{9} -90.9462 q^{10} +36.3168 q^{11} -5.13861 q^{12} -33.3499 q^{13} +110.805 q^{14} -4.57208 q^{15} +160.061 q^{16} -97.2404 q^{17} +141.209 q^{18} +102.339 q^{19} +338.115 q^{20} +5.57043 q^{21} -190.426 q^{22} -45.3534 q^{23} +15.8867 q^{24} +175.838 q^{25} +174.869 q^{26} +14.2161 q^{27} -411.945 q^{28} +39.2707 q^{29} +23.9735 q^{30} -95.4669 q^{31} -357.130 q^{32} -9.57314 q^{33} +509.876 q^{34} -366.528 q^{35} -524.980 q^{36} -253.143 q^{37} -536.611 q^{38} +8.79106 q^{39} -1045.33 q^{40} -119.918 q^{41} -29.2083 q^{42} +707.955 q^{44} -467.101 q^{45} +237.809 q^{46} -303.993 q^{47} -42.1922 q^{48} +103.562 q^{49} -922.000 q^{50} +25.6327 q^{51} -650.119 q^{52} +617.683 q^{53} -74.5418 q^{54} +629.903 q^{55} +1273.58 q^{56} -26.9767 q^{57} -205.914 q^{58} -507.907 q^{59} -89.1276 q^{60} +372.772 q^{61} +500.577 q^{62} +569.096 q^{63} +592.110 q^{64} -578.443 q^{65} +50.1964 q^{66} -386.618 q^{67} -1895.59 q^{68} +11.9552 q^{69} +1921.88 q^{70} -69.4996 q^{71} +1623.04 q^{72} +856.812 q^{73} +1327.35 q^{74} -46.3511 q^{75} +1994.99 q^{76} -767.447 q^{77} -46.0956 q^{78} +700.782 q^{79} +2776.20 q^{80} +723.376 q^{81} +628.787 q^{82} -774.745 q^{83} +108.589 q^{84} -1686.60 q^{85} -10.3518 q^{87} -2188.73 q^{88} +720.027 q^{89} +2449.23 q^{90} +704.750 q^{91} -884.113 q^{92} +25.1652 q^{93} +1593.97 q^{94} +1775.04 q^{95} +94.1398 q^{96} +797.619 q^{97} -543.025 q^{98} -978.029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * q^99

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