LMFDB - Embedded newform 1441.4.a.a.1.8

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			1.8
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)

$f(q)$	$=$	$q-4.71456 q^{2} -2.68555 q^{3} +14.2271 q^{4} -6.70082 q^{5} +12.6612 q^{6} -31.9614 q^{7} -29.3581 q^{8} -19.7878 q^{9} +O(q^{10})$	\(q-4.71456 q^{2} -2.68555 q^{3} +14.2271 q^{4} -6.70082 q^{5} +12.6612 q^{6} -31.9614 q^{7} -29.3581 q^{8} -19.7878 q^{9} +31.5915 q^{10} -11.0000 q^{11} -38.2076 q^{12} +27.2212 q^{13} +150.684 q^{14} +17.9954 q^{15} +24.5937 q^{16} -111.548 q^{17} +93.2909 q^{18} -86.6687 q^{19} -95.3333 q^{20} +85.8341 q^{21} +51.8602 q^{22} +145.512 q^{23} +78.8427 q^{24} -80.0990 q^{25} -128.336 q^{26} +125.651 q^{27} -454.719 q^{28} +113.591 q^{29} -84.8405 q^{30} +4.30010 q^{31} +118.916 q^{32} +29.5411 q^{33} +525.899 q^{34} +214.168 q^{35} -281.523 q^{36} -130.580 q^{37} +408.605 q^{38} -73.1040 q^{39} +196.723 q^{40} +130.083 q^{41} -404.670 q^{42} +385.965 q^{43} -156.498 q^{44} +132.595 q^{45} -686.023 q^{46} -91.8343 q^{47} -66.0477 q^{48} +678.533 q^{49} +377.632 q^{50} +299.567 q^{51} +387.279 q^{52} -236.384 q^{53} -592.390 q^{54} +73.7091 q^{55} +938.326 q^{56} +232.753 q^{57} -535.531 q^{58} -658.192 q^{59} +256.023 q^{60} +413.933 q^{61} -20.2731 q^{62} +632.446 q^{63} -757.387 q^{64} -182.404 q^{65} -139.273 q^{66} +112.054 q^{67} -1587.00 q^{68} -390.779 q^{69} -1009.71 q^{70} +321.609 q^{71} +580.932 q^{72} +98.6811 q^{73} +615.627 q^{74} +215.110 q^{75} -1233.04 q^{76} +351.576 q^{77} +344.653 q^{78} -298.043 q^{79} -164.798 q^{80} +196.828 q^{81} -613.283 q^{82} +330.218 q^{83} +1221.17 q^{84} +747.462 q^{85} -1819.66 q^{86} -305.054 q^{87} +322.939 q^{88} -735.350 q^{89} -625.126 q^{90} -870.029 q^{91} +2070.21 q^{92} -11.5482 q^{93} +432.959 q^{94} +580.752 q^{95} -319.355 q^{96} -1109.35 q^{97} -3198.99 q^{98} +217.666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.71456	−1.66685	−0.833425	−	0.552633i	$-0.813623\pi$
$2$	−4.71456	−1.66685	−0.833425	+	0.552633i	$0.813623\pi$
$3$	−2.68555	−0.516835	−0.258417	−	0.966033i	$-0.583201\pi$
$3$	−2.68555	−0.516835	−0.258417	+	0.966033i	$0.583201\pi$
$4$	14.2271	1.77839
$5$	−6.70082	−0.599340	−0.299670	−	0.954043i	$-0.596877\pi$
$5$	−6.70082	−0.599340	−0.299670	+	0.954043i	$0.596877\pi$
$6$	12.6612	0.861486
$7$	−31.9614	−1.72575	−0.862877	−	0.505413i	$-0.831340\pi$
$7$	−31.9614	−1.72575	−0.862877	+	0.505413i	$0.831340\pi$
$8$	−29.3581	−1.29746
$9$	−19.7878	−0.732882
$10$	31.5915	0.999009
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−38.2076	−0.919133
$13$	27.2212	0.580754	0.290377	−	0.956912i	$-0.406219\pi$
$13$	27.2212	0.580754	0.290377	+	0.956912i	$0.406219\pi$
$14$	150.684	2.87657
$15$	17.9954	0.309760
$16$	24.5937	0.384277
$17$	−111.548	−1.59143	−0.795715	−	0.605672i	$-0.792905\pi$
$17$	−111.548	−1.59143	−0.795715	+	0.605672i	$0.792905\pi$
$18$	93.2909	1.22160
$19$	−86.6687	−1.04648	−0.523241	−	0.852185i	$-0.675277\pi$
$19$	−86.6687	−1.04648	−0.523241	+	0.852185i	$0.675277\pi$
$20$	−95.3333	−1.06586
$21$	85.8341	0.891930
$22$	51.8602	0.502574
$23$	145.512	1.31918	0.659592	−	0.751623i	$-0.270729\pi$
$23$	145.512	1.31918	0.659592	+	0.751623i	$0.270729\pi$
$24$	78.8427	0.670571
$25$	−80.0990	−0.640792
$26$	−128.336	−0.968030
$27$	125.651	0.895614
$28$	−454.719	−3.06906
$29$	113.591	0.727355	0.363677	−	0.931525i	$-0.381521\pi$
$29$	113.591	0.727355	0.363677	+	0.931525i	$0.381521\pi$
$30$	−84.8405	−0.516323
$31$	4.30010	0.0249136	0.0124568	−	0.999922i	$-0.496035\pi$
$31$	4.30010	0.0249136	0.0124568	+	0.999922i	$0.496035\pi$
$32$	118.916	0.656925
$33$	29.5411	0.155832
$34$	525.899	2.65267
$35$	214.168	1.03431
$36$	−281.523	−1.30335
$37$	−130.580	−0.580194	−0.290097	−	0.956997i	$-0.593688\pi$
$37$	−130.580	−0.580194	−0.290097	+	0.956997i	$0.593688\pi$
$38$	408.605	1.74433
$39$	−73.1040	−0.300154
$40$	196.723	0.777617
$41$	130.083	0.495500	0.247750	−	0.968824i	$-0.420309\pi$
$41$	130.083	0.495500	0.247750	+	0.968824i	$0.420309\pi$
$42$	−404.670	−1.48671
$43$	385.965	1.36882	0.684408	−	0.729099i	$-0.260061\pi$
$43$	385.965	1.36882	0.684408	+	0.729099i	$0.260061\pi$
$44$	−156.498	−0.536204
$45$	132.595	0.439245
$46$	−686.023	−2.19888
$47$	−91.8343	−0.285009	−0.142504	−	0.989794i	$-0.545515\pi$
$47$	−91.8343	−0.285009	−0.142504	+	0.989794i	$0.545515\pi$
$48$	−66.0477	−0.198608
$49$	678.533	1.97823
$50$	377.632	1.06810
$51$	299.567	0.822506
$52$	387.279	1.03281
$53$	−236.384	−0.612638	−0.306319	−	0.951929i	$-0.599097\pi$
$53$	−236.384	−0.612638	−0.306319	+	0.951929i	$0.599097\pi$
$54$	−592.390	−1.49285
$55$	73.7091	0.180708
$56$	938.326	2.23909
$57$	232.753	0.540858
$58$	−535.531	−1.21239
$59$	−658.192	−1.45236	−0.726180	−	0.687504i	$-0.758706\pi$
$59$	−658.192	−1.45236	−0.726180	+	0.687504i	$0.758706\pi$
$60$	256.023	0.550873
$61$	413.933	0.868831	0.434415	−	0.900713i	$-0.356955\pi$
$61$	413.933	0.868831	0.434415	+	0.900713i	$0.356955\pi$
$62$	−20.2731	−0.0415272
$63$	632.446	1.26477
$64$	−757.387	−1.47927
$65$	−182.404	−0.348069
$66$	−139.273	−0.259748
$67$	112.054	0.204321	0.102161	−	0.994768i	$-0.467424\pi$
$67$	112.054	0.204321	0.102161	+	0.994768i	$0.467424\pi$
$68$	−1587.00	−2.83018
$69$	−390.779	−0.681801
$70$	−1009.71	−1.72405
$71$	321.609	0.537577	0.268789	−	0.963199i	$-0.413377\pi$
$71$	321.609	0.537577	0.268789	+	0.963199i	$0.413377\pi$
$72$	580.932	0.950882
$73$	98.6811	0.158216	0.0791079	−	0.996866i	$-0.474793\pi$
$73$	98.6811	0.158216	0.0791079	+	0.996866i	$0.474793\pi$
$74$	615.627	0.967097
$75$	215.110	0.331184
$76$	−1233.04	−1.86105
$77$	351.576	0.520335
$78$	344.653	0.500312
$79$	−298.043	−0.424461	−0.212230	−	0.977220i	$-0.568073\pi$
$79$	−298.043	−0.424461	−0.212230	+	0.977220i	$0.568073\pi$
$80$	−164.798	−0.230312
$81$	196.828	0.269997
$82$	−613.283	−0.825924
$83$	330.218	0.436701	0.218350	−	0.975870i	$-0.429932\pi$
$83$	330.218	0.436701	0.218350	+	0.975870i	$0.429932\pi$
$84$	1221.17	1.58620
$85$	747.462	0.953807
$86$	−1819.66	−2.28161
$87$	−305.054	−0.375922
$88$	322.939	0.391198
$89$	−735.350	−0.875808	−0.437904	−	0.899022i	$-0.644279\pi$
$89$	−735.350	−0.875808	−0.437904	+	0.899022i	$0.644279\pi$
$90$	−625.126	−0.732156
$91$	−870.029	−1.00224
$92$	2070.21	2.34602
$93$	−11.5482	−0.0128762
$94$	432.959	0.475067
$95$	580.752	0.627198
$96$	−319.355	−0.339522
$97$	−1109.35	−1.16121	−0.580606	−	0.814185i	$-0.697184\pi$
$97$	−1109.35	−1.16121	−0.580606	+	0.814185i	$0.697184\pi$
$98$	−3198.99	−3.29741
$99$	217.666	0.220972
$100$	−1139.58	−1.13958
$101$	1130.65	1.11390	0.556950	−	0.830546i	$-0.311972\pi$
$101$	1130.65	1.11390	0.556950	+	0.830546i	$0.311972\pi$
$102$	−1412.33	−1.37099
$103$	1704.44	1.63052	0.815262	−	0.579093i	$-0.196593\pi$
$103$	1704.44	1.63052	0.815262	+	0.579093i	$0.196593\pi$
$104$	−799.163	−0.753503
$105$	−575.159	−0.534569
$106$	1114.45	1.02118
$107$	−386.719	−0.349397	−0.174699	−	0.984622i	$-0.555895\pi$
$107$	−386.719	−0.349397	−0.174699	+	0.984622i	$0.555895\pi$
$108$	1787.65	1.59275
$109$	1512.84	1.32939	0.664695	−	0.747115i	$-0.268561\pi$
$109$	1512.84	1.32939	0.664695	+	0.747115i	$0.268561\pi$
$110$	−347.506	−0.301213
$111$	350.679	0.299865
$112$	−786.050	−0.663168
$113$	−251.329	−0.209230	−0.104615	−	0.994513i	$-0.533361\pi$
$113$	−251.329	−0.209230	−0.104615	+	0.994513i	$0.533361\pi$
$114$	−1097.33	−0.901530
$115$	−975.047	−0.790640
$116$	1616.07	1.29352
$117$	−538.648	−0.425624
$118$	3103.09	2.42087
$119$	3565.22	2.74642
$120$	−528.311	−0.401900
$121$	121.000	0.0909091
$122$	−1951.51	−1.44821
$123$	−349.344	−0.256092
$124$	61.1781	0.0443061
$125$	1374.33	0.983392
$126$	−2981.71	−2.10819
$127$	1294.04	0.904155	0.452078	−	0.891979i	$-0.350683\pi$
$127$	1294.04	0.904155	0.452078	+	0.891979i	$0.350683\pi$
$128$	2619.42	1.80880
$129$	−1036.53	−0.707452
$130$	859.957	0.580179
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	420.284	0.277129
$133$	2770.05	1.80597
$134$	−528.284	−0.340573
$135$	−841.966	−0.536777
$136$	3274.83	2.06481
$137$	587.496	0.366373	0.183187	−	0.983078i	$-0.441359\pi$
$137$	587.496	0.366373	0.183187	+	0.983078i	$0.441359\pi$
$138$	1842.35	1.13646
$139$	1094.96	0.668154	0.334077	−	0.942546i	$-0.391575\pi$
$139$	1094.96	0.668154	0.334077	+	0.942546i	$0.391575\pi$
$140$	3046.99	1.83941
$141$	246.626	0.147302
$142$	−1516.25	−0.896061
$143$	−299.433	−0.175104
$144$	−486.656	−0.281629
$145$	−761.152	−0.435933
$146$	−465.238	−0.263722
$147$	−1822.24	−1.02242
$148$	−1857.77	−1.03181
$149$	−1956.39	−1.07566	−0.537832	−	0.843052i	$-0.680757\pi$
$149$	−1956.39	−1.07566	−0.537832	+	0.843052i	$0.680757\pi$
$150$	−1014.15	−0.552033
$151$	972.404	0.524060	0.262030	−	0.965060i	$-0.415608\pi$
$151$	972.404	0.524060	0.262030	+	0.965060i	$0.415608\pi$
$152$	2544.43	1.35777
$153$	2207.28	1.16633
$154$	−1657.53	−0.867320
$155$	−28.8142	−0.0149317
$156$	−1040.06	−0.533790
$157$	3105.56	1.57867	0.789334	−	0.613964i	$-0.210426\pi$
$157$	3105.56	1.57867	0.789334	+	0.613964i	$0.210426\pi$
$158$	1405.14	0.707513
$159$	634.821	0.316633
$160$	−796.836	−0.393721
$161$	−4650.76	−2.27659
$162$	−927.958	−0.450045
$163$	1166.95	0.560753	0.280377	−	0.959890i	$-0.409541\pi$
$163$	1166.95	0.560753	0.280377	+	0.959890i	$0.409541\pi$
$164$	1850.70	0.881191
$165$	−197.950	−0.0933961
$166$	−1556.83	−0.727914
$167$	−726.482	−0.336628	−0.168314	−	0.985733i	$-0.553832\pi$
$167$	−726.482	−0.336628	−0.168314	+	0.985733i	$0.553832\pi$
$168$	−2519.93	−1.15724
$169$	−1456.01	−0.662725
$170$	−3523.96	−1.58985
$171$	1714.98	0.766948
$172$	5491.17	2.43429
$173$	2416.90	1.06216	0.531080	−	0.847322i	$-0.321786\pi$
$173$	2416.90	1.06216	0.531080	+	0.847322i	$0.321786\pi$
$174$	1438.20	0.626606
$175$	2560.08	1.10585
$176$	−270.531	−0.115864
$177$	1767.61	0.750631
$178$	3466.85	1.45984
$179$	−334.944	−0.139860	−0.0699299	−	0.997552i	$-0.522278\pi$
$179$	−334.944	−0.139860	−0.0699299	+	0.997552i	$0.522278\pi$
$180$	1886.44	0.781149
$181$	−1668.10	−0.685020	−0.342510	−	0.939514i	$-0.611277\pi$
$181$	−1668.10	−0.685020	−0.342510	+	0.939514i	$0.611277\pi$
$182$	4101.80	1.67058
$183$	−1111.64	−0.449042
$184$	−4271.94	−1.71158
$185$	874.992	0.347733
$186$	54.4445	0.0214627
$187$	1227.03	0.479834
$188$	−1306.54	−0.506856
$189$	−4015.99	−1.54561
$190$	−2737.99	−1.04545
$191$	1824.20	0.691070	0.345535	−	0.938406i	$-0.387698\pi$
$191$	1824.20	0.691070	0.345535	+	0.938406i	$0.387698\pi$
$192$	2034.00	0.764539
$193$	−205.139	−0.0765089	−0.0382544	−	0.999268i	$-0.512180\pi$
$193$	−205.139	−0.0765089	−0.0382544	+	0.999268i	$0.512180\pi$
$194$	5230.10	1.93556
$195$	489.857	0.179894
$196$	9653.56	3.51806
$197$	−1120.17	−0.405119	−0.202560	−	0.979270i	$-0.564926\pi$
$197$	−1120.17	−0.405119	−0.202560	+	0.979270i	$0.564926\pi$
$198$	−1026.20	−0.368327
$199$	2827.23	1.00712	0.503561	−	0.863960i	$-0.332023\pi$
$199$	2827.23	1.00712	0.503561	+	0.863960i	$0.332023\pi$
$200$	2351.55	0.831399
$201$	−300.926	−0.105600
$202$	−5330.52	−1.85670
$203$	−3630.52	−1.25524
$204$	4261.98	1.46274
$205$	−871.660	−0.296973
$206$	−8035.71	−2.71784
$207$	−2879.35	−0.966806
$208$	669.471	0.223170
$209$	953.356	0.315526
$210$	2711.62	0.891047
$211$	−4145.38	−1.35251	−0.676256	−	0.736667i	$-0.736399\pi$
$211$	−4145.38	−1.35251	−0.676256	+	0.736667i	$0.736399\pi$
$212$	−3363.06	−1.08951
$213$	−863.699	−0.277839
$214$	1823.21	0.582393
$215$	−2586.28	−0.820386
$216$	−3688.88	−1.16202
$217$	−137.437	−0.0429948
$218$	−7132.37	−2.21589
$219$	−265.013	−0.0817714
$220$	1048.67	0.321369
$221$	−3036.46	−0.924229
$222$	−1653.30	−0.499829
$223$	2956.27	0.887741	0.443870	−	0.896091i	$-0.353605\pi$
$223$	2956.27	0.887741	0.443870	+	0.896091i	$0.353605\pi$
$224$	−3800.73	−1.13369
$225$	1584.98	0.469625
$226$	1184.90	0.348755
$227$	−6168.27	−1.80354	−0.901768	−	0.432221i	$-0.857730\pi$
$227$	−6168.27	−1.80354	−0.901768	+	0.432221i	$0.857730\pi$
$228$	3311.41	0.961856
$229$	1832.53	0.528809	0.264404	−	0.964412i	$-0.414825\pi$
$229$	1832.53	0.528809	0.264404	+	0.964412i	$0.414825\pi$
$230$	4596.92	1.31788
$231$	−944.175	−0.268927
$232$	−3334.81	−0.943711
$233$	753.120	0.211753	0.105877	−	0.994379i	$-0.466235\pi$
$233$	753.120	0.211753	0.105877	+	0.994379i	$0.466235\pi$
$234$	2539.49	0.709451
$235$	615.365	0.170817
$236$	−9364.17	−2.58286
$237$	800.409	0.219376
$238$	−16808.5	−4.57786
$239$	−6800.96	−1.84066	−0.920330	−	0.391144i	$-0.872080\pi$
$239$	−6800.96	−1.84066	−0.920330	+	0.391144i	$0.872080\pi$
$240$	442.574	0.119033
$241$	−998.785	−0.266960	−0.133480	−	0.991051i	$-0.542615\pi$
$241$	−998.785	−0.266960	−0.133480	+	0.991051i	$0.542615\pi$
$242$	−570.462	−0.151532
$243$	−3921.17	−1.03516
$244$	5889.07	1.54512
$245$	−4546.73	−1.18563
$246$	1647.00	0.426866
$247$	−2359.23	−0.607749
$248$	−126.243	−0.0323243
$249$	−886.818	−0.225702
$250$	−6479.37	−1.63917
$251$	−4178.33	−1.05073	−0.525366	−	0.850877i	$-0.676071\pi$
$251$	−4178.33	−1.05073	−0.525366	+	0.850877i	$0.676071\pi$
$252$	8997.88	2.24926
$253$	−1600.63	−0.397749
$254$	−6100.85	−1.50709
$255$	−2007.35	−0.492961
$256$	−6290.33	−1.53572
$257$	−4777.23	−1.15951	−0.579757	−	0.814789i	$-0.696853\pi$
$257$	−4777.23	−1.15951	−0.579757	+	0.814789i	$0.696853\pi$
$258$	4886.78	1.17922
$259$	4173.52	1.00127
$260$	−2595.09	−0.619002
$261$	−2247.71	−0.533065
$262$	−617.608	−0.145633
$263$	4845.17	1.13599	0.567996	−	0.823032i	$-0.307719\pi$
$263$	4845.17	1.13599	0.567996	+	0.823032i	$0.307719\pi$
$264$	−867.270	−0.202185
$265$	1583.97	0.367178
$266$	−13059.6	−3.01028
$267$	1974.82	0.452648
$268$	1594.20	0.363363
$269$	−2658.22	−0.602508	−0.301254	−	0.953544i	$-0.597405\pi$
$269$	−2658.22	−0.602508	−0.301254	+	0.953544i	$0.597405\pi$
$270$	3969.50	0.894727
$271$	−5935.84	−1.33054	−0.665271	−	0.746602i	$-0.731684\pi$
$271$	−5935.84	−1.33054	−0.665271	+	0.746602i	$0.731684\pi$
$272$	−2743.37	−0.611549
$273$	2336.51	0.517992
$274$	−2769.79	−0.610689
$275$	881.089	0.193206
$276$	−5559.65	−1.21251
$277$	−4189.30	−0.908703	−0.454352	−	0.890822i	$-0.650129\pi$
$277$	−4189.30	−0.908703	−0.454352	+	0.890822i	$0.650129\pi$
$278$	−5162.27	−1.11371
$279$	−85.0896	−0.0182587
$280$	−6287.56	−1.34198
$281$	3958.70	0.840413	0.420207	−	0.907428i	$-0.361958\pi$
$281$	3958.70	0.840413	0.420207	+	0.907428i	$0.361958\pi$
$282$	−1162.73	−0.245531
$283$	5218.92	1.09623	0.548114	−	0.836403i	$-0.315346\pi$
$283$	5218.92	1.09623	0.548114	+	0.836403i	$0.315346\pi$
$284$	4575.57	0.956022
$285$	−1559.64	−0.324158
$286$	1411.70	0.291872
$287$	−4157.63	−0.855111
$288$	−2353.09	−0.481448
$289$	7529.90	1.53265
$290$	3588.50	0.726634
$291$	2979.22	0.600155
$292$	1403.95	0.281369
$293$	9090.43	1.81252	0.906261	−	0.422719i	$-0.138924\pi$
$293$	9090.43	1.81252	0.906261	+	0.422719i	$0.138924\pi$
$294$	8591.04	1.70422
$295$	4410.43	0.870458
$296$	3833.57	0.752777
$297$	−1382.16	−0.270038
$298$	9223.54	1.79297
$299$	3961.00	0.766122
$300$	3060.39	0.588973
$301$	−12336.0	−2.36224
$302$	−4584.46	−0.873530
$303$	−3036.42	−0.575702
$304$	−2131.51	−0.402139
$305$	−2773.69	−0.520725
$306$	−10406.4	−1.94410
$307$	3302.95	0.614036	0.307018	−	0.951704i	$-0.400669\pi$
$307$	3302.95	0.614036	0.307018	+	0.951704i	$0.400669\pi$
$308$	5001.90	0.925357
$309$	−4577.38	−0.842711
$310$	135.847	0.0248889
$311$	−10453.9	−1.90606	−0.953031	−	0.302872i	$-0.902055\pi$
$311$	−10453.9	−1.90606	−0.953031	+	0.302872i	$0.902055\pi$
$312$	2146.19	0.389437
$313$	−6115.12	−1.10430	−0.552152	−	0.833743i	$-0.686193\pi$
$313$	−6115.12	−1.10430	−0.552152	+	0.833743i	$0.686193\pi$
$314$	−14641.4	−2.63140
$315$	−4237.91	−0.758029
$316$	−4240.28	−0.754856
$317$	3390.49	0.600722	0.300361	−	0.953826i	$-0.402893\pi$
$317$	3390.49	0.600722	0.300361	+	0.953826i	$0.402893\pi$
$318$	−2992.91	−0.527779
$319$	−1249.50	−0.219306
$320$	5075.12	0.886586
$321$	1038.55	0.180581
$322$	21926.3	3.79473
$323$	9667.70	1.66540
$324$	2800.29	0.480160
$325$	−2180.39	−0.372143
$326$	−5501.67	−0.934691
$327$	−4062.80	−0.687075
$328$	−3818.98	−0.642889
$329$	2935.16	0.491855
$330$	933.246	0.155677
$331$	−5107.68	−0.848167	−0.424084	−	0.905623i	$-0.639404\pi$
$331$	−5107.68	−0.848167	−0.424084	+	0.905623i	$0.639404\pi$
$332$	4698.05	0.776623
$333$	2583.89	0.425214
$334$	3425.05	0.561109
$335$	−750.852	−0.122458
$336$	2110.98	0.342748
$337$	6791.75	1.09783	0.548917	−	0.835877i	$-0.315040\pi$
$337$	6791.75	1.09783	0.548917	+	0.835877i	$0.315040\pi$
$338$	6864.43	1.10466
$339$	674.956	0.108137
$340$	10634.2	1.69624
$341$	−47.3012	−0.00751173
$342$	−8085.40	−1.27839
$343$	−10724.1	−1.68818
$344$	−11331.2	−1.77598
$345$	2618.54	0.408630
$346$	−11394.6	−1.77046
$347$	−5614.39	−0.868576	−0.434288	−	0.900774i	$-0.643000\pi$
$347$	−5614.39	−0.868576	−0.434288	+	0.900774i	$0.643000\pi$
$348$	−4340.04	−0.668536
$349$	7863.96	1.20615	0.603077	−	0.797683i	$-0.293941\pi$
$349$	7863.96	1.20615	0.603077	+	0.797683i	$0.293941\pi$
$350$	−12069.6	−1.84329
$351$	3420.38	0.520131
$352$	−1308.08	−0.198070
$353$	6214.81	0.937057	0.468529	−	0.883448i	$-0.344784\pi$
$353$	6214.81	0.937057	0.468529	+	0.883448i	$0.344784\pi$
$354$	−8333.50	−1.25119
$355$	−2155.05	−0.322192
$356$	−10461.9	−1.55753
$357$	−9574.60	−1.41944
$358$	1579.11	0.233125
$359$	−13101.5	−1.92610	−0.963051	−	0.269318i	$-0.913202\pi$
$359$	−13101.5	−1.92610	−0.963051	+	0.269318i	$0.913202\pi$
$360$	−3892.72	−0.569902
$361$	652.462	0.0951249
$362$	7864.35	1.14183
$363$	−324.952	−0.0469850
$364$	−12378.0	−1.78237
$365$	−661.245	−0.0948250
$366$	5240.89	0.748486
$367$	9678.84	1.37665	0.688326	−	0.725401i	$-0.258346\pi$
$367$	9678.84	1.37665	0.688326	+	0.725401i	$0.258346\pi$
$368$	3578.67	0.506932
$369$	−2574.05	−0.363143
$370$	−4125.21	−0.579619
$371$	7555.16	1.05726
$372$	−164.297	−0.0228989
$373$	9048.65	1.25609	0.628045	−	0.778177i	$-0.283855\pi$
$373$	9048.65	1.25609	0.628045	+	0.778177i	$0.283855\pi$
$374$	−5784.89	−0.799811
$375$	−3690.84	−0.508251
$376$	2696.08	0.369786
$377$	3092.08	0.422414
$378$	18933.6	2.57630
$379$	−6226.71	−0.843917	−0.421959	−	0.906615i	$-0.638657\pi$
$379$	−6226.71	−0.843917	−0.421959	+	0.906615i	$0.638657\pi$
$380$	8262.41	1.11540
$381$	−3475.22	−0.467299
$382$	−8600.30	−1.15191
$383$	−2839.43	−0.378820	−0.189410	−	0.981898i	$-0.560658\pi$
$383$	−2839.43	−0.378820	−0.189410	+	0.981898i	$0.560658\pi$
$384$	−7034.59	−0.934850
$385$	−2355.85	−0.311857
$386$	967.139	0.127529
$387$	−7637.40	−1.00318
$388$	−15782.9	−2.06508
$389$	−11387.3	−1.48422	−0.742108	−	0.670281i	$-0.766174\pi$
$389$	−11387.3	−1.48422	−0.742108	+	0.670281i	$0.766174\pi$
$390$	−2309.46	−0.299857
$391$	−16231.5	−2.09939
$392$	−19920.4	−2.56667
$393$	−351.807	−0.0451561
$394$	5281.09	0.675273
$395$	1997.13	0.254396
$396$	3096.76	0.392974
$397$	−423.956	−0.0535963	−0.0267982	−	0.999641i	$-0.508531\pi$
$397$	−423.956	−0.0535963	−0.0267982	+	0.999641i	$0.508531\pi$
$398$	−13329.2	−1.67872
$399$	−7439.13	−0.933389
$400$	−1969.93	−0.246241
$401$	8295.81	1.03310	0.516550	−	0.856257i	$-0.327216\pi$
$401$	8295.81	1.03310	0.516550	+	0.856257i	$0.327216\pi$
$402$	1418.74	0.176020
$403$	117.054	0.0144687
$404$	16085.9	1.98095
$405$	−1318.91	−0.161820
$406$	17116.3	2.09229
$407$	1436.38	0.174935
$408$	−8794.73	−1.06717
$409$	−7525.72	−0.909836	−0.454918	−	0.890533i	$-0.650331\pi$
$409$	−7525.72	−0.909836	−0.454918	+	0.890533i	$0.650331\pi$
$410$	4109.50	0.495009
$411$	−1577.75	−0.189354
$412$	24249.3	2.89970
$413$	21036.8	2.50642
$414$	13574.9	1.61152
$415$	−2212.73	−0.261732
$416$	3237.04	0.381512
$417$	−2940.58	−0.345325
$418$	−4494.66	−0.525935
$419$	−5667.79	−0.660834	−0.330417	−	0.943835i	$-0.607189\pi$
$419$	−5667.79	−0.660834	−0.330417	+	0.943835i	$0.607189\pi$
$420$	−8182.85	−0.950672
$421$	−9376.34	−1.08545	−0.542726	−	0.839910i	$-0.682608\pi$
$421$	−9376.34	−1.08545	−0.542726	+	0.839910i	$0.682608\pi$
$422$	19543.7	2.25443
$423$	1817.20	0.208878
$424$	6939.78	0.794871
$425$	8934.86	1.01977
$426$	4071.96	0.463116
$427$	−13229.9	−1.49939
$428$	−5501.89	−0.621364
$429$	804.144	0.0904998
$430$	12193.2	1.36746
$431$	17123.5	1.91371	0.956853	−	0.290571i	$-0.0938452\pi$
$431$	17123.5	1.91371	0.956853	+	0.290571i	$0.0938452\pi$
$432$	3090.23	0.344164
$433$	−5756.48	−0.638889	−0.319444	−	0.947605i	$-0.603496\pi$
$433$	−5756.48	−0.638889	−0.319444	+	0.947605i	$0.603496\pi$
$434$	647.958	0.0716658
$435$	2044.11	0.225305
$436$	21523.3	2.36417
$437$	−12611.3	−1.38050
$438$	1249.42	0.136301
$439$	10674.5	1.16052	0.580259	−	0.814432i	$-0.302951\pi$
$439$	10674.5	1.16052	0.580259	+	0.814432i	$0.302951\pi$
$440$	−2163.96	−0.234460
$441$	−13426.7	−1.44981
$442$	14315.6	1.54055
$443$	−14810.1	−1.58837	−0.794184	−	0.607677i	$-0.792102\pi$
$443$	−14810.1	−1.58837	−0.794184	+	0.607677i	$0.792102\pi$
$444$	4989.15	0.533276
$445$	4927.45	0.524907
$446$	−13937.5	−1.47973
$447$	5254.00	0.555941
$448$	24207.2	2.55286
$449$	2980.47	0.313267	0.156634	−	0.987657i	$-0.449936\pi$
$449$	2980.47	0.313267	0.156634	+	0.987657i	$0.449936\pi$
$450$	−7472.50	−0.782794
$451$	−1430.91	−0.149399
$452$	−3575.68	−0.372093
$453$	−2611.44	−0.270853
$454$	29080.7	3.00622
$455$	5829.91	0.600682
$456$	−6833.19	−0.701740
$457$	−3516.98	−0.359995	−0.179997	−	0.983667i	$-0.557609\pi$
$457$	−3516.98	−0.359995	−0.179997	+	0.983667i	$0.557609\pi$
$458$	−8639.60	−0.881445
$459$	−14016.1	−1.42531
$460$	−13872.1	−1.40606
$461$	16436.9	1.66061	0.830307	−	0.557306i	$-0.188165\pi$
$461$	16436.9	1.66061	0.830307	+	0.557306i	$0.188165\pi$
$462$	4451.37	0.448261
$463$	1364.81	0.136994	0.0684970	−	0.997651i	$-0.478180\pi$
$463$	1364.81	0.136994	0.0684970	+	0.997651i	$0.478180\pi$
$464$	2793.62	0.279506
$465$	77.3822	0.00771723
$466$	−3550.63	−0.352961
$467$	−11798.1	−1.16906	−0.584528	−	0.811374i	$-0.698720\pi$
$467$	−11798.1	−1.16906	−0.584528	+	0.811374i	$0.698720\pi$
$468$	−7663.40	−0.756925
$469$	−3581.40	−0.352609
$470$	−2901.18	−0.284726
$471$	−8340.15	−0.815911
$472$	19323.3	1.88437
$473$	−4245.61	−0.412714
$474$	−3773.58	−0.365667
$475$	6942.07	0.670577
$476$	50722.8	4.88420
$477$	4677.52	0.448991
$478$	32063.6	3.06810
$479$	−9661.70	−0.921617	−0.460808	−	0.887500i	$-0.652440\pi$
$479$	−9661.70	−0.921617	−0.460808	+	0.887500i	$0.652440\pi$
$480$	2139.94	0.203489
$481$	−3554.54	−0.336950
$482$	4708.83	0.444982
$483$	12489.9	1.17662
$484$	1721.48	0.161672
$485$	7433.56	0.695960
$486$	18486.6	1.72545
$487$	6887.10	0.640830	0.320415	−	0.947277i	$-0.396178\pi$
$487$	6887.10	0.640830	0.320415	+	0.947277i	$0.396178\pi$
$488$	−12152.3	−1.12727
$489$	−3133.91	−0.289817
$490$	21435.8	1.97627
$491$	4126.08	0.379241	0.189621	−	0.981857i	$-0.439274\pi$
$491$	4126.08	0.379241	0.189621	+	0.981857i	$0.439274\pi$
$492$	−4970.15	−0.455430
$493$	−12670.8	−1.15753
$494$	11122.7	1.01303
$495$	−1458.54	−0.132437
$496$	105.756	0.00957372
$497$	−10279.1	−0.927727
$498$	4180.96	0.376211
$499$	−18897.2	−1.69530	−0.847649	−	0.530558i	$-0.821983\pi$
$499$	−18897.2	−1.69530	−0.847649	+	0.530558i	$0.821983\pi$
$500$	19552.8	1.74885
$501$	1951.01	0.173981
$502$	19699.0	1.75141
$503$	−1496.15	−0.132624	−0.0663121	−	0.997799i	$-0.521123\pi$
$503$	−1496.15	−0.132624	−0.0663121	+	0.997799i	$0.521123\pi$
$504$	−18567.4	−1.64099
$505$	−7576.28	−0.667604
$506$	7546.26	0.662988
$507$	3910.18	0.342519
$508$	18410.5	1.60794
$509$	−7695.38	−0.670121	−0.335061	−	0.942197i	$-0.608757\pi$
$509$	−7695.38	−0.670121	−0.335061	+	0.942197i	$0.608757\pi$
$510$	9463.77	0.821692
$511$	−3153.99	−0.273042
$512$	8700.79	0.751023
$513$	−10890.0	−0.937244
$514$	22522.5	1.93274
$515$	−11421.2	−0.977238
$516$	−14746.8	−1.25812
$517$	1010.18	0.0859334
$518$	−19676.3	−1.66897
$519$	−6490.72	−0.548961
$520$	5355.05	0.451605
$521$	−8253.40	−0.694027	−0.347013	−	0.937860i	$-0.612804\pi$
$521$	−8253.40	−0.694027	−0.347013	+	0.937860i	$0.612804\pi$
$522$	10597.0	0.888539
$523$	7775.72	0.650112	0.325056	−	0.945695i	$-0.394617\pi$
$523$	7775.72	0.650112	0.325056	+	0.945695i	$0.394617\pi$
$524$	1863.75	0.155379
$525$	−6875.22	−0.571542
$526$	−22842.8	−1.89353
$527$	−479.667	−0.0396482
$528$	726.525	0.0598825
$529$	9006.60	0.740249
$530$	−7467.71	−0.612031
$531$	13024.2	1.06441
$532$	39409.9	3.21172
$533$	3541.01	0.287764
$534$	−9310.42	−0.754496
$535$	2591.33	0.209408
$536$	−3289.68	−0.265098
$537$	899.510	0.0722844
$538$	12532.4	1.00429
$539$	−7463.86	−0.596459
$540$	−11978.7	−0.954598
$541$	−17142.8	−1.36234	−0.681170	−	0.732125i	$-0.738529\pi$
$541$	−17142.8	−1.36234	−0.681170	+	0.732125i	$0.738529\pi$
$542$	27984.9	2.21781
$543$	4479.76	0.354042
$544$	−13264.8	−1.04545
$545$	−10137.3	−0.796756
$546$	−11015.6	−0.863415
$547$	−9458.45	−0.739331	−0.369666	−	0.929165i	$-0.620528\pi$
$547$	−9458.45	−0.739331	−0.369666	+	0.929165i	$0.620528\pi$
$548$	8358.36	0.651554
$549$	−8190.82	−0.636750
$550$	−4153.95	−0.322045
$551$	−9844.77	−0.761164
$552$	11472.5	0.884607
$553$	9525.87	0.732515
$554$	19750.7	1.51467
$555$	−2349.84	−0.179721
$556$	15578.1	1.18824
$557$	−2603.94	−0.198083	−0.0990417	−	0.995083i	$-0.531578\pi$
$557$	−2603.94	−0.198083	−0.0990417	+	0.995083i	$0.531578\pi$
$558$	401.160	0.0304345
$559$	10506.4	0.794946
$560$	5267.18	0.397463
$561$	−3295.24	−0.247995
$562$	−18663.5	−1.40084
$563$	−19727.3	−1.47674	−0.738371	−	0.674395i	$-0.764404\pi$
$563$	−19727.3	−1.47674	−0.738371	+	0.674395i	$0.764404\pi$
$564$	3508.77	0.261961
$565$	1684.11	0.125400
$566$	−24604.9	−1.82725
$567$	−6290.90	−0.465949
$568$	−9441.83	−0.697483
$569$	11484.8	0.846168	0.423084	−	0.906090i	$-0.360948\pi$
$569$	11484.8	0.846168	0.423084	+	0.906090i	$0.360948\pi$
$570$	7353.02	0.540323
$571$	11487.6	0.841927	0.420964	−	0.907078i	$-0.361692\pi$
$571$	11487.6	0.841927	0.420964	+	0.907078i	$0.361692\pi$
$572$	−4260.07	−0.311403
$573$	−4898.98	−0.357169
$574$	19601.4	1.42534
$575$	−11655.3	−0.845323
$576$	14987.0	1.08413
$577$	22600.1	1.63060	0.815299	−	0.579040i	$-0.196573\pi$
$577$	22600.1	1.63060	0.815299	+	0.579040i	$0.196573\pi$
$578$	−35500.2	−2.55469
$579$	550.911	0.0395424
$580$	−10829.0	−0.775257
$581$	−10554.2	−0.753638
$582$	−14045.7	−1.00037
$583$	2600.22	0.184717
$584$	−2897.09	−0.205278
$585$	3609.38	0.255093
$586$	−42857.4	−3.02120
$587$	−11545.5	−0.811814	−0.405907	−	0.913914i	$-0.633044\pi$
$587$	−11545.5	−0.811814	−0.405907	+	0.913914i	$0.633044\pi$
$588$	−25925.1	−1.81826
$589$	−372.684	−0.0260716
$590$	−20793.2	−1.45092
$591$	3008.26	0.209380
$592$	−3211.44	−0.222955
$593$	20678.2	1.43196	0.715980	−	0.698121i	$-0.245980\pi$
$593$	20678.2	1.43196	0.715980	+	0.698121i	$0.245980\pi$
$594$	6516.29	0.450112
$595$	−23889.9	−1.64604
$596$	−27833.8	−1.91295
$597$	−7592.68	−0.520516
$598$	−18674.4	−1.27701
$599$	15704.2	1.07121	0.535605	−	0.844469i	$-0.320084\pi$
$599$	15704.2	1.07121	0.535605	+	0.844469i	$0.320084\pi$
$600$	−6315.22	−0.429696
$601$	27548.1	1.86973	0.934866	−	0.355001i	$-0.115520\pi$
$601$	27548.1	1.86973	0.934866	+	0.355001i	$0.115520\pi$
$602$	58158.8	3.93750
$603$	−2217.30	−0.149743
$604$	13834.5	0.931983
$605$	−810.800	−0.0544854
$606$	14315.4	0.959609
$607$	3390.52	0.226716	0.113358	−	0.993554i	$-0.463839\pi$
$607$	3390.52	0.226716	0.113358	+	0.993554i	$0.463839\pi$
$608$	−10306.3	−0.687460
$609$	9749.96	0.648750
$610$	13076.7	0.867970
$611$	−2499.84	−0.165520
$612$	31403.3	2.07419
$613$	16418.3	1.08178	0.540890	−	0.841094i	$-0.318088\pi$
$613$	16418.3	1.08178	0.540890	+	0.841094i	$0.318088\pi$
$614$	−15572.0	−1.02351
$615$	2340.89	0.153486
$616$	−10321.6	−0.675112
$617$	6462.94	0.421699	0.210849	−	0.977519i	$-0.432377\pi$
$617$	6462.94	0.421699	0.210849	+	0.977519i	$0.432377\pi$
$618$	21580.3	1.40467
$619$	6348.78	0.412244	0.206122	−	0.978526i	$-0.433916\pi$
$619$	6348.78	0.412244	0.206122	+	0.978526i	$0.433916\pi$
$620$	−409.943	−0.0265544
$621$	18283.7	1.18148
$622$	49285.5	3.17712
$623$	23502.8	1.51143
$624$	−1797.90	−0.115342
$625$	803.217	0.0514059
$626$	28830.1	1.84071
$627$	−2560.29	−0.163075
$628$	44183.2	2.80749
$629$	14565.9	0.923338
$630$	19979.9	1.26352
$631$	−7515.61	−0.474155	−0.237077	−	0.971491i	$-0.576189\pi$
$631$	−7515.61	−0.474155	−0.237077	+	0.971491i	$0.576189\pi$
$632$	8749.96	0.550720
$633$	11132.6	0.699025
$634$	−15984.7	−1.00131
$635$	−8671.15	−0.541896
$636$	9031.67	0.563096
$637$	18470.5	1.14887
$638$	5890.84	0.365550
$639$	−6363.94	−0.393981
$640$	−17552.3	−1.08409
$641$	−20338.0	−1.25320	−0.626601	−	0.779340i	$-0.715554\pi$
$641$	−20338.0	−1.25320	−0.626601	+	0.779340i	$0.715554\pi$
$642$	−4896.33	−0.301001
$643$	1376.18	0.0844030	0.0422015	−	0.999109i	$-0.486563\pi$
$643$	1376.18	0.0844030	0.0422015	+	0.999109i	$0.486563\pi$
$644$	−66166.8	−4.04866
$645$	6945.60	0.424004
$646$	−45579.0	−2.77598
$647$	20641.5	1.25425	0.627127	−	0.778917i	$-0.284231\pi$
$647$	20641.5	1.25425	0.627127	+	0.778917i	$0.284231\pi$
$648$	−5778.49	−0.350310
$649$	7240.11	0.437903
$650$	10279.6	0.620306
$651$	369.096	0.0222212
$652$	16602.4	0.997237
$653$	19778.8	1.18530	0.592652	−	0.805458i	$-0.298081\pi$
$653$	19778.8	1.18530	0.592652	+	0.805458i	$0.298081\pi$
$654$	19154.3	1.14525
$655$	−877.808	−0.0523646
$656$	3199.21	0.190409
$657$	−1952.68	−0.115953
$658$	−13838.0	−0.819849
$659$	19458.4	1.15022	0.575108	−	0.818077i	$-0.304960\pi$
$659$	19458.4	1.15022	0.575108	+	0.818077i	$0.304960\pi$
$660$	−2816.25	−0.166094
$661$	−6017.53	−0.354092	−0.177046	−	0.984203i	$-0.556654\pi$
$661$	−6017.53	−0.354092	−0.177046	+	0.984203i	$0.556654\pi$
$662$	24080.5	1.41377
$663$	8154.58	0.477674
$664$	−9694.57	−0.566600
$665$	−18561.6	−1.08239
$666$	−12181.9	−0.708767
$667$	16528.8	0.959515
$668$	−10335.7	−0.598656
$669$	−7939.21	−0.458816
$670$	3539.94	0.204119
$671$	−4553.26	−0.261962
$672$	10207.1	0.585931
$673$	−3010.00	−0.172403	−0.0862013	−	0.996278i	$-0.527473\pi$
$673$	−3010.00	−0.172403	−0.0862013	+	0.996278i	$0.527473\pi$
$674$	−32020.1	−1.82992
$675$	−10064.5	−0.573902
$676$	−20714.8	−1.17858
$677$	−8189.87	−0.464937	−0.232469	−	0.972604i	$-0.574680\pi$
$677$	−8189.87	−0.464937	−0.232469	+	0.972604i	$0.574680\pi$
$678$	−3182.12	−0.180249
$679$	35456.4	2.00397
$680$	−21944.0	−1.23752
$681$	16565.2	0.932130
$682$	223.004	0.0125209
$683$	−16345.4	−0.915725	−0.457862	−	0.889023i	$-0.651385\pi$
$683$	−16345.4	−0.915725	−0.457862	+	0.889023i	$0.651385\pi$
$684$	24399.2	1.36393
$685$	−3936.70	−0.219582
$686$	50559.5	2.81395
$687$	−4921.37	−0.273307
$688$	9492.31	0.526004
$689$	−6434.65	−0.355792
$690$	−12345.3	−0.681125
$691$	17953.6	0.988406	0.494203	−	0.869347i	$-0.335460\pi$
$691$	17953.6	0.988406	0.494203	+	0.869347i	$0.335460\pi$
$692$	34385.5	1.88893
$693$	−6956.91	−0.381344
$694$	26469.4	1.44779
$695$	−7337.15	−0.400452
$696$	8955.81	0.487743
$697$	−14510.4	−0.788553
$698$	−37075.1	−2.01048
$699$	−2022.54	−0.109442
$700$	36422.5	1.96663
$701$	−29272.2	−1.57717	−0.788584	−	0.614927i	$-0.789185\pi$
$701$	−29272.2	−1.57717	−0.788584	+	0.614927i	$0.789185\pi$
$702$	−16125.6	−0.866981
$703$	11317.2	0.607163
$704$	8331.26	0.446017
$705$	−1652.60	−0.0882842
$706$	−29300.1	−1.56193
$707$	−36137.2	−1.92232
$708$	25148.0	1.33491
$709$	−3229.58	−0.171071	−0.0855354	−	0.996335i	$-0.527260\pi$
$709$	−3229.58	−0.171071	−0.0855354	+	0.996335i	$0.527260\pi$
$710$	10160.1	0.537045
$711$	5897.61	0.311080
$712$	21588.5	1.13632
$713$	625.715	0.0328656
$714$	45140.1	2.36600
$715$	2006.45	0.104947
$716$	−4765.28	−0.248725
$717$	18264.3	0.951317
$718$	61767.9	3.21052
$719$	18070.6	0.937302	0.468651	−	0.883383i	$-0.344740\pi$
$719$	18070.6	0.937302	0.468651	+	0.883383i	$0.344740\pi$
$720$	3260.99	0.168792
$721$	−54476.5	−2.81388
$722$	−3076.07	−0.158559
$723$	2682.29	0.137974
$724$	−23732.2	−1.21823
$725$	−9098.51	−0.466083
$726$	1532.01	0.0783169
$727$	33376.1	1.70268	0.851342	−	0.524611i	$-0.175789\pi$
$727$	33376.1	1.70268	0.851342	+	0.524611i	$0.175789\pi$
$728$	25542.4	1.30036
$729$	5216.16	0.265008
$730$	3117.48	0.158059
$731$	−43053.5	−2.17837
$732$	−15815.4	−0.798571
$733$	26955.4	1.35828	0.679141	−	0.734008i	$-0.262353\pi$
$733$	26955.4	1.35828	0.679141	+	0.734008i	$0.262353\pi$
$734$	−45631.5	−2.29467
$735$	12210.5	0.612776
$736$	17303.7	0.866605
$737$	−1232.59	−0.0616052
$738$	12135.5	0.605304
$739$	−17300.2	−0.861160	−0.430580	−	0.902552i	$-0.641691\pi$
$739$	−17300.2	−0.861160	−0.430580	+	0.902552i	$0.641691\pi$
$740$	12448.6	0.618405
$741$	6335.83	0.314106
$742$	−35619.3	−1.76230
$743$	19591.2	0.967336	0.483668	−	0.875252i	$-0.339304\pi$
$743$	19591.2	0.967336	0.483668	+	0.875252i	$0.339304\pi$
$744$	339.032	0.0167063
$745$	13109.4	0.644688
$746$	−42660.4	−2.09371
$747$	−6534.29	−0.320050
$748$	17457.0	0.853331
$749$	12360.1	0.602974
$750$	17400.7	0.847178
$751$	2489.24	0.120950	0.0604752	−	0.998170i	$-0.480738\pi$
$751$	2489.24	0.120950	0.0604752	+	0.998170i	$0.480738\pi$
$752$	−2258.55	−0.109522
$753$	11221.1	0.543055
$754$	−14577.8	−0.704101
$755$	−6515.91	−0.314090
$756$	−57135.9	−2.74869
$757$	27061.7	1.29931	0.649653	−	0.760231i	$-0.274914\pi$
$757$	27061.7	1.29931	0.649653	+	0.760231i	$0.274914\pi$
$758$	29356.2	1.40668
$759$	4298.57	0.205571
$760$	−17049.8	−0.813763
$761$	−20277.2	−0.965895	−0.482948	−	0.875649i	$-0.660434\pi$
$761$	−20277.2	−0.965895	−0.482948	+	0.875649i	$0.660434\pi$
$762$	16384.1	0.778917
$763$	−48352.4	−2.29420
$764$	25953.1	1.22899
$765$	−14790.6	−0.699028
$766$	13386.7	0.631437
$767$	−17916.8	−0.843465
$768$	16893.0	0.793716
$769$	15838.4	0.742713	0.371356	−	0.928490i	$-0.378893\pi$
$769$	15838.4	0.742713	0.371356	+	0.928490i	$0.378893\pi$
$770$	11106.8	0.519819
$771$	12829.5	0.599277
$772$	−2918.53	−0.136062
$773$	−8607.52	−0.400506	−0.200253	−	0.979744i	$-0.564176\pi$
$773$	−8607.52	−0.400506	−0.200253	+	0.979744i	$0.564176\pi$
$774$	36007.0	1.67215
$775$	−344.434	−0.0159644
$776$	32568.4	1.50662
$777$	−11208.2	−0.517493
$778$	53686.2	2.47396
$779$	−11274.1	−0.518532
$780$	6969.25	0.319922
$781$	−3537.70	−0.162086
$782$	76524.3	3.49937
$783$	14272.8	0.651429
$784$	16687.6	0.760188
$785$	−20809.8	−0.946159
$786$	1658.62	0.0752684
$787$	6287.59	0.284788	0.142394	−	0.989810i	$-0.454520\pi$
$787$	6287.59	0.284788	0.142394	+	0.989810i	$0.454520\pi$
$788$	−15936.7	−0.720459
$789$	−13011.9	−0.587120
$790$	−9415.60	−0.424040
$791$	8032.82	0.361080
$792$	−6390.25	−0.286702
$793$	11267.8	0.504577
$794$	1998.77	0.0893370
$795$	−4253.83	−0.189771
$796$	40223.4	1.79105
$797$	−614.045	−0.0272906	−0.0136453	−	0.999907i	$-0.504344\pi$
$797$	−614.045	−0.0272906	−0.0136453	+	0.999907i	$0.504344\pi$
$798$	35072.2	1.55582
$799$	10243.9	0.453571
$800$	−9525.06	−0.420952
$801$	14551.0	0.641864
$802$	−39111.1	−1.72202
$803$	−1085.49	−0.0477038
$804$	−4281.31	−0.187799
$805$	31163.9	1.36445
$806$	−551.859	−0.0241171
$807$	7138.79	0.311397
$808$	−33193.7	−1.44524
$809$	−11828.4	−0.514046	−0.257023	−	0.966405i	$-0.582742\pi$
$809$	−11828.4	−0.514046	−0.257023	+	0.966405i	$0.582742\pi$
$810$	6218.08	0.269730
$811$	25142.3	1.08861	0.544306	−	0.838887i	$-0.316793\pi$
$811$	25142.3	1.08861	0.544306	+	0.838887i	$0.316793\pi$
$812$	−51651.9	−2.23230
$813$	15941.0	0.687670
$814$	−6771.89	−0.291591
$815$	−7819.54	−0.336082
$816$	7367.47	0.316070
$817$	−33451.1	−1.43244
$818$	35480.5	1.51656
$819$	17216.0	0.734523
$820$	−12401.2	−0.528133
$821$	−38050.9	−1.61752	−0.808761	−	0.588137i	$-0.799862\pi$
$821$	−38050.9	−1.61752	−0.808761	+	0.588137i	$0.799862\pi$
$822$	7438.40	0.315625
$823$	−6164.73	−0.261104	−0.130552	−	0.991441i	$-0.541675\pi$
$823$	−6164.73	−0.261104	−0.130552	+	0.991441i	$0.541675\pi$
$824$	−50039.2	−2.11553
$825$	−2366.21	−0.0998556
$826$	−99179.1	−4.17782
$827$	−8465.69	−0.355962	−0.177981	−	0.984034i	$-0.556957\pi$
$827$	−8465.69	−0.355962	−0.177981	+	0.984034i	$0.556957\pi$
$828$	−40964.9	−1.71936
$829$	32703.5	1.37013	0.685067	−	0.728480i	$-0.259773\pi$
$829$	32703.5	1.37013	0.685067	+	0.728480i	$0.259773\pi$
$830$	10432.1	0.436268
$831$	11250.6	0.469650
$832$	−20617.0	−0.859093
$833$	−75688.8	−3.14821
$834$	13863.5	0.575606
$835$	4868.03	0.201755
$836$	13563.5	0.561128
$837$	540.313	0.0223130
$838$	26721.1	1.10151
$839$	2863.60	0.117834	0.0589169	−	0.998263i	$-0.481235\pi$
$839$	2863.60	0.117834	0.0589169	+	0.998263i	$0.481235\pi$
$840$	16885.6	0.693580
$841$	−11486.1	−0.470955
$842$	44205.4	1.80928
$843$	−10631.3	−0.434355
$844$	−58976.8	−2.40529
$845$	9756.44	0.397197
$846$	−8567.30	−0.348168
$847$	−3867.33	−0.156887
$848$	−5813.56	−0.235423
$849$	−14015.7	−0.566569
$850$	−42124.0	−1.69981
$851$	−19000.9	−0.765383
$852$	−12287.9	−0.494105
$853$	36265.8	1.45571	0.727854	−	0.685732i	$-0.240518\pi$
$853$	36265.8	1.45571	0.727854	+	0.685732i	$0.240518\pi$
$854$	62373.1	2.49926
$855$	−11491.8	−0.459662
$856$	11353.3	0.453328
$857$	−5389.49	−0.214821	−0.107410	−	0.994215i	$-0.534256\pi$
$857$	−5389.49	−0.214821	−0.107410	+	0.994215i	$0.534256\pi$
$858$	−3791.19	−0.150850
$859$	−37368.1	−1.48426	−0.742132	−	0.670254i	$-0.766185\pi$
$859$	−37368.1	−1.48426	−0.742132	+	0.670254i	$0.766185\pi$
$860$	−36795.3	−1.45897
$861$	11165.5	0.441951
$862$	−80729.6	−3.18986
$863$	−27474.1	−1.08369	−0.541847	−	0.840477i	$-0.682275\pi$
$863$	−27474.1	−1.08369	−0.541847	+	0.840477i	$0.682275\pi$
$864$	14941.9	0.588351
$865$	−16195.2	−0.636595
$866$	27139.3	1.06493
$867$	−20221.9	−0.792126
$868$	−1955.34	−0.0764614
$869$	3278.47	0.127980
$870$	−9637.10	−0.375550
$871$	3050.24	0.118661
$872$	−44414.0	−1.72483
$873$	21951.6	0.851031
$874$	59456.7	2.30109
$875$	−43925.6	−1.69709
$876$	−3770.37	−0.145421
$877$	−38751.9	−1.49208	−0.746042	−	0.665899i	$-0.768048\pi$
$877$	−38751.9	−1.49208	−0.746042	+	0.665899i	$0.768048\pi$
$878$	−50325.7	−1.93441
$879$	−24412.8	−0.936774
$880$	1812.78	0.0694418
$881$	5165.77	0.197547	0.0987736	−	0.995110i	$-0.468508\pi$
$881$	5165.77	0.197547	0.0987736	+	0.995110i	$0.468508\pi$
$882$	63300.9	2.41661
$883$	7105.91	0.270819	0.135409	−	0.990790i	$-0.456765\pi$
$883$	7105.91	0.270819	0.135409	+	0.990790i	$0.456765\pi$
$884$	−43200.1	−1.64364
$885$	−11844.4	−0.449883
$886$	69823.0	2.64757
$887$	17356.1	0.657003	0.328501	−	0.944503i	$-0.393456\pi$
$887$	17356.1	0.657003	0.328501	+	0.944503i	$0.393456\pi$
$888$	−10295.3	−0.389061
$889$	−41359.5	−1.56035
$890$	−23230.8	−0.874940
$891$	−2165.11	−0.0814072
$892$	42059.1	1.57875
$893$	7959.16	0.298257
$894$	−24770.3	−0.926670
$895$	2244.40	0.0838235
$896$	−83720.4	−3.12154
$897$	−10637.5	−0.395959
$898$	−14051.6	−0.522169
$899$	488.452	0.0181210
$900$	22549.7	0.835175
$901$	26368.1	0.974970
$902$	6746.11	0.249025
$903$	33129.0	1.22089
$904$	7378.53	0.271467
$905$	11177.6	0.410560
$906$	12311.8	0.451471
$907$	−33677.9	−1.23292	−0.616459	−	0.787387i	$-0.711433\pi$
$907$	−33677.9	−1.23292	−0.616459	+	0.787387i	$0.711433\pi$
$908$	−87756.7	−3.20739
$909$	−22373.1	−0.816357
$910$	−27485.5	−1.00125
$911$	10383.0	0.377612	0.188806	−	0.982014i	$-0.439538\pi$
$911$	10383.0	0.377612	0.188806	+	0.982014i	$0.439538\pi$
$912$	5724.27	0.207839
$913$	−3632.40	−0.131670
$914$	16581.0	0.600057
$915$	7448.89	0.269129
$916$	26071.7	0.940428
$917$	−4186.95	−0.150780
$918$	66079.8	2.37577
$919$	−8423.49	−0.302356	−0.151178	−	0.988507i	$-0.548307\pi$
$919$	−8423.49	−0.302356	−0.151178	+	0.988507i	$0.548307\pi$
$920$	28625.5	1.02582
$921$	−8870.24	−0.317355
$922$	−77492.9	−2.76800
$923$	8754.59	0.312200
$924$	−13432.9	−0.478257
$925$	10459.3	0.371784
$926$	−6434.49	−0.228348
$927$	−33727.2	−1.19498
$928$	13507.8	0.477817
$929$	−8497.32	−0.300095	−0.150047	−	0.988679i	$-0.547943\pi$
$929$	−8497.32	−0.300095	−0.150047	+	0.988679i	$0.547943\pi$
$930$	−364.823	−0.0128635
$931$	−58807.5	−2.07018
$932$	10714.7	0.376580
$933$	28074.5	0.985120
$934$	55622.7	1.94864
$935$	−8222.08	−0.287584
$936$	15813.7	0.552229
$937$	38918.4	1.35689	0.678447	−	0.734649i	$-0.262653\pi$
$937$	38918.4	1.35689	0.678447	+	0.734649i	$0.262653\pi$
$938$	16884.7	0.587746
$939$	16422.5	0.570743
$940$	8754.87	0.303779
$941$	37235.2	1.28994	0.644969	−	0.764209i	$-0.276870\pi$
$941$	37235.2	1.28994	0.644969	+	0.764209i	$0.276870\pi$
$942$	39320.2	1.36000
$943$	18928.5	0.653656
$944$	−16187.4	−0.558109
$945$	26910.4	0.926345
$946$	20016.2	0.687932
$947$	9137.27	0.313539	0.156770	−	0.987635i	$-0.449892\pi$
$947$	9137.27	0.313539	0.156770	+	0.987635i	$0.449892\pi$
$948$	11387.5	0.390136
$949$	2686.22	0.0918845
$950$	−32728.8	−1.11775
$951$	−9105.33	−0.310474
$952$	−104668.	−3.56336
$953$	47642.6	1.61941	0.809704	−	0.586838i	$-0.199628\pi$
$953$	47642.6	1.61941	0.809704	+	0.586838i	$0.199628\pi$
$954$	−22052.5	−0.748401
$955$	−12223.6	−0.414186
$956$	−96758.0	−3.27341
$957$	3355.60	0.113345
$958$	45550.7	1.53620
$959$	−18777.2	−0.632270
$960$	−13629.5	−0.458219
$961$	−29772.5	−0.999379
$962$	16758.1	0.561645
$963$	7652.31	0.256067
$964$	−14209.8	−0.474759
$965$	1374.60	0.0458548
$966$	−58884.2	−1.96125
$967$	−1369.73	−0.0455508	−0.0227754	−	0.999741i	$-0.507250\pi$
$967$	−1369.73	−0.0455508	−0.0227754	+	0.999741i	$0.507250\pi$
$968$	−3552.33	−0.117951
$969$	−25963.1	−0.860738
$970$	−35046.0	−1.16006
$971$	−17005.2	−0.562020	−0.281010	−	0.959705i	$-0.590669\pi$
$971$	−17005.2	−0.562020	−0.281010	+	0.959705i	$0.590669\pi$
$972$	−55786.9	−1.84091
$973$	−34996.5	−1.15307
$974$	−32469.7	−1.06817
$975$	5855.55	0.192336
$976$	10180.1	0.333872
$977$	9892.31	0.323934	0.161967	−	0.986796i	$-0.448216\pi$
$977$	9892.31	0.323934	0.161967	+	0.986796i	$0.448216\pi$
$978$	14775.0	0.483081
$979$	8088.85	0.264066
$980$	−64686.8	−2.10851
$981$	−29935.7	−0.974286
$982$	−19452.7	−0.632138
$983$	8644.49	0.280485	0.140242	−	0.990117i	$-0.455212\pi$
$983$	8644.49	0.280485	0.140242	+	0.990117i	$0.455212\pi$
$984$	10256.1	0.332268
$985$	7506.03	0.242804
$986$	59737.3	1.92943
$987$	−7882.52	−0.254208
$988$	−33565.0	−1.08081
$989$	56162.4	1.80572
$990$	6876.38	0.220753
$991$	−22683.0	−0.727092	−0.363546	−	0.931576i	$-0.618434\pi$
$991$	−22683.0	−0.727092	−0.363546	+	0.931576i	$0.618434\pi$
$992$	511.352	0.0163664
$993$	13716.9	0.438362
$994$	48461.4	1.54638
$995$	−18944.8	−0.603608
$996$	−12616.9	−0.401386
$997$	−10587.9	−0.336331	−0.168166	−	0.985759i	$-0.553784\pi$
$997$	−10587.9	−0.336331	−0.168166	+	0.985759i	$0.553784\pi$
$998$	89091.9	2.82581
$999$	−16407.5	−0.519630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.8	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-4.71456 q^{2} -2.68555 q^{3} +14.2271 q^{4} -6.70082 q^{5} +12.6612 q^{6} -31.9614 q^{7} -29.3581 q^{8} -19.7878 q^{9} +O(q^{10})\)	\(q-4.71456 q^{2} -2.68555 q^{3} +14.2271 q^{4} -6.70082 q^{5} +12.6612 q^{6} -31.9614 q^{7} -29.3581 q^{8} -19.7878 q^{9} +31.5915 q^{10} -11.0000 q^{11} -38.2076 q^{12} +27.2212 q^{13} +150.684 q^{14} +17.9954 q^{15} +24.5937 q^{16} -111.548 q^{17} +93.2909 q^{18} -86.6687 q^{19} -95.3333 q^{20} +85.8341 q^{21} +51.8602 q^{22} +145.512 q^{23} +78.8427 q^{24} -80.0990 q^{25} -128.336 q^{26} +125.651 q^{27} -454.719 q^{28} +113.591 q^{29} -84.8405 q^{30} +4.30010 q^{31} +118.916 q^{32} +29.5411 q^{33} +525.899 q^{34} +214.168 q^{35} -281.523 q^{36} -130.580 q^{37} +408.605 q^{38} -73.1040 q^{39} +196.723 q^{40} +130.083 q^{41} -404.670 q^{42} +385.965 q^{43} -156.498 q^{44} +132.595 q^{45} -686.023 q^{46} -91.8343 q^{47} -66.0477 q^{48} +678.533 q^{49} +377.632 q^{50} +299.567 q^{51} +387.279 q^{52} -236.384 q^{53} -592.390 q^{54} +73.7091 q^{55} +938.326 q^{56} +232.753 q^{57} -535.531 q^{58} -658.192 q^{59} +256.023 q^{60} +413.933 q^{61} -20.2731 q^{62} +632.446 q^{63} -757.387 q^{64} -182.404 q^{65} -139.273 q^{66} +112.054 q^{67} -1587.00 q^{68} -390.779 q^{69} -1009.71 q^{70} +321.609 q^{71} +580.932 q^{72} +98.6811 q^{73} +615.627 q^{74} +215.110 q^{75} -1233.04 q^{76} +351.576 q^{77} +344.653 q^{78} -298.043 q^{79} -164.798 q^{80} +196.828 q^{81} -613.283 q^{82} +330.218 q^{83} +1221.17 q^{84} +747.462 q^{85} -1819.66 q^{86} -305.054 q^{87} +322.939 q^{88} -735.350 q^{89} -625.126 q^{90} -870.029 q^{91} +2070.21 q^{92} -11.5482 q^{93} +432.959 q^{94} +580.752 q^{95} -319.355 q^{96} -1109.35 q^{97} -3198.99 q^{98} +217.666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 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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