LMFDB - Embedded newform 1441.4.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.29699 q^{2} +7.09451 q^{3} +20.0581 q^{4} -14.8169 q^{5} -37.5796 q^{6} -28.7336 q^{7} -63.8717 q^{8} +23.3321 q^{9} +O(q^{10})$	\(q-5.29699 q^{2} +7.09451 q^{3} +20.0581 q^{4} -14.8169 q^{5} -37.5796 q^{6} -28.7336 q^{7} -63.8717 q^{8} +23.3321 q^{9} +78.4849 q^{10} -11.0000 q^{11} +142.303 q^{12} +55.2041 q^{13} +152.202 q^{14} -105.119 q^{15} +177.863 q^{16} +115.173 q^{17} -123.590 q^{18} -38.4603 q^{19} -297.199 q^{20} -203.851 q^{21} +58.2669 q^{22} -90.4970 q^{23} -453.139 q^{24} +94.5399 q^{25} -292.416 q^{26} -26.0221 q^{27} -576.343 q^{28} +149.065 q^{29} +556.812 q^{30} -31.6578 q^{31} -431.165 q^{32} -78.0396 q^{33} -610.068 q^{34} +425.743 q^{35} +467.998 q^{36} +175.006 q^{37} +203.724 q^{38} +391.646 q^{39} +946.380 q^{40} -254.531 q^{41} +1079.80 q^{42} +305.895 q^{43} -220.639 q^{44} -345.709 q^{45} +479.362 q^{46} -204.653 q^{47} +1261.85 q^{48} +482.623 q^{49} -500.777 q^{50} +817.093 q^{51} +1107.29 q^{52} -347.517 q^{53} +137.839 q^{54} +162.986 q^{55} +1835.27 q^{56} -272.857 q^{57} -789.599 q^{58} +303.713 q^{59} -2108.48 q^{60} +500.421 q^{61} +167.691 q^{62} -670.416 q^{63} +860.974 q^{64} -817.952 q^{65} +413.375 q^{66} +797.983 q^{67} +2310.15 q^{68} -642.032 q^{69} -2255.16 q^{70} -420.419 q^{71} -1490.26 q^{72} +176.088 q^{73} -927.004 q^{74} +670.714 q^{75} -771.442 q^{76} +316.070 q^{77} -2074.55 q^{78} +287.750 q^{79} -2635.38 q^{80} -814.580 q^{81} +1348.25 q^{82} -200.349 q^{83} -4088.87 q^{84} -1706.50 q^{85} -1620.32 q^{86} +1057.55 q^{87} +702.589 q^{88} +1318.96 q^{89} +1831.22 q^{90} -1586.21 q^{91} -1815.20 q^{92} -224.596 q^{93} +1084.04 q^{94} +569.862 q^{95} -3058.91 q^{96} -508.186 q^{97} -2556.45 q^{98} -256.653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) $ 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * 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 $

$2$	−5.29699	−1.87277	−0.936385	−	0.350976i	$-0.885850\pi$
$2$	−5.29699	−1.87277	−0.936385	+	0.350976i	$0.885850\pi$
$3$	7.09451	1.36534	0.682670	−	0.730727i	$-0.260819\pi$
$3$	7.09451	1.36534	0.682670	+	0.730727i	$0.260819\pi$
$4$	20.0581	2.50726
$5$	−14.8169	−1.32526	−0.662631	−	0.748946i	$-0.730560\pi$
$5$	−14.8169	−1.32526	−0.662631	+	0.748946i	$0.730560\pi$
$6$	−37.5796	−2.55697
$7$	−28.7336	−1.55147	−0.775736	−	0.631058i	$-0.782621\pi$
$7$	−28.7336	−1.55147	−0.775736	+	0.631058i	$0.782621\pi$
$8$	−63.8717	−2.82276
$9$	23.3321	0.864151
$10$	78.4849	2.48191
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	142.303	3.42327
$13$	55.2041	1.17776	0.588879	−	0.808221i	$-0.299569\pi$
$13$	55.2041	1.17776	0.588879	+	0.808221i	$0.299569\pi$
$14$	152.202	2.90555
$15$	−105.119	−1.80943
$16$	177.863	2.77911
$17$	115.173	1.64314	0.821572	−	0.570104i	$-0.193097\pi$
$17$	115.173	1.64314	0.821572	+	0.570104i	$0.193097\pi$
$18$	−123.590	−1.61836
$19$	−38.4603	−0.464390	−0.232195	−	0.972669i	$-0.574591\pi$
$19$	−38.4603	−0.464390	−0.232195	+	0.972669i	$0.574591\pi$
$20$	−297.199	−3.32278
$21$	−203.851	−2.11828
$22$	58.2669	0.564661
$23$	−90.4970	−0.820432	−0.410216	−	0.911988i	$-0.634547\pi$
$23$	−90.4970	−0.820432	−0.410216	+	0.911988i	$0.634547\pi$
$24$	−453.139	−3.85402
$25$	94.5399	0.756319
$26$	−292.416	−2.20567
$27$	−26.0221	−0.185480
$28$	−576.343	−3.88995
$29$	149.065	0.954509	0.477255	−	0.878765i	$-0.341632\pi$
$29$	149.065	0.954509	0.477255	+	0.878765i	$0.341632\pi$
$30$	556.812	3.38865
$31$	−31.6578	−0.183416	−0.0917081	−	0.995786i	$-0.529233\pi$
$31$	−31.6578	−0.183416	−0.0917081	+	0.995786i	$0.529233\pi$
$32$	−431.165	−2.38187
$33$	−78.0396	−0.411665
$34$	−610.068	−3.07723
$35$	425.743	2.05611
$36$	467.998	2.16666
$37$	175.006	0.777588	0.388794	−	0.921325i	$-0.372892\pi$
$37$	175.006	0.777588	0.388794	+	0.921325i	$0.372892\pi$
$38$	203.724	0.869695
$39$	391.646	1.60804
$40$	946.380	3.74089
$41$	−254.531	−0.969538	−0.484769	−	0.874642i	$-0.661096\pi$
$41$	−254.531	−0.969538	−0.484769	+	0.874642i	$0.661096\pi$
$42$	1079.80	3.96706
$43$	305.895	1.08485	0.542424	−	0.840105i	$-0.317507\pi$
$43$	305.895	1.08485	0.542424	+	0.840105i	$0.317507\pi$
$44$	−220.639	−0.755969
$45$	−345.709	−1.14523
$46$	479.362	1.53648
$47$	−204.653	−0.635141	−0.317571	−	0.948235i	$-0.602867\pi$
$47$	−204.653	−0.635141	−0.317571	+	0.948235i	$0.602867\pi$
$48$	1261.85	3.79443
$49$	482.623	1.40706
$50$	−500.777	−1.41641
$51$	817.093	2.24345
$52$	1107.29	2.95295
$53$	−347.517	−0.900662	−0.450331	−	0.892862i	$-0.648694\pi$
$53$	−347.517	−0.900662	−0.450331	+	0.892862i	$0.648694\pi$
$54$	137.839	0.347360
$55$	162.986	0.399581
$56$	1835.27	4.37943
$57$	−272.857	−0.634049
$58$	−789.599	−1.78758
$59$	303.713	0.670170	0.335085	−	0.942188i	$-0.391235\pi$
$59$	303.713	0.670170	0.335085	+	0.942188i	$0.391235\pi$
$60$	−2108.48	−4.53672
$61$	500.421	1.05037	0.525183	−	0.850989i	$-0.323997\pi$
$61$	500.421	1.05037	0.525183	+	0.850989i	$0.323997\pi$
$62$	167.691	0.343496
$63$	−670.416	−1.34071
$64$	860.974	1.68159
$65$	−817.952	−1.56084
$66$	413.375	0.770954
$67$	797.983	1.45506	0.727531	−	0.686074i	$-0.240668\pi$
$67$	797.983	1.45506	0.727531	+	0.686074i	$0.240668\pi$
$68$	2310.15	4.11980
$69$	−642.032	−1.12017
$70$	−2255.16	−3.85061
$71$	−420.419	−0.702740	−0.351370	−	0.936237i	$-0.614284\pi$
$71$	−420.419	−0.702740	−0.351370	+	0.936237i	$0.614284\pi$
$72$	−1490.26	−2.43929
$73$	176.088	0.282322	0.141161	−	0.989987i	$-0.454916\pi$
$73$	176.088	0.282322	0.141161	+	0.989987i	$0.454916\pi$
$74$	−927.004	−1.45624
$75$	670.714	1.03263
$76$	−771.442	−1.16435
$77$	316.070	0.467786
$78$	−2074.55	−3.01149
$79$	287.750	0.409803	0.204902	−	0.978783i	$-0.434313\pi$
$79$	287.750	0.409803	0.204902	+	0.978783i	$0.434313\pi$
$80$	−2635.38	−3.68305
$81$	−814.580	−1.11739
$82$	1348.25	1.81572
$83$	−200.349	−0.264954	−0.132477	−	0.991186i	$-0.542293\pi$
$83$	−200.349	−0.264954	−0.132477	+	0.991186i	$0.542293\pi$
$84$	−4088.87	−5.31110
$85$	−1706.50	−2.17760
$86$	−1620.32	−2.03167
$87$	1057.55	1.30323
$88$	702.589	0.851094
$89$	1318.96	1.57089	0.785447	−	0.618929i	$-0.212433\pi$
$89$	1318.96	1.57089	0.785447	+	0.618929i	$0.212433\pi$
$90$	1831.22	2.14475
$91$	−1586.21	−1.82726
$92$	−1815.20	−2.05704
$93$	−224.596	−0.250425
$94$	1084.04	1.18947
$95$	569.862	0.615438
$96$	−3058.91	−3.25207
$97$	−508.186	−0.531943	−0.265972	−	0.963981i	$-0.585693\pi$
$97$	−508.186	−0.531943	−0.265972	+	0.963981i	$0.585693\pi$
$98$	−2556.45	−2.63510
$99$	−256.653	−0.260551
$100$	1896.29	1.89629
$101$	1191.80	1.17414	0.587071	−	0.809535i	$-0.300281\pi$
$101$	1191.80	1.17414	0.587071	+	0.809535i	$0.300281\pi$
$102$	−4328.14	−4.20146
$103$	−1640.23	−1.56909	−0.784546	−	0.620071i	$-0.787104\pi$
$103$	−1640.23	−1.56909	−0.784546	+	0.620071i	$0.787104\pi$
$104$	−3525.98	−3.32453
$105$	3020.44	2.80728
$106$	1840.79	1.68673
$107$	−1383.23	−1.24974	−0.624869	−	0.780729i	$-0.714848\pi$
$107$	−1383.23	−1.24974	−0.624869	+	0.780729i	$0.714848\pi$
$108$	−521.954	−0.465046
$109$	−262.243	−0.230444	−0.115222	−	0.993340i	$-0.536758\pi$
$109$	−262.243	−0.230444	−0.115222	+	0.993340i	$0.536758\pi$
$110$	−863.334	−0.748324
$111$	1241.58	1.06167
$112$	−5110.66	−4.31171
$113$	181.283	0.150918	0.0754589	−	0.997149i	$-0.475958\pi$
$113$	181.283	0.150918	0.0754589	+	0.997149i	$0.475958\pi$
$114$	1445.32	1.18743
$115$	1340.88	1.08729
$116$	2989.97	2.39321
$117$	1288.03	1.01776
$118$	−1608.76	−1.25507
$119$	−3309.33	−2.54929
$120$	6714.10	5.10759
$121$	121.000	0.0909091
$122$	−2650.73	−1.96709
$123$	−1805.77	−1.32375
$124$	−634.995	−0.459873
$125$	451.324	0.322941
$126$	3551.19	2.51083
$127$	1566.01	1.09418	0.547090	−	0.837074i	$-0.315736\pi$
$127$	1566.01	1.09418	0.547090	+	0.837074i	$0.315736\pi$
$128$	−1111.25	−0.767357
$129$	2170.17	1.48119
$130$	4332.69	2.92309
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	−1565.33	−1.03215
$133$	1105.11	0.720487
$134$	−4226.91	−2.72500
$135$	385.566	0.245809
$136$	−7356.27	−4.63820
$137$	−2506.45	−1.56307	−0.781535	−	0.623861i	$-0.785563\pi$
$137$	−2506.45	−1.56307	−0.781535	+	0.623861i	$0.785563\pi$
$138$	3400.84	2.09782
$139$	−974.014	−0.594351	−0.297175	−	0.954823i	$-0.596045\pi$
$139$	−974.014	−0.594351	−0.297175	+	0.954823i	$0.596045\pi$
$140$	8539.60	5.15520
$141$	−1451.91	−0.867183
$142$	2226.95	1.31607
$143$	−607.245	−0.355107
$144$	4149.92	2.40157
$145$	−2208.69	−1.26497
$146$	−932.736	−0.528725
$147$	3423.97	1.92112
$148$	3510.29	1.94962
$149$	−2563.83	−1.40964	−0.704822	−	0.709384i	$-0.748973\pi$
$149$	−2563.83	−1.40964	−0.704822	+	0.709384i	$0.748973\pi$
$150$	−3552.77	−1.93388
$151$	2219.14	1.19597	0.597983	−	0.801509i	$-0.295969\pi$
$151$	2219.14	1.19597	0.597983	+	0.801509i	$0.295969\pi$
$152$	2456.53	1.31086
$153$	2687.22	1.41993
$154$	−1674.22	−0.876056
$155$	469.069	0.243074
$156$	7855.68	4.03178
$157$	−126.799	−0.0644564	−0.0322282	−	0.999481i	$-0.510260\pi$
$157$	−126.799	−0.0644564	−0.0322282	+	0.999481i	$0.510260\pi$
$158$	−1524.21	−0.767467
$159$	−2465.46	−1.22971
$160$	6388.52	3.15661
$161$	2600.31	1.27288
$162$	4314.82	2.09262
$163$	767.941	0.369017	0.184509	−	0.982831i	$-0.440931\pi$
$163$	767.941	0.369017	0.184509	+	0.982831i	$0.440931\pi$
$164$	−5105.41	−2.43089
$165$	1156.30	0.545564
$166$	1061.25	0.496198
$167$	−2430.38	−1.12616	−0.563079	−	0.826403i	$-0.690383\pi$
$167$	−2430.38	−1.12616	−0.563079	+	0.826403i	$0.690383\pi$
$168$	13020.3	5.97941
$169$	850.491	0.387115
$170$	9039.31	4.07814
$171$	−897.359	−0.401303
$172$	6135.67	2.72000
$173$	302.299	0.132852	0.0664259	−	0.997791i	$-0.478840\pi$
$173$	302.299	0.132852	0.0664259	+	0.997791i	$0.478840\pi$
$174$	−5601.82	−2.44065
$175$	−2716.48	−1.17341
$176$	−1956.49	−0.837933
$177$	2154.69	0.915009
$178$	−6986.53	−2.94192
$179$	−3300.92	−1.37834	−0.689169	−	0.724601i	$-0.742024\pi$
$179$	−3300.92	−1.37834	−0.689169	+	0.724601i	$0.742024\pi$
$180$	−6934.26	−2.87139
$181$	−689.684	−0.283225	−0.141613	−	0.989922i	$-0.545229\pi$
$181$	−689.684	−0.283225	−0.141613	+	0.989922i	$0.545229\pi$
$182$	8402.17	3.42203
$183$	3550.24	1.43411
$184$	5780.20	2.31588
$185$	−2593.04	−1.03051
$186$	1189.68	0.468989
$187$	−1266.90	−0.495427
$188$	−4104.95	−1.59247
$189$	747.709	0.287766
$190$	−3018.55	−1.15257
$191$	−3116.96	−1.18081	−0.590406	−	0.807106i	$-0.701032\pi$
$191$	−3116.96	−1.18081	−0.590406	+	0.807106i	$0.701032\pi$
$192$	6108.19	2.29594
$193$	3616.97	1.34899	0.674495	−	0.738280i	$-0.264362\pi$
$193$	3616.97	1.34899	0.674495	+	0.738280i	$0.264362\pi$
$194$	2691.86	0.996207
$195$	−5802.97	−2.13107
$196$	9680.50	3.52788
$197$	−2649.22	−0.958119	−0.479059	−	0.877783i	$-0.659022\pi$
$197$	−2649.22	−0.958119	−0.479059	+	0.877783i	$0.659022\pi$
$198$	1359.49	0.487953
$199$	−5255.43	−1.87210	−0.936049	−	0.351870i	$-0.885546\pi$
$199$	−5255.43	−1.87210	−0.936049	+	0.351870i	$0.885546\pi$
$200$	−6038.43	−2.13491
$201$	5661.30	1.98665
$202$	−6312.95	−2.19890
$203$	−4283.20	−1.48089
$204$	16389.4	5.62492
$205$	3771.35	1.28489
$206$	8688.27	2.93855
$207$	−2111.48	−0.708977
$208$	9818.77	3.27312
$209$	423.064	0.140019
$210$	−15999.2	−5.25739
$211$	−1652.30	−0.539096	−0.269548	−	0.962987i	$-0.586874\pi$
$211$	−1652.30	−0.539096	−0.269548	+	0.962987i	$0.586874\pi$
$212$	−6970.53	−2.25820
$213$	−2982.66	−0.959478
$214$	7326.97	2.34047
$215$	−4532.40	−1.43771
$216$	1662.07	0.523564
$217$	909.643	0.284565
$218$	1389.10	0.431568
$219$	1249.26	0.385466
$220$	3269.19	1.00186
$221$	6358.00	1.93523
$222$	−6576.64	−1.98827
$223$	−6589.25	−1.97869	−0.989347	−	0.145577i	$-0.953496\pi$
$223$	−6589.25	−1.97869	−0.989347	+	0.145577i	$0.953496\pi$
$224$	12389.0	3.69541
$225$	2205.81	0.653574
$226$	−960.256	−0.282634
$227$	−2466.42	−0.721154	−0.360577	−	0.932730i	$-0.617420\pi$
$227$	−2466.42	−0.721154	−0.360577	+	0.932730i	$0.617420\pi$
$228$	−5473.00	−1.58973
$229$	19.1010	0.00551193	0.00275596	−	0.999996i	$-0.499123\pi$
$229$	19.1010	0.00551193	0.00275596	+	0.999996i	$0.499123\pi$
$230$	−7102.65	−2.03624
$231$	2242.36	0.638687
$232$	−9521.07	−2.69435
$233$	−5215.13	−1.46633	−0.733164	−	0.680052i	$-0.761957\pi$
$233$	−5215.13	−1.46633	−0.733164	+	0.680052i	$0.761957\pi$
$234$	−6822.66	−1.90603
$235$	3032.31	0.841729
$236$	6091.91	1.68029
$237$	2041.45	0.559520
$238$	17529.5	4.77423
$239$	−3691.46	−0.999083	−0.499542	−	0.866290i	$-0.666498\pi$
$239$	−3691.46	−0.999083	−0.499542	+	0.866290i	$0.666498\pi$
$240$	−18696.7	−5.02861
$241$	5782.15	1.54548	0.772741	−	0.634721i	$-0.218885\pi$
$241$	5782.15	1.54548	0.772741	+	0.634721i	$0.218885\pi$
$242$	−640.936	−0.170252
$243$	−5076.45	−1.34014
$244$	10037.5	2.63355
$245$	−7150.96	−1.86473
$246$	9565.16	2.47907
$247$	−2123.17	−0.546939
$248$	2022.04	0.517740
$249$	−1421.38	−0.361752
$250$	−2390.66	−0.604794
$251$	−2268.17	−0.570380	−0.285190	−	0.958471i	$-0.592057\pi$
$251$	−2268.17	−0.570380	−0.285190	+	0.958471i	$0.592057\pi$
$252$	−13447.3	−3.36150
$253$	995.467	0.247370
$254$	−8295.14	−2.04915
$255$	−12106.8	−2.97316
$256$	−1001.51	−0.244509
$257$	4913.06	1.19248	0.596241	−	0.802805i	$-0.296660\pi$
$257$	4913.06	1.19248	0.596241	+	0.802805i	$0.296660\pi$
$258$	−11495.4	−2.77392
$259$	−5028.55	−1.20641
$260$	−16406.6	−3.91343
$261$	3478.01	0.824840
$262$	−693.906	−0.163625
$263$	4873.16	1.14255	0.571277	−	0.820757i	$-0.306448\pi$
$263$	4873.16	1.14255	0.571277	+	0.820757i	$0.306448\pi$
$264$	4984.53	1.16203
$265$	5149.11	1.19361
$266$	−5853.73	−1.34931
$267$	9357.38	2.14480
$268$	16006.0	3.64823
$269$	−6662.54	−1.51012	−0.755060	−	0.655656i	$-0.772392\pi$
$269$	−6662.54	−1.51012	−0.755060	+	0.655656i	$0.772392\pi$
$270$	−2042.34	−0.460344
$271$	8000.02	1.79323	0.896617	−	0.442807i	$-0.146017\pi$
$271$	8000.02	1.79323	0.896617	+	0.442807i	$0.146017\pi$
$272$	20485.0	4.56648
$273$	−11253.4	−2.49483
$274$	13276.7	2.92727
$275$	−1039.94	−0.228039
$276$	−12878.0	−2.80856
$277$	1389.62	0.301424	0.150712	−	0.988578i	$-0.451843\pi$
$277$	1389.62	0.301424	0.150712	+	0.988578i	$0.451843\pi$
$278$	5159.34	1.11308
$279$	−738.641	−0.158499
$280$	−27192.9	−5.80389
$281$	252.067	0.0535127	0.0267563	−	0.999642i	$-0.491482\pi$
$281$	252.067	0.0535127	0.0267563	+	0.999642i	$0.491482\pi$
$282$	7690.75	1.62403
$283$	−72.7990	−0.0152914	−0.00764568	−	0.999971i	$-0.502434\pi$
$283$	−72.7990	−0.0152914	−0.00764568	+	0.999971i	$0.502434\pi$
$284$	−8432.81	−1.76195
$285$	4042.89	0.840281
$286$	3216.57	0.665034
$287$	7313.60	1.50421
$288$	−10060.0	−2.05830
$289$	8351.73	1.69992
$290$	11699.4	2.36901
$291$	−3605.33	−0.726283
$292$	3531.99	0.707857
$293$	−8845.25	−1.76363	−0.881817	−	0.471592i	$-0.843680\pi$
$293$	−8845.25	−1.76363	−0.881817	+	0.471592i	$0.843680\pi$
$294$	−18136.7	−3.59781
$295$	−4500.08	−0.888151
$296$	−11177.9	−2.19494
$297$	286.243	0.0559242
$298$	13580.6	2.63994
$299$	−4995.81	−0.966271
$300$	13453.3	2.58908
$301$	−8789.47	−1.68311
$302$	−11754.8	−2.23977
$303$	8455.23	1.60310
$304$	−6840.67	−1.29059
$305$	−7414.68	−1.39201
$306$	−14234.2	−2.65919
$307$	−9743.03	−1.81128	−0.905642	−	0.424043i	$-0.860610\pi$
$307$	−9743.03	−1.81128	−0.905642	+	0.424043i	$0.860610\pi$
$308$	6339.77	1.17286
$309$	−11636.6	−2.14234
$310$	−2484.65	−0.455222
$311$	−4677.06	−0.852771	−0.426385	−	0.904542i	$-0.640213\pi$
$311$	−4677.06	−0.852771	−0.426385	+	0.904542i	$0.640213\pi$
$312$	−25015.1	−4.53911
$313$	7525.50	1.35900	0.679499	−	0.733676i	$-0.262197\pi$
$313$	7525.50	1.35900	0.679499	+	0.733676i	$0.262197\pi$
$314$	671.653	0.120712
$315$	9933.47	1.77679
$316$	5771.73	1.02748
$317$	−6770.08	−1.19951	−0.599757	−	0.800182i	$-0.704736\pi$
$317$	−6770.08	−1.19951	−0.599757	+	0.800182i	$0.704736\pi$
$318$	13059.5	2.30296
$319$	−1639.72	−0.287795
$320$	−12757.0	−2.22855
$321$	−9813.35	−1.70632
$322$	−13773.8	−2.38380
$323$	−4429.58	−0.763059
$324$	−16338.9	−2.80160
$325$	5218.99	0.890761
$326$	−4067.78	−0.691084
$327$	−1860.49	−0.314634
$328$	16257.3	2.73677
$329$	5880.41	0.985404
$330$	−6124.93	−1.02172
$331$	−6015.19	−0.998867	−0.499433	−	0.866352i	$-0.666458\pi$
$331$	−6015.19	−0.998867	−0.499433	+	0.866352i	$0.666458\pi$
$332$	−4018.63	−0.664310
$333$	4083.25	0.671954
$334$	12873.7	2.10903
$335$	−11823.6	−1.92834
$336$	−36257.6	−5.88695
$337$	−3183.75	−0.514628	−0.257314	−	0.966328i	$-0.582838\pi$
$337$	−3183.75	−0.514628	−0.257314	+	0.966328i	$0.582838\pi$
$338$	−4505.04	−0.724976
$339$	1286.12	0.206054
$340$	−34229.1	−5.45981
$341$	348.235	0.0553020
$342$	4753.31	0.751548
$343$	−4011.86	−0.631546
$344$	−19538.0	−3.06227
$345$	9512.91	1.48452
$346$	−1601.27	−0.248801
$347$	8092.71	1.25199	0.625993	−	0.779829i	$-0.284694\pi$
$347$	8092.71	1.25199	0.625993	+	0.779829i	$0.284694\pi$
$348$	21212.4	3.26754
$349$	−9893.83	−1.51749	−0.758746	−	0.651387i	$-0.774188\pi$
$349$	−9893.83	−1.51749	−0.758746	+	0.651387i	$0.774188\pi$
$350$	14389.1	2.19752
$351$	−1436.52	−0.218450
$352$	4742.82	0.718162
$353$	6341.58	0.956171	0.478086	−	0.878313i	$-0.341331\pi$
$353$	6341.58	0.956171	0.478086	+	0.878313i	$0.341331\pi$
$354$	−11413.4	−1.71360
$355$	6229.29	0.931314
$356$	26455.9	3.93865
$357$	−23478.1	−3.48065
$358$	17485.0	2.58131
$359$	−3089.94	−0.454264	−0.227132	−	0.973864i	$-0.572935\pi$
$359$	−3089.94	−0.454264	−0.227132	+	0.973864i	$0.572935\pi$
$360$	22081.0	3.23270
$361$	−5379.80	−0.784342
$362$	3653.25	0.530416
$363$	858.436	0.124122
$364$	−31816.5	−4.58142
$365$	−2609.07	−0.374151
$366$	−18805.6	−2.68575
$367$	−2152.55	−0.306164	−0.153082	−	0.988214i	$-0.548920\pi$
$367$	−2152.55	−0.306164	−0.153082	+	0.988214i	$0.548920\pi$
$368$	−16096.1	−2.28007
$369$	−5938.74	−0.837827
$370$	13735.3	1.92990
$371$	9985.42	1.39735
$372$	−4504.98	−0.627882
$373$	−3823.34	−0.530737	−0.265368	−	0.964147i	$-0.585494\pi$
$373$	−3823.34	−0.530737	−0.265368	+	0.964147i	$0.585494\pi$
$374$	6710.75	0.927820
$375$	3201.92	0.440924
$376$	13071.5	1.79285
$377$	8229.02	1.12418
$378$	−3960.61	−0.538920
$379$	−257.929	−0.0349576	−0.0174788	−	0.999847i	$-0.505564\pi$
$379$	−257.929	−0.0349576	−0.0174788	+	0.999847i	$0.505564\pi$
$380$	11430.4	1.54307
$381$	11110.1	1.49393
$382$	16510.5	2.21139
$383$	11924.5	1.59090	0.795448	−	0.606022i	$-0.207236\pi$
$383$	11924.5	1.59090	0.795448	+	0.606022i	$0.207236\pi$
$384$	−7883.78	−1.04770
$385$	−4683.17	−0.619939
$386$	−19159.0	−2.52635
$387$	7137.16	0.937473
$388$	−10193.3	−1.33372
$389$	4901.58	0.638869	0.319435	−	0.947608i	$-0.396507\pi$
$389$	4901.58	0.638869	0.319435	+	0.947608i	$0.396507\pi$
$390$	30738.3	3.99101
$391$	−10422.8	−1.34809
$392$	−30825.9	−3.97180
$393$	929.381	0.119290
$394$	14032.9	1.79433
$395$	−4263.56	−0.543096
$396$	−5147.97	−0.653271
$397$	11129.9	1.40704	0.703520	−	0.710675i	$-0.251610\pi$
$397$	11129.9	1.40704	0.703520	+	0.710675i	$0.251610\pi$
$398$	27838.0	3.50601
$399$	7840.18	0.983709
$400$	16815.2	2.10189
$401$	10164.4	1.26580	0.632899	−	0.774234i	$-0.281865\pi$
$401$	10164.4	1.26580	0.632899	+	0.774234i	$0.281865\pi$
$402$	−29987.9	−3.72054
$403$	−1747.64	−0.216020
$404$	23905.2	2.94389
$405$	12069.5	1.48084
$406$	22688.0	2.77337
$407$	−1925.06	−0.234452
$408$	−52189.2	−6.33272
$409$	−16404.4	−1.98325	−0.991623	−	0.129167i	$-0.958770\pi$
$409$	−16404.4	−1.98325	−0.991623	+	0.129167i	$0.958770\pi$
$410$	−19976.8	−2.40630
$411$	−17782.0	−2.13412
$412$	−32899.9	−3.93413
$413$	−8726.78	−1.03975
$414$	11184.5	1.32775
$415$	2968.55	0.351133
$416$	−23802.1	−2.80527
$417$	−6910.15	−0.811491
$418$	−2240.96	−0.262223
$419$	993.904	0.115884	0.0579420	−	0.998320i	$-0.481546\pi$
$419$	993.904	0.115884	0.0579420	+	0.998320i	$0.481546\pi$
$420$	60584.3	7.03860
$421$	−6645.86	−0.769357	−0.384679	−	0.923051i	$-0.625688\pi$
$421$	−6645.86	−0.769357	−0.384679	+	0.923051i	$0.625688\pi$
$422$	8752.24	1.00960
$423$	−4774.97	−0.548858
$424$	22196.5	2.54235
$425$	10888.4	1.24274
$426$	15799.1	1.79688
$427$	−14378.9	−1.62961
$428$	−27745.0	−3.13343
$429$	−4308.11	−0.484842
$430$	24008.1	2.69250
$431$	−1863.45	−0.208258	−0.104129	−	0.994564i	$-0.533206\pi$
$431$	−1863.45	−0.208258	−0.104129	+	0.994564i	$0.533206\pi$
$432$	−4628.36	−0.515468
$433$	8093.18	0.898229	0.449115	−	0.893474i	$-0.351739\pi$
$433$	8093.18	0.898229	0.449115	+	0.893474i	$0.351739\pi$
$434$	−4818.37	−0.532924
$435$	−15669.5	−1.72712
$436$	−5260.11	−0.577783
$437$	3480.54	0.381000
$438$	−6617.31	−0.721888
$439$	−18111.5	−1.96906	−0.984529	−	0.175223i	$-0.943935\pi$
$439$	−18111.5	−1.96906	−0.984529	+	0.175223i	$0.943935\pi$
$440$	−10410.2	−1.12792
$441$	11260.6	1.21592
$442$	−33678.3	−3.62423
$443$	10717.3	1.14943	0.574713	−	0.818355i	$-0.305114\pi$
$443$	10717.3	1.14943	0.574713	+	0.818355i	$0.305114\pi$
$444$	24903.8	2.66189
$445$	−19542.9	−2.08185
$446$	34903.2	3.70564
$447$	−18189.1	−1.92464
$448$	−24738.9	−2.60894
$449$	−2805.04	−0.294828	−0.147414	−	0.989075i	$-0.547095\pi$
$449$	−2805.04	−0.294828	−0.147414	+	0.989075i	$0.547095\pi$
$450$	−11684.2	−1.22399
$451$	2799.84	0.292327
$452$	3636.20	0.378391
$453$	15743.7	1.63290
$454$	13064.6	1.35055
$455$	23502.8	2.42160
$456$	17427.9	1.78977
$457$	15726.5	1.60975	0.804874	−	0.593446i	$-0.202233\pi$
$457$	15726.5	1.60975	0.804874	+	0.593446i	$0.202233\pi$
$458$	−101.178	−0.0103226
$459$	−2997.03	−0.304770
$460$	26895.6	2.72612
$461$	10710.4	1.08207	0.541036	−	0.840999i	$-0.318032\pi$
$461$	10710.4	1.08207	0.541036	+	0.840999i	$0.318032\pi$
$462$	−11877.8	−1.19611
$463$	−8511.12	−0.854310	−0.427155	−	0.904178i	$-0.640484\pi$
$463$	−8511.12	−0.854310	−0.427155	+	0.904178i	$0.640484\pi$
$464$	26513.2	2.65269
$465$	3327.82	0.331879
$466$	27624.5	2.74609
$467$	1629.43	0.161459	0.0807293	−	0.996736i	$-0.474275\pi$
$467$	1629.43	0.161459	0.0807293	+	0.996736i	$0.474275\pi$
$468$	25835.4	2.55180
$469$	−22929.0	−2.25749
$470$	−16062.1	−1.57636
$471$	−899.577	−0.0880049
$472$	−19398.7	−1.89173
$473$	−3364.84	−0.327094
$474$	−10813.5	−1.04785
$475$	−3636.03	−0.351227
$476$	−66378.9	−6.39175
$477$	−8108.28	−0.778308
$478$	19553.6	1.87105
$479$	−11404.3	−1.08785	−0.543923	−	0.839135i	$-0.683062\pi$
$479$	−11404.3	−1.08785	−0.543923	+	0.839135i	$0.683062\pi$
$480$	45323.5	4.30984
$481$	9661.03	0.915811
$482$	−30628.0	−2.89433
$483$	18447.9	1.73791
$484$	2427.03	0.227933
$485$	7529.73	0.704964
$486$	26889.9	2.50978
$487$	12351.2	1.14926	0.574629	−	0.818414i	$-0.305147\pi$
$487$	12351.2	1.14926	0.574629	+	0.818414i	$0.305147\pi$
$488$	−31962.8	−2.96493
$489$	5448.17	0.503834
$490$	37878.6	3.49220
$491$	−10322.8	−0.948797	−0.474399	−	0.880310i	$-0.657334\pi$
$491$	−10322.8	−0.948797	−0.474399	+	0.880310i	$0.657334\pi$
$492$	−36220.4	−3.31899
$493$	17168.3	1.56840
$494$	11246.4	1.02429
$495$	3802.80	0.345299
$496$	−5630.75	−0.509734
$497$	12080.2	1.09028
$498$	7529.04	0.677478
$499$	8412.50	0.754700	0.377350	−	0.926071i	$-0.376835\pi$
$499$	8412.50	0.754700	0.377350	+	0.926071i	$0.376835\pi$
$500$	9052.70	0.809698
$501$	−17242.4	−1.53759
$502$	12014.5	1.06819
$503$	7085.86	0.628117	0.314058	−	0.949404i	$-0.398311\pi$
$503$	7085.86	0.628117	0.314058	+	0.949404i	$0.398311\pi$
$504$	42820.6	3.78449
$505$	−17658.7	−1.55605
$506$	−5272.98	−0.463266
$507$	6033.82	0.528543
$508$	31411.2	2.74340
$509$	−16654.4	−1.45028	−0.725141	−	0.688600i	$-0.758225\pi$
$509$	−16654.4	−1.45028	−0.725141	+	0.688600i	$0.758225\pi$
$510$	64129.5	5.56804
$511$	−5059.65	−0.438015
$512$	14195.0	1.22527
$513$	1000.82	0.0861348
$514$	−26024.4	−2.23324
$515$	24303.1	2.07946
$516$	43529.6	3.71373
$517$	2251.18	0.191502
$518$	26636.2	2.25932
$519$	2144.66	0.181388
$520$	52244.0	4.40587
$521$	7112.16	0.598061	0.299030	−	0.954244i	$-0.403337\pi$
$521$	7112.16	0.598061	0.299030	+	0.954244i	$0.403337\pi$
$522$	−18423.0	−1.54474
$523$	−10186.2	−0.851650	−0.425825	−	0.904806i	$-0.640016\pi$
$523$	−10186.2	−0.851650	−0.425825	+	0.904806i	$0.640016\pi$
$524$	2627.61	0.219061
$525$	−19272.1	−1.60210
$526$	−25813.1	−2.13974
$527$	−3646.11	−0.301379
$528$	−13880.4	−1.14406
$529$	−3977.29	−0.326891
$530$	−27274.8	−2.23536
$531$	7086.25	0.579128
$532$	22166.3	1.80645
$533$	−14051.1	−1.14188
$534$	−49566.0	−4.01672
$535$	20495.2	1.65623
$536$	−50968.6	−4.10729
$537$	−23418.4	−1.88190
$538$	35291.4	2.82811
$539$	−5308.85	−0.424245
$540$	7733.72	0.616308
$541$	3913.21	0.310983	0.155492	−	0.987837i	$-0.450304\pi$
$541$	3913.21	0.310983	0.155492	+	0.987837i	$0.450304\pi$
$542$	−42376.0	−3.35831
$543$	−4892.97	−0.386699
$544$	−49658.4	−3.91376
$545$	3885.63	0.305398
$546$	59609.3	4.67224
$547$	24076.2	1.88195	0.940974	−	0.338478i	$-0.109912\pi$
$547$	24076.2	1.88195	0.940974	+	0.338478i	$0.109912\pi$
$548$	−50274.7	−3.91903
$549$	11675.9	0.907676
$550$	5508.55	0.427064
$551$	−5733.11	−0.443264
$552$	41007.7	3.16196
$553$	−8268.12	−0.635798
$554$	−7360.82	−0.564497
$555$	−18396.3	−1.40699
$556$	−19536.9	−1.49020
$557$	6019.64	0.457918	0.228959	−	0.973436i	$-0.426468\pi$
$557$	6019.64	0.457918	0.228959	+	0.973436i	$0.426468\pi$
$558$	3912.58	0.296833
$559$	16886.6	1.27769
$560$	75724.0	5.71415
$561$	−8988.03	−0.676426
$562$	−1335.20	−0.100217
$563$	11990.8	0.897603	0.448802	−	0.893631i	$-0.351851\pi$
$563$	11990.8	0.897603	0.448802	+	0.893631i	$0.351851\pi$
$564$	−29122.6	−2.17426
$565$	−2686.05	−0.200006
$566$	385.616	0.0286372
$567$	23405.9	1.73360
$568$	26852.9	1.98366
$569$	−16925.3	−1.24701	−0.623503	−	0.781821i	$-0.714291\pi$
$569$	−16925.3	−1.24701	−0.623503	+	0.781821i	$0.714291\pi$
$570$	−21415.2	−1.57365
$571$	−14064.5	−1.03079	−0.515394	−	0.856953i	$-0.672354\pi$
$571$	−14064.5	−1.03079	−0.515394	+	0.856953i	$0.672354\pi$
$572$	−12180.2	−0.890348
$573$	−22113.3	−1.61221
$574$	−38740.1	−2.81704
$575$	−8555.58	−0.620508
$576$	20088.3	1.45315
$577$	2912.16	0.210112	0.105056	−	0.994466i	$-0.466498\pi$
$577$	2912.16	0.210112	0.105056	+	0.994466i	$0.466498\pi$
$578$	−44239.0	−3.18357
$579$	25660.6	1.84183
$580$	−44302.1	−3.17163
$581$	5756.76	0.411069
$582$	19097.4	1.36016
$583$	3822.68	0.271560
$584$	−11247.0	−0.796928
$585$	−19084.5	−1.34880
$586$	46853.2	3.30288
$587$	−11593.9	−0.815217	−0.407609	−	0.913157i	$-0.633637\pi$
$587$	−11593.9	−0.815217	−0.407609	+	0.913157i	$0.633637\pi$
$588$	68678.4	4.81675
$589$	1217.57	0.0851766
$590$	23836.9	1.66330
$591$	−18794.9	−1.30816
$592$	31127.1	2.16100
$593$	15540.4	1.07617	0.538083	−	0.842892i	$-0.319149\pi$
$593$	15540.4	1.07617	0.538083	+	0.842892i	$0.319149\pi$
$594$	−1516.23	−0.104733
$595$	49033.9	3.37848
$596$	−51425.6	−3.53435
$597$	−37284.7	−2.55605
$598$	26462.7	1.80960
$599$	−19131.2	−1.30497	−0.652487	−	0.757800i	$-0.726274\pi$
$599$	−19131.2	−1.30497	−0.652487	+	0.757800i	$0.726274\pi$
$600$	−42839.7	−2.91487
$601$	19828.0	1.34576	0.672881	−	0.739751i	$-0.265057\pi$
$601$	19828.0	1.34576	0.672881	+	0.739751i	$0.265057\pi$
$602$	46557.7	3.15208
$603$	18618.6	1.25739
$604$	44511.7	2.99860
$605$	−1792.84	−0.120478
$606$	−44787.3	−3.00224
$607$	−12708.7	−0.849801	−0.424900	−	0.905240i	$-0.639691\pi$
$607$	−12708.7	−0.849801	−0.424900	+	0.905240i	$0.639691\pi$
$608$	16582.8	1.10612
$609$	−30387.2	−2.02192
$610$	39275.5	2.60691
$611$	−11297.7	−0.748043
$612$	53900.5	3.56013
$613$	−12342.6	−0.813232	−0.406616	−	0.913599i	$-0.633291\pi$
$613$	−12342.6	−0.813232	−0.406616	+	0.913599i	$0.633291\pi$
$614$	51608.8	3.39212
$615$	26755.9	1.75431
$616$	−20187.9	−1.32045
$617$	26432.0	1.72465	0.862327	−	0.506353i	$-0.169007\pi$
$617$	26432.0	1.72465	0.862327	+	0.506353i	$0.169007\pi$
$618$	61639.0	4.01211
$619$	−7993.89	−0.519065	−0.259533	−	0.965734i	$-0.583569\pi$
$619$	−7993.89	−0.519065	−0.259533	+	0.965734i	$0.583569\pi$
$620$	9408.64	0.609452
$621$	2354.92	0.152173
$622$	24774.3	1.59704
$623$	−37898.6	−2.43720
$624$	69659.4	4.46892
$625$	−18504.7	−1.18430
$626$	−39862.5	−2.54509
$627$	3001.43	0.191173
$628$	−2543.35	−0.161609
$629$	20155.9	1.27769
$630$	−52617.5	−3.32751
$631$	−175.085	−0.0110460	−0.00552300	−	0.999985i	$-0.501758\pi$
$631$	−175.085	−0.0110460	−0.00552300	+	0.999985i	$0.501758\pi$
$632$	−18379.1	−1.15678
$633$	−11722.3	−0.736049
$634$	35861.1	2.24641
$635$	−23203.4	−1.45007
$636$	−49452.5	−3.08320
$637$	26642.7	1.65718
$638$	8685.58	0.538974
$639$	−9809.24	−0.607273
$640$	16465.3	1.01695
$641$	−30108.4	−1.85524	−0.927621	−	0.373522i	$-0.878150\pi$
$641$	−30108.4	−1.85524	−0.927621	+	0.373522i	$0.878150\pi$
$642$	51981.2	3.19554
$643$	16113.7	0.988278	0.494139	−	0.869383i	$-0.335483\pi$
$643$	16113.7	0.988278	0.494139	+	0.869383i	$0.335483\pi$
$644$	52157.3	3.19144
$645$	−32155.2	−1.96296
$646$	23463.4	1.42903
$647$	−25887.5	−1.57302	−0.786508	−	0.617580i	$-0.788113\pi$
$647$	−25887.5	−1.57302	−0.786508	+	0.617580i	$0.788113\pi$
$648$	52028.6	3.15413
$649$	−3340.84	−0.202064
$650$	−27644.9	−1.66819
$651$	6453.47	0.388528
$652$	15403.5	0.925224
$653$	−13886.1	−0.832165	−0.416083	−	0.909327i	$-0.636597\pi$
$653$	−13886.1	−0.832165	−0.416083	+	0.909327i	$0.636597\pi$
$654$	9854.99	0.589236
$655$	−1941.01	−0.115789
$656$	−45271.6	−2.69445
$657$	4108.50	0.243969
$658$	−31148.5	−1.84543
$659$	−895.597	−0.0529401	−0.0264700	−	0.999650i	$-0.508427\pi$
$659$	−895.597	−0.0529401	−0.0264700	+	0.999650i	$0.508427\pi$
$660$	23193.3	1.36787
$661$	−10659.3	−0.627231	−0.313616	−	0.949550i	$-0.601540\pi$
$661$	−10659.3	−0.627231	−0.313616	+	0.949550i	$0.601540\pi$
$662$	31862.4	1.87065
$663$	45106.9	2.64224
$664$	12796.7	0.747901
$665$	−16374.2	−0.954834
$666$	−21628.9	−1.25841
$667$	−13490.0	−0.783110
$668$	−48748.8	−2.82358
$669$	−46747.5	−2.70159
$670$	62629.6	3.61133
$671$	−5504.63	−0.316697
$672$	87893.6	5.04549
$673$	−10899.0	−0.624259	−0.312129	−	0.950040i	$-0.601042\pi$
$673$	−10899.0	−0.624259	−0.312129	+	0.950040i	$0.601042\pi$
$674$	16864.3	0.963780
$675$	−2460.12	−0.140282
$676$	17059.2	0.970599
$677$	18155.9	1.03071	0.515353	−	0.856978i	$-0.327661\pi$
$677$	18155.9	1.03071	0.515353	+	0.856978i	$0.327661\pi$
$678$	−6812.55	−0.385891
$679$	14602.0	0.825294
$680$	108997.	6.14683
$681$	−17498.0	−0.984619
$682$	−1844.60	−0.103568
$683$	23210.7	1.30034	0.650169	−	0.759790i	$-0.274698\pi$
$683$	23210.7	1.30034	0.650169	+	0.759790i	$0.274698\pi$
$684$	−17999.3	−1.00617
$685$	37137.8	2.07148
$686$	21250.8	1.18274
$687$	135.512	0.00752565
$688$	54407.4	3.01491
$689$	−19184.3	−1.06076
$690$	−50389.8	−2.78016
$691$	6066.98	0.334007	0.167003	−	0.985956i	$-0.446591\pi$
$691$	6066.98	0.334007	0.167003	+	0.985956i	$0.446591\pi$
$692$	6063.55	0.333095
$693$	7374.58	0.404238
$694$	−42867.0	−2.34468
$695$	14431.8	0.787671
$696$	−67547.3	−3.67870
$697$	−29315.0	−1.59309
$698$	52407.5	2.84191
$699$	−36998.8	−2.00203
$700$	−54487.4	−2.94204
$701$	24037.5	1.29512	0.647562	−	0.762013i	$-0.275789\pi$
$701$	24037.5	1.29512	0.647562	+	0.762013i	$0.275789\pi$
$702$	7609.26	0.409107
$703$	−6730.78	−0.361104
$704$	−9470.72	−0.507019
$705$	21512.8	1.14925
$706$	−33591.3	−1.79069
$707$	−34244.7	−1.82165
$708$	43219.1	2.29417
$709$	−31954.1	−1.69261	−0.846306	−	0.532697i	$-0.821178\pi$
$709$	−31954.1	−1.69261	−0.846306	+	0.532697i	$0.821178\pi$
$710$	−32996.5	−1.74414
$711$	6713.82	0.354132
$712$	−84244.3	−4.43426
$713$	2864.93	0.150480
$714$	124363.	6.51845
$715$	8997.47	0.470610
$716$	−66210.3	−3.45586
$717$	−26189.1	−1.36409
$718$	16367.4	0.850732
$719$	12437.4	0.645111	0.322556	−	0.946551i	$-0.395458\pi$
$719$	12437.4	0.645111	0.322556	+	0.946551i	$0.395458\pi$
$720$	−61488.8	−3.18271
$721$	47129.7	2.43440
$722$	28496.8	1.46889
$723$	41021.5	2.11011
$724$	−13833.8	−0.710121
$725$	14092.6	0.721914
$726$	−4547.13	−0.232451
$727$	799.512	0.0407871	0.0203936	−	0.999792i	$-0.493508\pi$
$727$	799.512	0.0407871	0.0203936	+	0.999792i	$0.493508\pi$
$728$	101314.	5.15791
$729$	−14021.3	−0.712355
$730$	13820.2	0.700699
$731$	35230.7	1.78256
$732$	71211.2	3.59568
$733$	−13547.3	−0.682646	−0.341323	−	0.939946i	$-0.610875\pi$
$733$	−13547.3	−0.682646	−0.341323	+	0.939946i	$0.610875\pi$
$734$	11402.0	0.573374
$735$	−50732.6	−2.54598
$736$	39019.2	1.95417
$737$	−8777.82	−0.438718
$738$	31457.4	1.56906
$739$	6157.09	0.306485	0.153242	−	0.988189i	$-0.451028\pi$
$739$	6157.09	0.306485	0.153242	+	0.988189i	$0.451028\pi$
$740$	−52011.5	−2.58376
$741$	−15062.8	−0.746757
$742$	−52892.7	−2.61692
$743$	−34108.0	−1.68412	−0.842060	−	0.539384i	$-0.818657\pi$
$743$	−34108.0	−1.68412	−0.842060	+	0.539384i	$0.818657\pi$
$744$	14345.4	0.706890
$745$	37987.9	1.86815
$746$	20252.2	0.993947
$747$	−4674.57	−0.228960
$748$	−25411.6	−1.24217
$749$	39745.3	1.93893
$750$	−16960.5	−0.825749
$751$	−25158.9	−1.22245	−0.611226	−	0.791456i	$-0.709323\pi$
$751$	−25158.9	−1.22245	−0.611226	+	0.791456i	$0.709323\pi$
$752$	−36400.1	−1.76513
$753$	−16091.5	−0.778763
$754$	−43589.1	−2.10533
$755$	−32880.7	−1.58497
$756$	14997.6	0.721506
$757$	12332.1	0.592096	0.296048	−	0.955173i	$-0.404331\pi$
$757$	12332.1	0.592096	0.296048	+	0.955173i	$0.404331\pi$
$758$	1366.25	0.0654675
$759$	7062.35	0.337743
$760$	−36398.1	−1.73723
$761$	−29913.3	−1.42491	−0.712454	−	0.701719i	$-0.752416\pi$
$761$	−29913.3	−1.42491	−0.712454	+	0.701719i	$0.752416\pi$
$762$	−58849.9	−2.79778
$763$	7535.21	0.357527
$764$	−62520.3	−2.96061
$765$	−39816.2	−1.88177
$766$	−63163.9	−2.97938
$767$	16766.2	0.789298
$768$	−7105.21	−0.333838
$769$	−25504.4	−1.19599	−0.597993	−	0.801501i	$-0.704035\pi$
$769$	−25504.4	−1.19599	−0.597993	+	0.801501i	$0.704035\pi$
$770$	24806.7	1.16100
$771$	34855.7	1.62814
$772$	72549.5	3.38227
$773$	−31123.1	−1.44815	−0.724076	−	0.689720i	$-0.757734\pi$
$773$	−31123.1	−1.44815	−0.724076	+	0.689720i	$0.757734\pi$
$774$	−37805.5	−1.75567
$775$	−2992.92	−0.138721
$776$	32458.7	1.50155
$777$	−35675.1	−1.64715
$778$	−25963.7	−1.19646
$779$	9789.34	0.450243
$780$	−116397.	−5.34317
$781$	4624.61	0.211884
$782$	55209.4	2.52466
$783$	−3878.99	−0.177042
$784$	85840.7	3.91038
$785$	1878.77	0.0854217
$786$	−4922.92	−0.223403
$787$	−23365.2	−1.05830	−0.529149	−	0.848529i	$-0.677489\pi$
$787$	−23365.2	−1.05830	−0.529149	+	0.848529i	$0.677489\pi$
$788$	−53138.4	−2.40226
$789$	34572.7	1.55998
$790$	22584.1	1.01709
$791$	−5208.93	−0.234145
$792$	16392.9	0.735474
$793$	27625.3	1.23708
$794$	−58955.1	−2.63506
$795$	36530.4	1.62969
$796$	−105414.	−4.69384
$797$	24978.3	1.11013	0.555066	−	0.831806i	$-0.312693\pi$
$797$	24978.3	1.11013	0.555066	+	0.831806i	$0.312693\pi$
$798$	−41529.4	−1.84226
$799$	−23570.4	−1.04363
$800$	−40762.3	−1.80146
$801$	30774.1	1.35749
$802$	−53840.7	−2.37055
$803$	−1936.97	−0.0851234
$804$	113555.	4.98107
$805$	−38528.5	−1.68689
$806$	9257.22	0.404555
$807$	−47267.5	−2.06183
$808$	−76122.2	−3.31432
$809$	3140.16	0.136467	0.0682337	−	0.997669i	$-0.478264\pi$
$809$	3140.16	0.136467	0.0682337	+	0.997669i	$0.478264\pi$
$810$	−63932.2	−2.77327
$811$	12821.1	0.555127	0.277563	−	0.960707i	$-0.410473\pi$
$811$	12821.1	0.555127	0.277563	+	0.960707i	$0.410473\pi$
$812$	−85912.8	−3.71299
$813$	56756.2	2.44837
$814$	10197.0	0.439074
$815$	−11378.5	−0.489045
$816$	145331.	6.23480
$817$	−11764.8	−0.503792
$818$	86894.2	3.71416
$819$	−37009.7	−1.57903
$820$	75646.2	3.22156
$821$	39845.2	1.69380	0.846898	−	0.531755i	$-0.178467\pi$
$821$	39845.2	1.69380	0.846898	+	0.531755i	$0.178467\pi$
$822$	94191.4	3.99672
$823$	36261.4	1.53583	0.767917	−	0.640549i	$-0.221293\pi$
$823$	36261.4	1.53583	0.767917	+	0.640549i	$0.221293\pi$
$824$	104764.	4.42917
$825$	−7377.86	−0.311350
$826$	46225.7	1.94721
$827$	−27018.5	−1.13606	−0.568032	−	0.823007i	$-0.692295\pi$
$827$	−27018.5	−1.13606	−0.568032	+	0.823007i	$0.692295\pi$
$828$	−42352.4	−1.77759
$829$	−11954.2	−0.500828	−0.250414	−	0.968139i	$-0.580567\pi$
$829$	−11954.2	−0.500828	−0.250414	+	0.968139i	$0.580567\pi$
$830$	−15724.4	−0.657592
$831$	9858.69	0.411545
$832$	47529.3	1.98051
$833$	55584.9	2.31201
$834$	36603.0	1.51973
$835$	36010.6	1.49245
$836$	8485.86	0.351064
$837$	823.800	0.0340199
$838$	−5264.70	−0.217024
$839$	8474.84	0.348729	0.174365	−	0.984681i	$-0.444213\pi$
$839$	8474.84	0.348729	0.174365	+	0.984681i	$0.444213\pi$
$840$	−192921.	−7.92428
$841$	−2168.48	−0.0889122
$842$	35203.1	1.44083
$843$	1788.29	0.0730630
$844$	−33142.1	−1.35166
$845$	−12601.6	−0.513028
$846$	25293.0	1.02788
$847$	−3476.77	−0.141043
$848$	−61810.4	−2.50304
$849$	−516.474	−0.0208779
$850$	−57675.8	−2.32737
$851$	−15837.5	−0.637958
$852$	−59826.6	−2.40567
$853$	17419.9	0.699234	0.349617	−	0.936893i	$-0.386312\pi$
$853$	17419.9	0.699234	0.349617	+	0.936893i	$0.386312\pi$
$854$	76165.0	3.05189
$855$	13296.1	0.531831
$856$	88349.4	3.52771
$857$	2571.81	0.102510	0.0512552	−	0.998686i	$-0.483678\pi$
$857$	2571.81	0.102510	0.0512552	+	0.998686i	$0.483678\pi$
$858$	22820.0	0.907998
$859$	17952.8	0.713085	0.356543	−	0.934279i	$-0.383955\pi$
$859$	17952.8	0.713085	0.356543	+	0.934279i	$0.383955\pi$
$860$	−90911.5	−3.60472
$861$	51886.4	2.05376
$862$	9870.68	0.390020
$863$	−250.966	−0.00989916	−0.00494958	−	0.999988i	$-0.501576\pi$
$863$	−250.966	−0.00989916	−0.00494958	+	0.999988i	$0.501576\pi$
$864$	11219.8	0.441789
$865$	−4479.13	−0.176063
$866$	−42869.5	−1.68218
$867$	59251.4	2.32097
$868$	18245.7	0.713479
$869$	−3165.25	−0.123560
$870$	83001.4	3.23450
$871$	44051.9	1.71371
$872$	16749.9	0.650487
$873$	−11857.0	−0.459679
$874$	−18436.4	−0.713525
$875$	−12968.2	−0.501034
$876$	25057.8	0.966465
$877$	−28132.5	−1.08320	−0.541600	−	0.840636i	$-0.682181\pi$
$877$	−28132.5	−1.08320	−0.541600	+	0.840636i	$0.682181\pi$
$878$	95936.6	3.68759
$879$	−62752.7	−2.40796
$880$	28989.1	1.11048
$881$	−469.997	−0.0179734	−0.00898672	−	0.999960i	$-0.502861\pi$
$881$	−469.997	−0.0179734	−0.00898672	+	0.999960i	$0.502861\pi$
$882$	−59647.2	−2.27713
$883$	−14033.4	−0.534839	−0.267419	−	0.963580i	$-0.586171\pi$
$883$	−14033.4	−0.534839	−0.267419	+	0.963580i	$0.586171\pi$
$884$	127529.	4.85213
$885$	−31925.8	−1.21263
$886$	−56769.6	−2.15261
$887$	36973.7	1.39961	0.699806	−	0.714333i	$-0.253270\pi$
$887$	36973.7	1.39961	0.699806	+	0.714333i	$0.253270\pi$
$888$	−79301.9	−2.99684
$889$	−44997.1	−1.69759
$890$	103518.	3.89882
$891$	8960.38	0.336907
$892$	−132168.	−4.96111
$893$	7871.00	0.294953
$894$	96347.6	3.60441
$895$	48909.4	1.82666
$896$	31930.3	1.19053
$897$	−35442.8	−1.31929
$898$	14858.2	0.552145
$899$	−4719.08	−0.175072
$900$	44244.4	1.63868
$901$	−40024.4	−1.47992
$902$	−14830.7	−0.547460
$903$	−62357.0	−2.29802
$904$	−11578.9	−0.426004
$905$	10219.0	0.375348
$906$	−83394.3	−3.05805
$907$	−18543.0	−0.678842	−0.339421	−	0.940635i	$-0.610231\pi$
$907$	−18543.0	−0.678842	−0.339421	+	0.940635i	$0.610231\pi$
$908$	−49471.7	−1.80812
$909$	27807.1	1.01464
$910$	−124494.	−4.53509
$911$	−780.982	−0.0284030	−0.0142015	−	0.999899i	$-0.504521\pi$
$911$	−780.982	−0.0284030	−0.0142015	+	0.999899i	$0.504521\pi$
$912$	−48531.2	−1.76209
$913$	2203.84	0.0798866
$914$	−83303.2	−3.01469
$915$	−52603.5	−1.90057
$916$	383.131	0.0138199
$917$	−3764.11	−0.135553
$918$	15875.2	0.570763
$919$	−2385.79	−0.0856363	−0.0428182	−	0.999083i	$-0.513634\pi$
$919$	−2385.79	−0.0856363	−0.0428182	+	0.999083i	$0.513634\pi$
$920$	−85644.6	−3.06915
$921$	−69122.0	−2.47302
$922$	−56733.2	−2.02647
$923$	−23208.8	−0.827657
$924$	44977.6	1.60136
$925$	16545.0	0.588105
$926$	45083.3	1.59992
$927$	−38269.9	−1.35593
$928$	−64271.9	−2.27352
$929$	30130.3	1.06410	0.532048	−	0.846714i	$-0.321423\pi$
$929$	30130.3	1.06410	0.532048	+	0.846714i	$0.321423\pi$
$930$	−17627.4	−0.621533
$931$	−18561.8	−0.653425
$932$	−104606.	−3.67647
$933$	−33181.5	−1.16432
$934$	−8631.09	−0.302375
$935$	18771.5	0.656570
$936$	−82268.5	−2.87289
$937$	3949.46	0.137698	0.0688490	−	0.997627i	$-0.478067\pi$
$937$	3949.46	0.137698	0.0688490	+	0.997627i	$0.478067\pi$
$938$	121455.	4.22775
$939$	53389.7	1.85549
$940$	60822.5	2.11044
$941$	−34024.3	−1.17871	−0.589353	−	0.807876i	$-0.700617\pi$
$941$	−34024.3	−1.17871	−0.589353	+	0.807876i	$0.700617\pi$
$942$	4765.05	0.164813
$943$	23034.3	0.795440
$944$	54019.3	1.86248
$945$	−11078.7	−0.381366
$946$	17823.5	0.612572
$947$	20290.0	0.696236	0.348118	−	0.937451i	$-0.386821\pi$
$947$	20290.0	0.696236	0.348118	+	0.937451i	$0.386821\pi$
$948$	40947.6	1.40287
$949$	9720.77	0.332507
$950$	19260.0	0.657767
$951$	−48030.4	−1.63774
$952$	211373.	7.19603
$953$	29397.7	0.999248	0.499624	−	0.866242i	$-0.333471\pi$
$953$	29397.7	0.999248	0.499624	+	0.866242i	$0.333471\pi$
$954$	42949.5	1.45759
$955$	46183.6	1.56489
$956$	−74043.8	−2.50497
$957$	−11633.0	−0.392938
$958$	60408.7	2.03728
$959$	72019.5	2.42506
$960$	−90504.3	−3.04272
$961$	−28788.8	−0.966359
$962$	−51174.4	−1.71510
$963$	−32273.7	−1.07996
$964$	115979.	3.87493
$965$	−53592.1	−1.78776
$966$	−97718.5	−3.25470
$967$	22814.0	0.758684	0.379342	−	0.925257i	$-0.376150\pi$
$967$	22814.0	0.758684	0.379342	+	0.925257i	$0.376150\pi$
$968$	−7728.48	−0.256614
$969$	−31425.7	−1.04183
$970$	−39884.9	−1.32023
$971$	27533.7	0.909987	0.454994	−	0.890495i	$-0.349642\pi$
$971$	27533.7	0.909987	0.454994	+	0.890495i	$0.349642\pi$
$972$	−101824.	−3.36009
$973$	27987.0	0.922118
$974$	−65424.4	−2.15229
$975$	37026.2	1.21619
$976$	89006.4	2.91908
$977$	30248.8	0.990526	0.495263	−	0.868743i	$-0.335072\pi$
$977$	30248.8	0.990526	0.495263	+	0.868743i	$0.335072\pi$
$978$	−28858.9	−0.943564
$979$	−14508.6	−0.473642
$980$	−143435.	−4.67536
$981$	−6118.68	−0.199138
$982$	54679.5	1.77688
$983$	−24809.5	−0.804984	−0.402492	−	0.915423i	$-0.631856\pi$
$983$	−24809.5	−0.804984	−0.402492	+	0.915423i	$0.631856\pi$
$984$	115338.	3.73662
$985$	39253.2	1.26976
$986$	−90940.1	−2.93725
$987$	41718.7	1.34541
$988$	−42586.7	−1.37132
$989$	−27682.6	−0.890044
$990$	−20143.4	−0.646665
$991$	13366.7	0.428462	0.214231	−	0.976783i	$-0.431275\pi$
$991$	13366.7	0.428462	0.214231	+	0.976783i	$0.431275\pi$
$992$	13649.7	0.436874
$993$	−42674.8	−1.36379
$994$	−63988.5	−2.04184
$995$	77869.0	2.48102
$996$	−28510.2	−0.907008
$997$	19600.4	0.622619	0.311309	−	0.950309i	$-0.399232\pi$
$997$	19600.4	0.622619	0.311309	+	0.950309i	$0.399232\pi$
$998$	−44560.9	−1.41338
$999$	−4554.01	−0.144227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.4	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.4	✓	77	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-5.29699 q^{2} +7.09451 q^{3} +20.0581 q^{4} -14.8169 q^{5} -37.5796 q^{6} -28.7336 q^{7} -63.8717 q^{8} +23.3321 q^{9} +O(q^{10})\)	\(q-5.29699 q^{2} +7.09451 q^{3} +20.0581 q^{4} -14.8169 q^{5} -37.5796 q^{6} -28.7336 q^{7} -63.8717 q^{8} +23.3321 q^{9} +78.4849 q^{10} -11.0000 q^{11} +142.303 q^{12} +55.2041 q^{13} +152.202 q^{14} -105.119 q^{15} +177.863 q^{16} +115.173 q^{17} -123.590 q^{18} -38.4603 q^{19} -297.199 q^{20} -203.851 q^{21} +58.2669 q^{22} -90.4970 q^{23} -453.139 q^{24} +94.5399 q^{25} -292.416 q^{26} -26.0221 q^{27} -576.343 q^{28} +149.065 q^{29} +556.812 q^{30} -31.6578 q^{31} -431.165 q^{32} -78.0396 q^{33} -610.068 q^{34} +425.743 q^{35} +467.998 q^{36} +175.006 q^{37} +203.724 q^{38} +391.646 q^{39} +946.380 q^{40} -254.531 q^{41} +1079.80 q^{42} +305.895 q^{43} -220.639 q^{44} -345.709 q^{45} +479.362 q^{46} -204.653 q^{47} +1261.85 q^{48} +482.623 q^{49} -500.777 q^{50} +817.093 q^{51} +1107.29 q^{52} -347.517 q^{53} +137.839 q^{54} +162.986 q^{55} +1835.27 q^{56} -272.857 q^{57} -789.599 q^{58} +303.713 q^{59} -2108.48 q^{60} +500.421 q^{61} +167.691 q^{62} -670.416 q^{63} +860.974 q^{64} -817.952 q^{65} +413.375 q^{66} +797.983 q^{67} +2310.15 q^{68} -642.032 q^{69} -2255.16 q^{70} -420.419 q^{71} -1490.26 q^{72} +176.088 q^{73} -927.004 q^{74} +670.714 q^{75} -771.442 q^{76} +316.070 q^{77} -2074.55 q^{78} +287.750 q^{79} -2635.38 q^{80} -814.580 q^{81} +1348.25 q^{82} -200.349 q^{83} -4088.87 q^{84} -1706.50 q^{85} -1620.32 q^{86} +1057.55 q^{87} +702.589 q^{88} +1318.96 q^{89} +1831.22 q^{90} -1586.21 q^{91} -1815.20 q^{92} -224.596 q^{93} +1084.04 q^{94} +569.862 q^{95} -3058.91 q^{96} -508.186 q^{97} -2556.45 q^{98} -256.653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

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