LMFDB - Embedded newform 1441.4.a.a.1.12

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			1.12
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)

$f(q)$	$=$	$q-4.48446 q^{2} -6.75386 q^{3} +12.1104 q^{4} -4.87147 q^{5} +30.2874 q^{6} -3.19104 q^{7} -18.4329 q^{8} +18.6146 q^{9} +O(q^{10})$	\(q-4.48446 q^{2} -6.75386 q^{3} +12.1104 q^{4} -4.87147 q^{5} +30.2874 q^{6} -3.19104 q^{7} -18.4329 q^{8} +18.6146 q^{9} +21.8459 q^{10} -11.0000 q^{11} -81.7919 q^{12} -54.9098 q^{13} +14.3101 q^{14} +32.9012 q^{15} -14.2214 q^{16} -19.9576 q^{17} -83.4763 q^{18} +158.702 q^{19} -58.9955 q^{20} +21.5518 q^{21} +49.3291 q^{22} +84.2889 q^{23} +124.493 q^{24} -101.269 q^{25} +246.241 q^{26} +56.6341 q^{27} -38.6448 q^{28} -185.819 q^{29} -147.544 q^{30} -81.4787 q^{31} +211.239 q^{32} +74.2924 q^{33} +89.4991 q^{34} +15.5451 q^{35} +225.430 q^{36} -111.233 q^{37} -711.693 q^{38} +370.853 q^{39} +89.7955 q^{40} -245.243 q^{41} -96.6484 q^{42} -256.718 q^{43} -133.214 q^{44} -90.6803 q^{45} -377.990 q^{46} -13.5048 q^{47} +96.0495 q^{48} -332.817 q^{49} +454.136 q^{50} +134.791 q^{51} -664.979 q^{52} +471.427 q^{53} -253.973 q^{54} +53.5862 q^{55} +58.8203 q^{56} -1071.85 q^{57} +833.298 q^{58} -188.400 q^{59} +398.447 q^{60} +285.419 q^{61} +365.388 q^{62} -59.3999 q^{63} -833.521 q^{64} +267.491 q^{65} -333.161 q^{66} +816.361 q^{67} -241.695 q^{68} -569.275 q^{69} -69.7114 q^{70} -123.672 q^{71} -343.121 q^{72} +612.096 q^{73} +498.820 q^{74} +683.954 q^{75} +1921.94 q^{76} +35.1015 q^{77} -1663.07 q^{78} +977.443 q^{79} +69.2793 q^{80} -885.091 q^{81} +1099.78 q^{82} -207.296 q^{83} +261.001 q^{84} +97.2230 q^{85} +1151.24 q^{86} +1254.99 q^{87} +202.762 q^{88} -277.513 q^{89} +406.653 q^{90} +175.219 q^{91} +1020.77 q^{92} +550.295 q^{93} +60.5619 q^{94} -773.113 q^{95} -1426.68 q^{96} +1379.41 q^{97} +1492.51 q^{98} -204.760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.48446	−1.58550	−0.792748	−	0.609549i	$-0.791351\pi$
$2$	−4.48446	−1.58550	−0.792748	+	0.609549i	$0.791351\pi$
$3$	−6.75386	−1.29978	−0.649890	−	0.760028i	$-0.725185\pi$
$3$	−6.75386	−1.29978	−0.649890	+	0.760028i	$0.725185\pi$
$4$	12.1104	1.51380
$5$	−4.87147	−0.435718	−0.217859	−	0.975980i	$-0.569907\pi$
$5$	−4.87147	−0.435718	−0.217859	+	0.975980i	$0.569907\pi$
$6$	30.2874	2.06080
$7$	−3.19104	−0.172300	−0.0861501	−	0.996282i	$-0.527456\pi$
$7$	−3.19104	−0.172300	−0.0861501	+	0.996282i	$0.527456\pi$
$8$	−18.4329	−0.814628
$9$	18.6146	0.689428
$10$	21.8459	0.690829
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−81.7919	−1.96761
$13$	−54.9098	−1.17148	−0.585739	−	0.810499i	$-0.699196\pi$
$13$	−54.9098	−1.17148	−0.585739	+	0.810499i	$0.699196\pi$
$14$	14.3101	0.273181
$15$	32.9012	0.566337
$16$	−14.2214	−0.222210
$17$	−19.9576	−0.284731	−0.142366	−	0.989814i	$-0.545471\pi$
$17$	−19.9576	−0.284731	−0.142366	+	0.989814i	$0.545471\pi$
$18$	−83.4763	−1.09309
$19$	158.702	1.91625	0.958125	−	0.286351i	$-0.0924424\pi$
$19$	158.702	1.91625	0.958125	+	0.286351i	$0.0924424\pi$
$20$	−58.9955	−0.659590
$21$	21.5518	0.223952
$22$	49.3291	0.478045
$23$	84.2889	0.764150	0.382075	−	0.924131i	$-0.375210\pi$
$23$	84.2889	0.764150	0.382075	+	0.924131i	$0.375210\pi$
$24$	124.493	1.05884
$25$	−101.269	−0.810150
$26$	246.241	1.85738
$27$	56.6341	0.403675
$28$	−38.6448	−0.260828
$29$	−185.819	−1.18985	−0.594926	−	0.803781i	$-0.702819\pi$
$29$	−185.819	−1.18985	−0.594926	+	0.803781i	$0.702819\pi$
$30$	−147.544	−0.897926
$31$	−81.4787	−0.472065	−0.236032	−	0.971745i	$-0.575847\pi$
$31$	−81.4787	−0.472065	−0.236032	+	0.971745i	$0.575847\pi$
$32$	211.239	1.16694
$33$	74.2924	0.391898
$34$	89.4991	0.451440
$35$	15.5451	0.0750743
$36$	225.430	1.04366
$37$	−111.233	−0.494232	−0.247116	−	0.968986i	$-0.579483\pi$
$37$	−111.233	−0.494232	−0.247116	+	0.968986i	$0.579483\pi$
$38$	−711.693	−3.03821
$39$	370.853	1.52266
$40$	89.7955	0.354948
$41$	−245.243	−0.934161	−0.467080	−	0.884215i	$-0.654694\pi$
$41$	−245.243	−0.934161	−0.467080	+	0.884215i	$0.654694\pi$
$42$	−96.6484	−0.355076
$43$	−256.718	−0.910445	−0.455222	−	0.890378i	$-0.650440\pi$
$43$	−256.718	−0.910445	−0.455222	+	0.890378i	$0.650440\pi$
$44$	−133.214	−0.456428
$45$	−90.6803	−0.300396
$46$	−377.990	−1.21156
$47$	−13.5048	−0.0419124	−0.0209562	−	0.999780i	$-0.506671\pi$
$47$	−13.5048	−0.0419124	−0.0209562	+	0.999780i	$0.506671\pi$
$48$	96.0495	0.288824
$49$	−332.817	−0.970313
$50$	454.136	1.28449
$51$	134.791	0.370088
$52$	−664.979	−1.77338
$53$	471.427	1.22180	0.610900	−	0.791708i	$-0.290808\pi$
$53$	471.427	1.22180	0.610900	+	0.791708i	$0.290808\pi$
$54$	−253.973	−0.640026
$55$	53.5862	0.131374
$56$	58.8203	0.140361
$57$	−1071.85	−2.49070
$58$	833.298	1.88651
$59$	−188.400	−0.415722	−0.207861	−	0.978158i	$-0.566650\pi$
$59$	−188.400	−0.415722	−0.207861	+	0.978158i	$0.566650\pi$
$60$	398.447	0.857322
$61$	285.419	0.599085	0.299542	−	0.954083i	$-0.403166\pi$
$61$	285.419	0.599085	0.299542	+	0.954083i	$0.403166\pi$
$62$	365.388	0.748457
$63$	−59.3999	−0.118789
$64$	−833.521	−1.62797
$65$	267.491	0.510434
$66$	−333.161	−0.621354
$67$	816.361	1.48857	0.744287	−	0.667860i	$-0.232790\pi$
$67$	816.361	1.48857	0.744287	+	0.667860i	$0.232790\pi$
$68$	−241.695	−0.431026
$69$	−569.275	−0.993227
$70$	−69.7114	−0.119030
$71$	−123.672	−0.206721	−0.103361	−	0.994644i	$-0.532960\pi$
$71$	−123.672	−0.206721	−0.103361	+	0.994644i	$0.532960\pi$
$72$	−343.121	−0.561627
$73$	612.096	0.981375	0.490688	−	0.871336i	$-0.336746\pi$
$73$	612.096	0.981375	0.490688	+	0.871336i	$0.336746\pi$
$74$	498.820	0.783603
$75$	683.954	1.05302
$76$	1921.94	2.90082
$77$	35.1015	0.0519505
$78$	−1663.07	−2.41418
$79$	977.443	1.39204	0.696019	−	0.718024i	$-0.254953\pi$
$79$	977.443	1.39204	0.696019	+	0.718024i	$0.254953\pi$
$80$	69.2793	0.0968208
$81$	−885.091	−1.21412
$82$	1099.78	1.48111
$83$	−207.296	−0.274141	−0.137071	−	0.990561i	$-0.543769\pi$
$83$	−207.296	−0.274141	−0.137071	+	0.990561i	$0.543769\pi$
$84$	261.001	0.339019
$85$	97.2230	0.124062
$86$	1151.24	1.44351
$87$	1254.99	1.54655
$88$	202.762	0.245620
$89$	−277.513	−0.330521	−0.165260	−	0.986250i	$-0.552846\pi$
$89$	−277.513	−0.330521	−0.165260	+	0.986250i	$0.552846\pi$
$90$	406.653	0.476277
$91$	175.219	0.201846
$92$	1020.77	1.15677
$93$	550.295	0.613580
$94$	60.5619	0.0664520
$95$	−773.113	−0.834944
$96$	−1426.68	−1.51677
$97$	1379.41	1.44389	0.721946	−	0.691950i	$-0.243248\pi$
$97$	1379.41	1.44389	0.721946	+	0.691950i	$0.243248\pi$
$98$	1492.51	1.53843
$99$	−204.760	−0.207870
$100$	−1226.40	−1.22640
$101$	−77.7180	−0.0765666	−0.0382833	−	0.999267i	$-0.512189\pi$
$101$	−77.7180	−0.0765666	−0.0382833	+	0.999267i	$0.512189\pi$
$102$	−604.464	−0.586773
$103$	1148.50	1.09869	0.549344	−	0.835596i	$-0.314878\pi$
$103$	1148.50	1.09869	0.549344	+	0.835596i	$0.314878\pi$
$104$	1012.15	0.954320
$105$	−104.989	−0.0975800
$106$	−2114.09	−1.93716
$107$	1174.39	1.06105	0.530524	−	0.847670i	$-0.321995\pi$
$107$	1174.39	1.06105	0.530524	+	0.847670i	$0.321995\pi$
$108$	685.861	0.611083
$109$	−76.8158	−0.0675011	−0.0337506	−	0.999430i	$-0.510745\pi$
$109$	−76.8158	−0.0675011	−0.0337506	+	0.999430i	$0.510745\pi$
$110$	−240.305	−0.208293
$111$	751.251	0.642393
$112$	45.3812	0.0382868
$113$	883.527	0.735533	0.367766	−	0.929918i	$-0.380123\pi$
$113$	883.527	0.735533	0.367766	+	0.929918i	$0.380123\pi$
$114$	4806.67	3.94900
$115$	−410.611	−0.332954
$116$	−2250.34	−1.80120
$117$	−1022.12	−0.807650
$118$	844.874	0.659127
$119$	63.6856	0.0490592
$120$	−606.466	−0.461354
$121$	121.000	0.0909091
$122$	−1279.95	−0.949847
$123$	1656.34	1.21420
$124$	−986.739	−0.714611
$125$	1102.26	0.788715
$126$	266.376	0.188339
$127$	1646.72	1.15057	0.575286	−	0.817952i	$-0.304891\pi$
$127$	1646.72	1.15057	0.575286	+	0.817952i	$0.304891\pi$
$128$	2047.98	1.41420
$129$	1733.84	1.18338
$130$	−1199.56	−0.809292
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	899.711	0.593256
$133$	−506.425	−0.330170
$134$	−3660.94	−2.36013
$135$	−275.891	−0.175889
$136$	367.877	0.231950
$137$	−1395.05	−0.869976	−0.434988	−	0.900436i	$-0.643247\pi$
$137$	−1395.05	−0.869976	−0.434988	+	0.900436i	$0.643247\pi$
$138$	2552.89	1.57476
$139$	−1934.97	−1.18074	−0.590368	−	0.807134i	$-0.701017\pi$
$139$	−1934.97	−1.18074	−0.590368	+	0.807134i	$0.701017\pi$
$140$	188.257	0.113647
$141$	91.2097	0.0544769
$142$	554.604	0.327756
$143$	604.007	0.353214
$144$	−264.726	−0.153198
$145$	905.212	0.518440
$146$	−2744.92	−1.55597
$147$	2247.80	1.26119
$148$	−1347.07	−0.748168
$149$	−2258.49	−1.24176	−0.620881	−	0.783905i	$-0.713225\pi$
$149$	−2258.49	−1.24176	−0.620881	+	0.783905i	$0.713225\pi$
$150$	−3067.17	−1.66955
$151$	2654.01	1.43033	0.715166	−	0.698954i	$-0.246351\pi$
$151$	2654.01	1.43033	0.715166	+	0.698954i	$0.246351\pi$
$152$	−2925.34	−1.56103
$153$	−371.502	−0.196302
$154$	−157.411	−0.0823673
$155$	396.921	0.205687
$156$	4491.17	2.30501
$157$	−996.543	−0.506578	−0.253289	−	0.967391i	$-0.581512\pi$
$157$	−996.543	−0.506578	−0.253289	+	0.967391i	$0.581512\pi$
$158$	−4383.31	−2.20707
$159$	−3183.95	−1.58807
$160$	−1029.04	−0.508457
$161$	−268.969	−0.131663
$162$	3969.16	1.92498
$163$	3801.01	1.82649	0.913245	−	0.407410i	$-0.133568\pi$
$163$	3801.01	1.82649	0.913245	+	0.407410i	$0.133568\pi$
$164$	−2970.00	−1.41413
$165$	−361.914	−0.170757
$166$	929.612	0.434650
$167$	−811.408	−0.375980	−0.187990	−	0.982171i	$-0.560197\pi$
$167$	−811.408	−0.375980	−0.187990	+	0.982171i	$0.560197\pi$
$168$	−397.264	−0.182438
$169$	818.081	0.372363
$170$	−435.993	−0.196701
$171$	2954.17	1.32112
$172$	−3108.96	−1.37823
$173$	113.858	0.0500374	0.0250187	−	0.999687i	$-0.492035\pi$
$173$	113.858	0.0500374	0.0250187	+	0.999687i	$0.492035\pi$
$174$	−5627.97	−2.45204
$175$	323.153	0.139589
$176$	156.436	0.0669988
$177$	1272.43	0.540348
$178$	1244.50	0.524040
$179$	28.9115	0.0120723	0.00603616	−	0.999982i	$-0.498079\pi$
$179$	28.9115	0.0120723	0.00603616	+	0.999982i	$0.498079\pi$
$180$	−1098.18	−0.454740
$181$	2780.95	1.14202	0.571012	−	0.820942i	$-0.306551\pi$
$181$	2780.95	1.14202	0.571012	+	0.820942i	$0.306551\pi$
$182$	−785.765	−0.320026
$183$	−1927.68	−0.778678
$184$	−1553.69	−0.622498
$185$	541.868	0.215346
$186$	−2467.78	−0.972829
$187$	219.534	0.0858497
$188$	−163.549	−0.0634470
$189$	−180.722	−0.0695533
$190$	3466.99	1.32380
$191$	1872.05	0.709198	0.354599	−	0.935018i	$-0.384617\pi$
$191$	1872.05	0.709198	0.354599	+	0.935018i	$0.384617\pi$
$192$	5629.48	2.11600
$193$	−1831.98	−0.683260	−0.341630	−	0.939835i	$-0.610979\pi$
$193$	−1831.98	−0.683260	−0.341630	+	0.939835i	$0.610979\pi$
$194$	−6185.89	−2.28928
$195$	−1806.60	−0.663452
$196$	−4030.55	−1.46886
$197$	2495.61	0.902561	0.451281	−	0.892382i	$-0.350967\pi$
$197$	2495.61	0.902561	0.451281	+	0.892382i	$0.350967\pi$
$198$	918.239	0.329578
$199$	3081.11	1.09756	0.548779	−	0.835967i	$-0.315093\pi$
$199$	3081.11	1.09756	0.548779	+	0.835967i	$0.315093\pi$
$200$	1866.68	0.659971
$201$	−5513.59	−1.93482
$202$	348.523	0.121396
$203$	592.956	0.205012
$204$	1632.37	0.560239
$205$	1194.70	0.407031
$206$	−5150.39	−1.74197
$207$	1569.00	0.526826
$208$	780.895	0.260314
$209$	−1745.72	−0.577771
$210$	470.820	0.154713
$211$	−4804.18	−1.56746	−0.783729	−	0.621103i	$-0.786685\pi$
$211$	−4804.18	−1.56746	−0.783729	+	0.621103i	$0.786685\pi$
$212$	5709.17	1.84956
$213$	835.265	0.268692
$214$	−5266.49	−1.68229
$215$	1250.59	0.396697
$216$	−1043.93	−0.328845
$217$	260.002	0.0813368
$218$	344.478	0.107023
$219$	−4134.01	−1.27557
$220$	648.950	0.198874
$221$	1095.87	0.333557
$222$	−3368.96	−1.01851
$223$	−980.002	−0.294286	−0.147143	−	0.989115i	$-0.547008\pi$
$223$	−980.002	−0.294286	−0.147143	+	0.989115i	$0.547008\pi$
$224$	−674.072	−0.201064
$225$	−1885.07	−0.558540
$226$	−3962.14	−1.16619
$227$	−1825.50	−0.533757	−0.266879	−	0.963730i	$-0.585992\pi$
$227$	−1825.50	−0.533757	−0.266879	+	0.963730i	$0.585992\pi$
$228$	−12980.5	−3.77043
$229$	1949.29	0.562501	0.281251	−	0.959634i	$-0.409251\pi$
$229$	1949.29	0.562501	0.281251	+	0.959634i	$0.409251\pi$
$230$	1841.37	0.527897
$231$	−237.070	−0.0675242
$232$	3425.19	0.969287
$233$	3125.42	0.878769	0.439385	−	0.898299i	$-0.355197\pi$
$233$	3125.42	0.878769	0.439385	+	0.898299i	$0.355197\pi$
$234$	4583.66	1.28053
$235$	65.7884	0.0182620
$236$	−2281.60	−0.629321
$237$	−6601.51	−1.80934
$238$	−285.596	−0.0777832
$239$	3540.69	0.958276	0.479138	−	0.877740i	$-0.340949\pi$
$239$	3540.69	0.958276	0.479138	+	0.877740i	$0.340949\pi$
$240$	−467.903	−0.125846
$241$	4834.35	1.29215	0.646074	−	0.763275i	$-0.276410\pi$
$241$	4834.35	1.29215	0.646074	+	0.763275i	$0.276410\pi$
$242$	−542.620	−0.144136
$243$	4448.66	1.17441
$244$	3456.54	0.906894
$245$	1621.31	0.422783
$246$	−7427.79	−1.92512
$247$	−8714.29	−2.24485
$248$	1501.89	0.384557
$249$	1400.05	0.356323
$250$	−4943.05	−1.25050
$251$	−5306.51	−1.33444	−0.667219	−	0.744862i	$-0.732515\pi$
$251$	−5306.51	−1.33444	−0.667219	+	0.744862i	$0.732515\pi$
$252$	−719.356	−0.179822
$253$	−927.178	−0.230400
$254$	−7384.65	−1.82423
$255$	−656.630	−0.161254
$256$	−2515.93	−0.614242
$257$	−5498.69	−1.33463	−0.667313	−	0.744778i	$-0.732556\pi$
$257$	−5498.69	−1.33463	−0.667313	+	0.744778i	$0.732556\pi$
$258$	−7775.32	−1.87624
$259$	354.949	0.0851562
$260$	3239.43	0.772695
$261$	−3458.94	−0.820317
$262$	−587.465	−0.138525
$263$	2417.53	0.566811	0.283405	−	0.959000i	$-0.408536\pi$
$263$	2417.53	0.566811	0.283405	+	0.959000i	$0.408536\pi$
$264$	−1369.43	−0.319251
$265$	−2296.54	−0.532360
$266$	2271.04	0.523484
$267$	1874.28	0.429604
$268$	9886.46	2.25340
$269$	−1527.78	−0.346284	−0.173142	−	0.984897i	$-0.555392\pi$
$269$	−1527.78	−0.346284	−0.173142	+	0.984897i	$0.555392\pi$
$270$	1237.22	0.278871
$271$	−1104.95	−0.247679	−0.123839	−	0.992302i	$-0.539521\pi$
$271$	−1104.95	−0.247679	−0.123839	+	0.992302i	$0.539521\pi$
$272$	283.826	0.0632701
$273$	−1183.41	−0.262355
$274$	6256.03	1.37934
$275$	1113.96	0.244269
$276$	−6894.15	−1.50355
$277$	−3027.50	−0.656696	−0.328348	−	0.944557i	$-0.606492\pi$
$277$	−3027.50	−0.656696	−0.328348	+	0.944557i	$0.606492\pi$
$278$	8677.31	1.87205
$279$	−1516.69	−0.325455
$280$	−286.541	−0.0611576
$281$	−4892.36	−1.03862	−0.519312	−	0.854585i	$-0.673812\pi$
$281$	−4892.36	−1.03862	−0.519312	+	0.854585i	$0.673812\pi$
$282$	−409.026	−0.0863729
$283$	−3876.02	−0.814154	−0.407077	−	0.913394i	$-0.633452\pi$
$283$	−3876.02	−0.814154	−0.407077	+	0.913394i	$0.633452\pi$
$284$	−1497.72	−0.312935
$285$	5221.49	1.08524
$286$	−2708.65	−0.560020
$287$	782.583	0.160956
$288$	3932.12	0.804522
$289$	−4514.69	−0.918928
$290$	−4059.39	−0.821985
$291$	−9316.31	−1.87674
$292$	7412.73	1.48561
$293$	1281.42	0.255499	0.127750	−	0.991806i	$-0.459225\pi$
$293$	1281.42	0.255499	0.127750	+	0.991806i	$0.459225\pi$
$294$	−10080.2	−1.99962
$295$	917.787	0.181138
$296$	2050.35	0.402615
$297$	−622.975	−0.121713
$298$	10128.1	1.96881
$299$	−4628.28	−0.895185
$300$	8282.96	1.59406
$301$	819.198	0.156870
$302$	−11901.8	−2.26779
$303$	524.896	0.0995198
$304$	−2256.97	−0.425809
$305$	−1390.41	−0.261032
$306$	1665.99	0.311236
$307$	3039.34	0.565031	0.282516	−	0.959263i	$-0.408831\pi$
$307$	3039.34	0.565031	0.282516	+	0.959263i	$0.408831\pi$
$308$	425.093	0.0786426
$309$	−7756.78	−1.42805
$310$	−1779.98	−0.326116
$311$	2871.88	0.523632	0.261816	−	0.965118i	$-0.415679\pi$
$311$	2871.88	0.523632	0.261816	+	0.965118i	$0.415679\pi$
$312$	−6835.90	−1.24041
$313$	−1649.34	−0.297847	−0.148924	−	0.988849i	$-0.547581\pi$
$313$	−1649.34	−0.297847	−0.148924	+	0.988849i	$0.547581\pi$
$314$	4468.96	0.803178
$315$	289.365	0.0517583
$316$	11837.2	2.10727
$317$	−10915.0	−1.93391	−0.966954	−	0.254950i	$-0.917941\pi$
$317$	−10915.0	−1.93391	−0.966954	+	0.254950i	$0.917941\pi$
$318$	14278.3	2.51788
$319$	2044.01	0.358754
$320$	4060.48	0.709336
$321$	−7931.63	−1.37913
$322$	1206.18	0.208751
$323$	−3167.31	−0.545616
$324$	−10718.8	−1.83793
$325$	5560.64	0.949074
$326$	−17045.5	−2.89590
$327$	518.803	0.0877366
$328$	4520.55	0.760993
$329$	43.0945	0.00722151
$330$	1622.99	0.270735
$331$	−4036.11	−0.670226	−0.335113	−	0.942178i	$-0.608774\pi$
$331$	−4036.11	−0.670226	−0.335113	+	0.942178i	$0.608774\pi$
$332$	−2510.44	−0.414995
$333$	−2070.55	−0.340737
$334$	3638.73	0.596115
$335$	−3976.88	−0.648598
$336$	−306.498	−0.0497644
$337$	−8637.19	−1.39614	−0.698068	−	0.716032i	$-0.745957\pi$
$337$	−8637.19	−1.39614	−0.698068	+	0.716032i	$0.745957\pi$
$338$	−3668.65	−0.590380
$339$	−5967.21	−0.956031
$340$	1177.41	0.187806
$341$	896.265	0.142333
$342$	−13247.9	−2.09463
$343$	2156.56	0.339485
$344$	4732.06	0.741674
$345$	2773.21	0.432767
$346$	−510.592	−0.0793341
$347$	−2712.40	−0.419623	−0.209812	−	0.977742i	$-0.567285\pi$
$347$	−2712.40	−0.419623	−0.209812	+	0.977742i	$0.567285\pi$
$348$	15198.5	2.34116
$349$	7111.92	1.09081	0.545404	−	0.838173i	$-0.316376\pi$
$349$	7111.92	1.09081	0.545404	+	0.838173i	$0.316376\pi$
$350$	−1449.17	−0.221318
$351$	−3109.76	−0.472897
$352$	−2323.63	−0.351846
$353$	−5225.99	−0.787965	−0.393982	−	0.919118i	$-0.628903\pi$
$353$	−5225.99	−0.787965	−0.393982	+	0.919118i	$0.628903\pi$
$354$	−5706.16	−0.856720
$355$	602.467	0.0900722
$356$	−3360.80	−0.500342
$357$	−430.123	−0.0637662
$358$	−129.653	−0.0191406
$359$	−1898.26	−0.279070	−0.139535	−	0.990217i	$-0.544561\pi$
$359$	−1898.26	−0.279070	−0.139535	+	0.990217i	$0.544561\pi$
$360$	1671.50	0.244711
$361$	18327.3	2.67201
$362$	−12471.1	−1.81068
$363$	−817.216	−0.118162
$364$	2121.98	0.305554
$365$	−2981.81	−0.427603
$366$	8644.60	1.23459
$367$	−6179.65	−0.878952	−0.439476	−	0.898254i	$-0.644836\pi$
$367$	−6179.65	−0.878952	−0.439476	+	0.898254i	$0.644836\pi$
$368$	−1198.71	−0.169802
$369$	−4565.10	−0.644037
$370$	−2429.99	−0.341430
$371$	−1504.34	−0.210516
$372$	6664.29	0.928837
$373$	−3495.42	−0.485218	−0.242609	−	0.970124i	$-0.578003\pi$
$373$	−3495.42	−0.485218	−0.242609	+	0.970124i	$0.578003\pi$
$374$	−984.490	−0.136114
$375$	−7444.52	−1.02516
$376$	248.934	0.0341430
$377$	10203.3	1.39389
$378$	810.440	0.110277
$379$	−7561.46	−1.02482	−0.512409	−	0.858742i	$-0.671247\pi$
$379$	−7561.46	−1.02482	−0.512409	+	0.858742i	$0.671247\pi$
$380$	−9362.70	−1.26394
$381$	−11121.7	−1.49549
$382$	−8395.14	−1.12443
$383$	−2588.81	−0.345383	−0.172692	−	0.984976i	$-0.555246\pi$
$383$	−2588.81	−0.345383	−0.172692	+	0.984976i	$0.555246\pi$
$384$	−13831.8	−1.83815
$385$	−170.996	−0.0226357
$386$	8215.47	1.08331
$387$	−4778.69	−0.627686
$388$	16705.2	2.18576
$389$	6118.04	0.797422	0.398711	−	0.917077i	$-0.369458\pi$
$389$	6118.04	0.797422	0.398711	+	0.917077i	$0.369458\pi$
$390$	8101.62	1.05190
$391$	−1682.20	−0.217577
$392$	6134.80	0.790444
$393$	−884.755	−0.113562
$394$	−11191.4	−1.43101
$395$	−4761.59	−0.606536
$396$	−2479.73	−0.314674
$397$	8254.09	1.04348	0.521739	−	0.853105i	$-0.325283\pi$
$397$	8254.09	1.04348	0.521739	+	0.853105i	$0.325283\pi$
$398$	−13817.1	−1.74018
$399$	3420.32	0.429148
$400$	1440.19	0.180023
$401$	2192.09	0.272987	0.136494	−	0.990641i	$-0.456417\pi$
$401$	2192.09	0.272987	0.136494	+	0.990641i	$0.456417\pi$
$402$	24725.5	3.06765
$403$	4473.97	0.553014
$404$	−941.196	−0.115907
$405$	4311.70	0.529013
$406$	−2659.09	−0.325045
$407$	1223.56	0.149016
$408$	−2484.59	−0.301484
$409$	9250.72	1.11838	0.559192	−	0.829038i	$-0.311112\pi$
$409$	9250.72	1.11838	0.559192	+	0.829038i	$0.311112\pi$
$410$	−5357.57	−0.645346
$411$	9421.93	1.13078
$412$	13908.8	1.66319
$413$	601.193	0.0716290
$414$	−7036.12	−0.835281
$415$	1009.84	0.119448
$416$	−11599.1	−1.36705
$417$	13068.5	1.53470
$418$	7828.62	0.916054
$419$	−105.145	−0.0122593	−0.00612967	−	0.999981i	$-0.501951\pi$
$419$	−105.145	−0.0122593	−0.00612967	+	0.999981i	$0.501951\pi$
$420$	−1271.46	−0.147717
$421$	14292.9	1.65462	0.827310	−	0.561746i	$-0.189870\pi$
$421$	14292.9	1.65462	0.827310	+	0.561746i	$0.189870\pi$
$422$	21544.2	2.48520
$423$	−251.386	−0.0288956
$424$	−8689.77	−0.995313
$425$	2021.08	0.230675
$426$	−3745.72	−0.426011
$427$	−910.785	−0.103222
$428$	14222.3	1.60622
$429$	−4079.38	−0.459101
$430$	−5608.25	−0.628962
$431$	1234.05	0.137917	0.0689583	−	0.997620i	$-0.478032\pi$
$431$	1234.05	0.137917	0.0689583	+	0.997620i	$0.478032\pi$
$432$	−805.417	−0.0897006
$433$	2359.60	0.261882	0.130941	−	0.991390i	$-0.458200\pi$
$433$	2359.60	0.261882	0.130941	+	0.991390i	$0.458200\pi$
$434$	−1165.97	−0.128959
$435$	−6113.67	−0.673858
$436$	−930.270	−0.102183
$437$	13376.8	1.46430
$438$	18538.8	2.02242
$439$	−910.994	−0.0990419	−0.0495209	−	0.998773i	$-0.515769\pi$
$439$	−910.994	−0.0990419	−0.0495209	+	0.998773i	$0.515769\pi$
$440$	−987.751	−0.107021
$441$	−6195.25	−0.668961
$442$	−4914.37	−0.528853
$443$	13173.0	1.41280	0.706398	−	0.707815i	$-0.250319\pi$
$443$	13173.0	1.41280	0.706398	+	0.707815i	$0.250319\pi$
$444$	9097.95	0.972454
$445$	1351.90	0.144014
$446$	4394.78	0.466589
$447$	15253.5	1.61402
$448$	2659.80	0.280500
$449$	−14539.8	−1.52823	−0.764113	−	0.645083i	$-0.776823\pi$
$449$	−14539.8	−1.52823	−0.764113	+	0.645083i	$0.776823\pi$
$450$	8453.54	0.885563
$451$	2697.68	0.281660
$452$	10699.9	1.11345
$453$	−17924.8	−1.85912
$454$	8186.40	0.846270
$455$	−853.577	−0.0879479
$456$	19757.3	2.02900
$457$	17617.7	1.80333	0.901667	−	0.432432i	$-0.142344\pi$
$457$	17617.7	1.80333	0.901667	+	0.432432i	$0.142344\pi$
$458$	−8741.52	−0.891844
$459$	−1130.28	−0.114939
$460$	−4972.66	−0.504025
$461$	4229.39	0.427293	0.213647	−	0.976911i	$-0.431466\pi$
$461$	4229.39	0.427293	0.213647	+	0.976911i	$0.431466\pi$
$462$	1063.13	0.107059
$463$	721.259	0.0723969	0.0361984	−	0.999345i	$-0.488475\pi$
$463$	721.259	0.0723969	0.0361984	+	0.999345i	$0.488475\pi$
$464$	2642.61	0.264397
$465$	−2680.75	−0.267348
$466$	−14015.8	−1.39329
$467$	6879.78	0.681709	0.340855	−	0.940116i	$-0.389284\pi$
$467$	6879.78	0.681709	0.340855	+	0.940116i	$0.389284\pi$
$468$	−12378.3	−1.22262
$469$	−2605.04	−0.256481
$470$	−295.026	−0.0289543
$471$	6730.51	0.658440
$472$	3472.77	0.338659
$473$	2823.90	0.274509
$474$	29604.2	2.86871
$475$	−16071.6	−1.55245
$476$	771.258	0.0742659
$477$	8775.40	0.842344
$478$	−15878.1	−1.51934
$479$	−19239.1	−1.83519	−0.917596	−	0.397514i	$-0.869873\pi$
$479$	−19239.1	−1.83519	−0.917596	+	0.397514i	$0.869873\pi$
$480$	6950.02	0.660882
$481$	6107.77	0.578982
$482$	−21679.4	−2.04870
$483$	1816.58	0.171133
$484$	1465.36	0.137618
$485$	−6719.74	−0.629129
$486$	−19949.8	−1.86202
$487$	−5502.90	−0.512033	−0.256017	−	0.966672i	$-0.582410\pi$
$487$	−5502.90	−0.512033	−0.256017	+	0.966672i	$0.582410\pi$
$488$	−5261.11	−0.488031
$489$	−25671.5	−2.37404
$490$	−7270.71	−0.670320
$491$	−11061.4	−1.01669	−0.508345	−	0.861154i	$-0.669742\pi$
$491$	−11061.4	−1.01669	−0.508345	+	0.861154i	$0.669742\pi$
$492$	20058.9	1.83806
$493$	3708.50	0.338788
$494$	39078.9	3.55920
$495$	997.484	0.0905729
$496$	1158.74	0.104897
$497$	394.644	0.0356181
$498$	−6278.46	−0.564949
$499$	−7431.23	−0.666669	−0.333334	−	0.942809i	$-0.608174\pi$
$499$	−7431.23	−0.666669	−0.333334	+	0.942809i	$0.608174\pi$
$500$	13348.8	1.19396
$501$	5480.13	0.488691
$502$	23796.8	2.11575
$503$	−14249.7	−1.26314	−0.631571	−	0.775318i	$-0.717590\pi$
$503$	−14249.7	−1.26314	−0.631571	+	0.775318i	$0.717590\pi$
$504$	1094.91	0.0967685
$505$	378.601	0.0333614
$506$	4157.89	0.365298
$507$	−5525.20	−0.483990
$508$	19942.4	1.74174
$509$	−13687.3	−1.19191	−0.595954	−	0.803019i	$-0.703226\pi$
$509$	−13687.3	−1.19191	−0.595954	+	0.803019i	$0.703226\pi$
$510$	2944.63	0.255668
$511$	−1953.22	−0.169091
$512$	−5101.26	−0.440324
$513$	8987.94	0.773542
$514$	24658.7	2.11604
$515$	−5594.88	−0.478718
$516$	20997.4	1.79140
$517$	148.553	0.0126371
$518$	−1591.76	−0.135015
$519$	−768.981	−0.0650376
$520$	−4930.65	−0.415814
$521$	17810.7	1.49770	0.748849	−	0.662740i	$-0.230607\pi$
$521$	17810.7	1.49770	0.748849	+	0.662740i	$0.230607\pi$
$522$	15511.5	1.30061
$523$	−10370.3	−0.867042	−0.433521	−	0.901143i	$-0.642729\pi$
$523$	−10370.3	−0.867042	−0.433521	+	0.901143i	$0.642729\pi$
$524$	1586.46	0.132261
$525$	−2182.53	−0.181435
$526$	−10841.3	−0.898677
$527$	1626.12	0.134412
$528$	−1056.54	−0.0870837
$529$	−5062.39	−0.416075
$530$	10298.8	0.844056
$531$	−3506.99	−0.286611
$532$	−6133.01	−0.499811
$533$	13466.3	1.09435
$534$	−8405.16	−0.681136
$535$	−5720.99	−0.462318
$536$	−15047.9	−1.21263
$537$	−195.264	−0.0156914
$538$	6851.28	0.549033
$539$	3660.99	0.292560
$540$	−3341.15	−0.266260
$541$	−3520.61	−0.279784	−0.139892	−	0.990167i	$-0.544676\pi$
$541$	−3520.61	−0.279784	−0.139892	+	0.990167i	$0.544676\pi$
$542$	4955.11	0.392694
$543$	−18782.1	−1.48438
$544$	−4215.82	−0.332264
$545$	374.206	0.0294114
$546$	5306.94	0.415964
$547$	16054.6	1.25493	0.627465	−	0.778645i	$-0.284093\pi$
$547$	16054.6	1.25493	0.627465	+	0.778645i	$0.284093\pi$
$548$	−16894.6	−1.31697
$549$	5312.95	0.413026
$550$	−4995.49	−0.387288
$551$	−29489.8	−2.28005
$552$	10493.4	0.809110
$553$	−3119.06	−0.239848
$554$	13576.7	1.04119
$555$	−3659.70	−0.279902
$556$	−23433.3	−1.78740
$557$	−8592.78	−0.653658	−0.326829	−	0.945083i	$-0.605980\pi$
$557$	−8592.78	−0.653658	−0.326829	+	0.945083i	$0.605980\pi$
$558$	6801.54	0.516007
$559$	14096.3	1.06657
$560$	−221.073	−0.0166822
$561$	−1482.70	−0.111586
$562$	21939.6	1.64674
$563$	−10780.8	−0.807025	−0.403512	−	0.914974i	$-0.632211\pi$
$563$	−10780.8	−0.807025	−0.403512	+	0.914974i	$0.632211\pi$
$564$	1104.59	0.0824671
$565$	−4304.08	−0.320485
$566$	17381.9	1.29084
$567$	2824.36	0.209193
$568$	2279.64	0.168401
$569$	5970.60	0.439895	0.219948	−	0.975512i	$-0.429411\pi$
$569$	5970.60	0.439895	0.219948	+	0.975512i	$0.429411\pi$
$570$	−23415.6	−1.72065
$571$	395.985	0.0290218	0.0145109	−	0.999895i	$-0.495381\pi$
$571$	395.985	0.0290218	0.0145109	+	0.999895i	$0.495381\pi$
$572$	7314.77	0.534696
$573$	−12643.6	−0.921802
$574$	−3509.46	−0.255195
$575$	−8535.83	−0.619076
$576$	−15515.6	−1.12237
$577$	−4361.76	−0.314701	−0.157350	−	0.987543i	$-0.550295\pi$
$577$	−4361.76	−0.314701	−0.157350	+	0.987543i	$0.550295\pi$
$578$	20246.0	1.45696
$579$	12373.0	0.888087
$580$	10962.5	0.784814
$581$	661.491	0.0472345
$582$	41778.6	2.97557
$583$	−5185.69	−0.368387
$584$	−11282.7	−0.799456
$585$	4979.24	0.351908
$586$	−5746.47	−0.405093
$587$	−857.285	−0.0602793	−0.0301396	−	0.999546i	$-0.509595\pi$
$587$	−857.285	−0.0602793	−0.0301396	+	0.999546i	$0.509595\pi$
$588$	27221.7	1.90919
$589$	−12930.8	−0.904593
$590$	−4115.78	−0.287193
$591$	−16855.0	−1.17313
$592$	1581.89	0.109823
$593$	−950.603	−0.0658290	−0.0329145	−	0.999458i	$-0.510479\pi$
$593$	−950.603	−0.0658290	−0.0329145	+	0.999458i	$0.510479\pi$
$594$	2793.71	0.192975
$595$	−310.243	−0.0213760
$596$	−27351.2	−1.87978
$597$	−20809.4	−1.42659
$598$	20755.4	1.41931
$599$	−12558.0	−0.856602	−0.428301	−	0.903636i	$-0.640888\pi$
$599$	−12558.0	−0.856602	−0.428301	+	0.903636i	$0.640888\pi$
$600$	−12607.3	−0.857817
$601$	−1815.97	−0.123253	−0.0616263	−	0.998099i	$-0.519629\pi$
$601$	−1815.97	−0.123253	−0.0616263	+	0.998099i	$0.519629\pi$
$602$	−3673.66	−0.248716
$603$	15196.2	1.02626
$604$	32141.1	2.16524
$605$	−589.448	−0.0396107
$606$	−2353.88	−0.157788
$607$	3725.20	0.249096	0.124548	−	0.992214i	$-0.460252\pi$
$607$	3725.20	0.249096	0.124548	+	0.992214i	$0.460252\pi$
$608$	33524.0	2.23615
$609$	−4004.74	−0.266470
$610$	6235.25	0.413865
$611$	741.547	0.0490995
$612$	−4499.04	−0.297161
$613$	17165.5	1.13101	0.565505	−	0.824745i	$-0.308681\pi$
$613$	17165.5	1.13101	0.565505	+	0.824745i	$0.308681\pi$
$614$	−13629.8	−0.895855
$615$	−8068.81	−0.529050
$616$	−647.023	−0.0423203
$617$	−5420.72	−0.353695	−0.176848	−	0.984238i	$-0.556590\pi$
$617$	−5420.72	−0.353695	−0.176848	+	0.984238i	$0.556590\pi$
$618$	34785.0	2.26417
$619$	16964.8	1.10157	0.550785	−	0.834647i	$-0.314329\pi$
$619$	16964.8	1.10157	0.550785	+	0.834647i	$0.314329\pi$
$620$	4806.87	0.311369
$621$	4773.62	0.308468
$622$	−12878.9	−0.830217
$623$	885.557	0.0569488
$624$	−5274.05	−0.338351
$625$	7288.95	0.466493
$626$	7396.40	0.472236
$627$	11790.4	0.750975
$628$	−12068.5	−0.766858
$629$	2219.94	0.140723
$630$	−1297.65	−0.0820626
$631$	−11768.5	−0.742469	−0.371235	−	0.928539i	$-0.621065\pi$
$631$	−11768.5	−0.742469	−0.371235	+	0.928539i	$0.621065\pi$
$632$	−18017.1	−1.13399
$633$	32446.8	2.03735
$634$	48948.0	3.06621
$635$	−8021.95	−0.501325
$636$	−38558.9	−2.40402
$637$	18274.9	1.13670
$638$	−9166.28	−0.568803
$639$	−2302.11	−0.142519
$640$	−9976.70	−0.616193
$641$	−21560.2	−1.32851	−0.664256	−	0.747505i	$-0.731251\pi$
$641$	−21560.2	−1.32851	−0.664256	+	0.747505i	$0.731251\pi$
$642$	35569.1	2.18661
$643$	27508.3	1.68713	0.843563	−	0.537031i	$-0.180454\pi$
$643$	27508.3	1.68713	0.843563	+	0.537031i	$0.180454\pi$
$644$	−3257.33	−0.199312
$645$	−8446.34	−0.515619
$646$	14203.7	0.865072
$647$	−26033.9	−1.58191	−0.790956	−	0.611873i	$-0.790416\pi$
$647$	−26033.9	−1.58191	−0.790956	+	0.611873i	$0.790416\pi$
$648$	16314.8	0.989054
$649$	2072.40	0.125345
$650$	−24936.5	−1.50475
$651$	−1756.02	−0.105720
$652$	46031.7	2.76494
$653$	−26293.8	−1.57574	−0.787868	−	0.615845i	$-0.788815\pi$
$653$	−26293.8	−1.57574	−0.787868	+	0.615845i	$0.788815\pi$
$654$	−2326.55	−0.139106
$655$	−638.163	−0.0380689
$656$	3487.71	0.207580
$657$	11393.9	0.676588
$658$	−193.256	−0.0114497
$659$	5701.85	0.337045	0.168522	−	0.985698i	$-0.446100\pi$
$659$	5701.85	0.337045	0.168522	+	0.985698i	$0.446100\pi$
$660$	−4382.92	−0.258492
$661$	−5677.70	−0.334095	−0.167047	−	0.985949i	$-0.553423\pi$
$661$	−5677.70	−0.334095	−0.167047	+	0.985949i	$0.553423\pi$
$662$	18099.8	1.06264
$663$	−7401.33	−0.433550
$664$	3821.07	0.223323
$665$	2467.04	0.143861
$666$	9285.31	0.540238
$667$	−15662.5	−0.909225
$668$	−9826.48	−0.569159
$669$	6618.79	0.382507
$670$	17834.2	1.02835
$671$	−3139.61	−0.180631
$672$	4552.59	0.261339
$673$	−21182.3	−1.21325	−0.606624	−	0.794989i	$-0.707477\pi$
$673$	−21182.3	−1.21325	−0.606624	+	0.794989i	$0.707477\pi$
$674$	38733.2	2.21357
$675$	−5735.26	−0.327037
$676$	9907.29	0.563683
$677$	−14362.4	−0.815350	−0.407675	−	0.913127i	$-0.633660\pi$
$677$	−14362.4	−0.815350	−0.407675	+	0.913127i	$0.633660\pi$
$678$	26759.7	1.51578
$679$	−4401.74	−0.248783
$680$	−1792.10	−0.101065
$681$	12329.2	0.693767
$682$	−4019.27	−0.225668
$683$	30057.9	1.68395	0.841973	−	0.539520i	$-0.181394\pi$
$683$	30057.9	1.68395	0.841973	+	0.539520i	$0.181394\pi$
$684$	35776.2	1.99991
$685$	6795.93	0.379064
$686$	−9671.02	−0.538253
$687$	−13165.2	−0.731128
$688$	3650.90	0.202310
$689$	−25885.9	−1.43131
$690$	−12436.3	−0.686150
$691$	−24038.5	−1.32340	−0.661698	−	0.749770i	$-0.730164\pi$
$691$	−24038.5	−1.32340	−0.661698	+	0.749770i	$0.730164\pi$
$692$	1378.87	0.0757466
$693$	653.399	0.0358161
$694$	12163.6	0.665311
$695$	9426.17	0.514468
$696$	−23133.2	−1.25986
$697$	4894.47	0.265985
$698$	−31893.1	−1.72947
$699$	−21108.6	−1.14221
$700$	3913.51	0.211310
$701$	10279.9	0.553874	0.276937	−	0.960888i	$-0.410681\pi$
$701$	10279.9	0.553874	0.276937	+	0.960888i	$0.410681\pi$
$702$	13945.6	0.749777
$703$	−17652.9	−0.947071
$704$	9168.73	0.490852
$705$	−444.326	−0.0237366
$706$	23435.8	1.24932
$707$	248.001	0.0131924
$708$	15409.6	0.817978
$709$	990.163	0.0524490	0.0262245	−	0.999656i	$-0.491652\pi$
$709$	990.163	0.0524490	0.0262245	+	0.999656i	$0.491652\pi$
$710$	−2701.74	−0.142809
$711$	18194.7	0.959710
$712$	5115.38	0.269251
$713$	−6867.75	−0.360728
$714$	1928.87	0.101101
$715$	−2942.41	−0.153902
$716$	350.130	0.0182751
$717$	−23913.3	−1.24555
$718$	8512.66	0.442465
$719$	−7821.40	−0.405687	−0.202843	−	0.979211i	$-0.565018\pi$
$719$	−7821.40	−0.405687	−0.202843	+	0.979211i	$0.565018\pi$
$720$	1289.60	0.0667510
$721$	−3664.91	−0.189304
$722$	−82188.2	−4.23647
$723$	−32650.5	−1.67951
$724$	33678.4	1.72880
$725$	18817.6	0.963958
$726$	3664.78	0.187345
$727$	17846.2	0.910424	0.455212	−	0.890383i	$-0.349563\pi$
$727$	17846.2	0.910424	0.455212	+	0.890383i	$0.349563\pi$
$728$	−3229.81	−0.164429
$729$	−6148.13	−0.312357
$730$	13371.8	0.677963
$731$	5123.48	0.259232
$732$	−23345.0	−1.17876
$733$	35150.3	1.77122	0.885612	−	0.464425i	$-0.153739\pi$
$733$	35150.3	1.77122	0.885612	+	0.464425i	$0.153739\pi$
$734$	27712.4	1.39358
$735$	−10950.1	−0.549524
$736$	17805.1	0.891718
$737$	−8979.97	−0.448822
$738$	20472.0	1.02112
$739$	32356.2	1.61061	0.805305	−	0.592860i	$-0.202001\pi$
$739$	32356.2	1.61061	0.805305	+	0.592860i	$0.202001\pi$
$740$	6562.24	0.325990
$741$	58855.0	2.91781
$742$	6746.17	0.333773
$743$	13297.0	0.656552	0.328276	−	0.944582i	$-0.393532\pi$
$743$	13297.0	0.656552	0.328276	+	0.944582i	$0.393532\pi$
$744$	−10143.6	−0.499840
$745$	11002.2	0.541058
$746$	15675.1	0.769311
$747$	−3858.73	−0.189001
$748$	2658.64	0.129959
$749$	−3747.52	−0.182819
$750$	33384.7	1.62538
$751$	−32549.2	−1.58154	−0.790770	−	0.612114i	$-0.790319\pi$
$751$	−32549.2	−1.58154	−0.790770	+	0.612114i	$0.790319\pi$
$752$	192.058	0.00931335
$753$	35839.4	1.73447
$754$	−45756.2	−2.21000
$755$	−12928.9	−0.623222
$756$	−2188.61	−0.105290
$757$	7509.37	0.360545	0.180273	−	0.983617i	$-0.442302\pi$
$757$	7509.37	0.360545	0.180273	+	0.983617i	$0.442302\pi$
$758$	33909.1	1.62485
$759$	6262.02	0.299469
$760$	14250.7	0.680169
$761$	−8454.63	−0.402733	−0.201367	−	0.979516i	$-0.564538\pi$
$761$	−8454.63	−0.402733	−0.201367	+	0.979516i	$0.564538\pi$
$762$	49874.8	2.37110
$763$	245.123	0.0116305
$764$	22671.3	1.07358
$765$	1809.76	0.0855322
$766$	11609.4	0.547604
$767$	10345.0	0.487010
$768$	16992.3	0.798379
$769$	13449.0	0.630666	0.315333	−	0.948981i	$-0.397884\pi$
$769$	13449.0	0.630666	0.315333	+	0.948981i	$0.397884\pi$
$770$	766.825	0.0358889
$771$	37137.3	1.73472
$772$	−22186.1	−1.03432
$773$	−14082.6	−0.655260	−0.327630	−	0.944806i	$-0.606250\pi$
$773$	−14082.6	−0.655260	−0.327630	+	0.944806i	$0.606250\pi$
$774$	21429.9	0.995194
$775$	8251.24	0.382443
$776$	−25426.5	−1.17623
$777$	−2397.27	−0.110684
$778$	−27436.1	−1.26431
$779$	−38920.6	−1.79008
$780$	−21878.6	−1.00433
$781$	1360.40	0.0623288
$782$	7543.78	0.344968
$783$	−10523.7	−0.480314
$784$	4733.14	0.215613
$785$	4854.63	0.220725
$786$	3967.65	0.180053
$787$	31440.2	1.42404	0.712022	−	0.702157i	$-0.247780\pi$
$787$	31440.2	1.42404	0.712022	+	0.702157i	$0.247780\pi$
$788$	30222.8	1.36630
$789$	−16327.6	−0.736729
$790$	21353.2	0.961660
$791$	−2819.37	−0.126732
$792$	3774.33	0.169337
$793$	−15672.3	−0.701815
$794$	−37015.2	−1.65443
$795$	15510.5	0.691951
$796$	37313.5	1.66148
$797$	34623.6	1.53881	0.769404	−	0.638763i	$-0.220553\pi$
$797$	34623.6	1.53881	0.769404	+	0.638763i	$0.220553\pi$
$798$	−15338.3	−0.680413
$799$	269.524	0.0119338
$800$	−21391.9	−0.945397
$801$	−5165.79	−0.227870
$802$	−9830.36	−0.432821
$803$	−6733.06	−0.295896
$804$	−66771.7	−2.92893
$805$	1310.28	0.0573680
$806$	−20063.4	−0.876801
$807$	10318.4	0.450093
$808$	1432.57	0.0623733
$809$	−17036.4	−0.740379	−0.370190	−	0.928956i	$-0.620707\pi$
$809$	−17036.4	−0.740379	−0.370190	+	0.928956i	$0.620707\pi$
$810$	−19335.7	−0.838748
$811$	−41333.7	−1.78967	−0.894836	−	0.446395i	$-0.852707\pi$
$811$	−41333.7	−1.78967	−0.894836	+	0.446395i	$0.852707\pi$
$812$	7180.94	0.310347
$813$	7462.67	0.321928
$814$	−5487.02	−0.236265
$815$	−18516.5	−0.795835
$816$	−1916.92	−0.0822372
$817$	−40741.7	−1.74464
$818$	−41484.5	−1.77319
$819$	3261.63	0.139158
$820$	14468.3	0.616163
$821$	28983.8	1.23208	0.616042	−	0.787713i	$-0.288735\pi$
$821$	28983.8	1.23208	0.616042	+	0.787713i	$0.288735\pi$
$822$	−42252.3	−1.79284
$823$	−30714.9	−1.30092	−0.650458	−	0.759543i	$-0.725423\pi$
$823$	−30714.9	−1.30092	−0.650458	+	0.759543i	$0.725423\pi$
$824$	−21170.2	−0.895022
$825$	−7523.50	−0.317496
$826$	−2696.03	−0.113568
$827$	42146.7	1.77217	0.886085	−	0.463522i	$-0.153415\pi$
$827$	42146.7	1.77217	0.886085	+	0.463522i	$0.153415\pi$
$828$	19001.2	0.797510
$829$	−44522.2	−1.86528	−0.932641	−	0.360806i	$-0.882502\pi$
$829$	−44522.2	−1.86528	−0.932641	+	0.360806i	$0.882502\pi$
$830$	−4528.58	−0.189385
$831$	20447.3	0.853561
$832$	45768.4	1.90713
$833$	6642.24	0.276278
$834$	−58605.3	−2.43326
$835$	3952.76	0.163821
$836$	−21141.4	−0.874630
$837$	−4614.47	−0.190561
$838$	471.518	0.0194371
$839$	−23962.7	−0.986037	−0.493018	−	0.870019i	$-0.664106\pi$
$839$	−23962.7	−0.986037	−0.493018	+	0.870019i	$0.664106\pi$
$840$	1935.26	0.0794914
$841$	10139.7	0.415747
$842$	−64096.1	−2.62339
$843$	33042.3	1.34998
$844$	−58180.6	−2.37282
$845$	−3985.26	−0.162245
$846$	1127.33	0.0458138
$847$	−386.116	−0.0156637
$848$	−6704.36	−0.271496
$849$	26178.1	1.05822
$850$	−9063.46	−0.365734
$851$	−9375.70	−0.377667
$852$	10115.4	0.406746
$853$	2703.82	0.108531	0.0542656	−	0.998527i	$-0.482718\pi$
$853$	2703.82	0.108531	0.0542656	+	0.998527i	$0.482718\pi$
$854$	4084.38	0.163659
$855$	−14391.2	−0.575634
$856$	−21647.4	−0.864360
$857$	2148.71	0.0856458	0.0428229	−	0.999083i	$-0.486365\pi$
$857$	2148.71	0.0856458	0.0428229	+	0.999083i	$0.486365\pi$
$858$	18293.8	0.727903
$859$	−23174.4	−0.920491	−0.460246	−	0.887792i	$-0.652239\pi$
$859$	−23174.4	−0.920491	−0.460246	+	0.887792i	$0.652239\pi$
$860$	15145.2	0.600520
$861$	−5285.45	−0.209207
$862$	−5534.05	−0.218666
$863$	20817.6	0.821137	0.410568	−	0.911830i	$-0.365330\pi$
$863$	20817.6	0.821137	0.410568	+	0.911830i	$0.365330\pi$
$864$	11963.3	0.471065
$865$	−554.657	−0.0218022
$866$	−10581.5	−0.415213
$867$	30491.6	1.19440
$868$	3148.73	0.123128
$869$	−10751.9	−0.419715
$870$	27416.5	1.06840
$871$	−44826.2	−1.74383
$872$	1415.94	0.0549883
$873$	25677.0	0.995459
$874$	−59987.8	−2.32165
$875$	−3517.37	−0.135896
$876$	−50064.5	−1.93096
$877$	−7127.76	−0.274444	−0.137222	−	0.990540i	$-0.543817\pi$
$877$	−7127.76	−0.274444	−0.137222	+	0.990540i	$0.543817\pi$
$878$	4085.32	0.157031
$879$	−8654.51	−0.332093
$880$	−762.073	−0.0291926
$881$	−17205.0	−0.657946	−0.328973	−	0.944339i	$-0.606703\pi$
$881$	−17205.0	−0.657946	−0.328973	+	0.944339i	$0.606703\pi$
$882$	27782.3	1.06064
$883$	−34925.3	−1.33107	−0.665533	−	0.746368i	$-0.731796\pi$
$883$	−34925.3	−1.33107	−0.665533	+	0.746368i	$0.731796\pi$
$884$	13271.4	0.504938
$885$	−6198.60	−0.235439
$886$	−59073.9	−2.23998
$887$	−43176.0	−1.63439	−0.817197	−	0.576358i	$-0.804473\pi$
$887$	−43176.0	−1.63439	−0.817197	+	0.576358i	$0.804473\pi$
$888$	−13847.8	−0.523311
$889$	−5254.75	−0.198244
$890$	−6062.54	−0.228333
$891$	9736.00	0.366070
$892$	−11868.2	−0.445490
$893$	−2143.24	−0.0803146
$894$	−68403.8	−2.55902
$895$	−140.842	−0.00526013
$896$	−6535.20	−0.243667
$897$	31258.7	1.16354
$898$	65203.0	2.42300
$899$	15140.3	0.561687
$900$	−22829.0	−0.845518
$901$	−9408.55	−0.347885
$902$	−12097.6	−0.446571
$903$	−5532.75	−0.203896
$904$	−16286.0	−0.599186
$905$	−13547.3	−0.497600
$906$	80383.1	2.94763
$907$	−578.620	−0.0211827	−0.0105914	−	0.999944i	$-0.503371\pi$
$907$	−578.620	−0.0211827	−0.0105914	+	0.999944i	$0.503371\pi$
$908$	−22107.6	−0.808002
$909$	−1446.69	−0.0527872
$910$	3827.83	0.139441
$911$	−36852.8	−1.34027	−0.670136	−	0.742238i	$-0.733764\pi$
$911$	−36852.8	−1.34027	−0.670136	+	0.742238i	$0.733764\pi$
$912$	15243.2	0.553459
$913$	2280.26	0.0826566
$914$	−79006.1	−2.85918
$915$	9390.64	0.339284
$916$	23606.7	0.851514
$917$	−418.027	−0.0150539
$918$	5068.70	0.182235
$919$	−44403.9	−1.59385	−0.796925	−	0.604078i	$-0.793542\pi$
$919$	−44403.9	−1.59385	−0.796925	+	0.604078i	$0.793542\pi$
$920$	7568.76	0.271233
$921$	−20527.3	−0.734416
$922$	−18966.5	−0.677472
$923$	6790.82	0.242170
$924$	−2871.02	−0.102218
$925$	11264.4	0.400402
$926$	−3234.46	−0.114785
$927$	21378.8	0.757466
$928$	−39252.2	−1.38849
$929$	−19683.0	−0.695131	−0.347566	−	0.937656i	$-0.612992\pi$
$929$	−19683.0	−0.695131	−0.347566	+	0.937656i	$0.612992\pi$
$930$	12021.7	0.423879
$931$	−52818.8	−1.85936
$932$	37850.1	1.33028
$933$	−19396.3	−0.680607
$934$	−30852.1	−1.08085
$935$	−1069.45	−0.0374062
$936$	18840.7	0.657935
$937$	25316.6	0.882667	0.441333	−	0.897343i	$-0.354506\pi$
$937$	25316.6	0.882667	0.441333	+	0.897343i	$0.354506\pi$
$938$	11682.2	0.406650
$939$	11139.4	0.387136
$940$	796.724	0.0276450
$941$	39353.5	1.36332	0.681661	−	0.731668i	$-0.261258\pi$
$941$	39353.5	1.36332	0.681661	+	0.731668i	$0.261258\pi$
$942$	−30182.7	−1.04395
$943$	−20671.3	−0.713839
$944$	2679.32	0.0923776
$945$	880.381	0.0303056
$946$	−12663.7	−0.435234
$947$	4827.46	0.165651	0.0828255	−	0.996564i	$-0.473606\pi$
$947$	4827.46	0.165651	0.0828255	+	0.996564i	$0.473606\pi$
$948$	−79946.9	−2.73898
$949$	−33610.0	−1.14966
$950$	72072.3	2.46140
$951$	73718.5	2.51366
$952$	−1173.91	−0.0399650
$953$	15097.5	0.513175	0.256587	−	0.966521i	$-0.417402\pi$
$953$	15097.5	0.513175	0.256587	+	0.966521i	$0.417402\pi$
$954$	−39352.9	−1.33553
$955$	−9119.65	−0.309010
$956$	42879.1	1.45064
$957$	−13804.9	−0.466301
$958$	86277.0	2.90969
$959$	4451.65	0.149897
$960$	−27423.9	−0.921981
$961$	−23152.2	−0.777155
$962$	−27390.1	−0.917974
$963$	21860.7	0.731517
$964$	58545.9	1.95605
$965$	8924.47	0.297709
$966$	−8146.39	−0.271331
$967$	45147.6	1.50140	0.750698	−	0.660645i	$-0.229717\pi$
$967$	45147.6	1.50140	0.750698	+	0.660645i	$0.229717\pi$
$968$	−2230.38	−0.0740571
$969$	21391.6	0.709181
$970$	30134.4	0.997482
$971$	−15018.2	−0.496351	−0.248176	−	0.968715i	$-0.579831\pi$
$971$	−15018.2	−0.496351	−0.248176	+	0.968715i	$0.579831\pi$
$972$	53875.0	1.77782
$973$	6174.58	0.203441
$974$	24677.5	0.811827
$975$	−37555.8	−1.23359
$976$	−4059.07	−0.133123
$977$	39991.1	1.30955	0.654775	−	0.755824i	$-0.272764\pi$
$977$	39991.1	1.30955	0.654775	+	0.755824i	$0.272764\pi$
$978$	115123.	3.76403
$979$	3052.65	0.0996557
$980$	19634.7	0.640008
$981$	−1429.89	−0.0465372
$982$	49604.5	1.61196
$983$	−50045.7	−1.62381	−0.811907	−	0.583787i	$-0.801570\pi$
$983$	−50045.7	−1.62381	−0.811907	+	0.583787i	$0.801570\pi$
$984$	−30531.2	−0.989124
$985$	−12157.3	−0.393262
$986$	−16630.6	−0.537147
$987$	−291.054	−0.00938638
$988$	−105534.	−3.39825
$989$	−21638.5	−0.695716
$990$	−4473.18	−0.143603
$991$	39320.3	1.26039	0.630197	−	0.776436i	$-0.282974\pi$
$991$	39320.3	1.26039	0.630197	+	0.776436i	$0.282974\pi$
$992$	−17211.5	−0.550871
$993$	27259.3	0.871146
$994$	−1769.77	−0.0564724
$995$	−15009.6	−0.478226
$996$	16955.1	0.539402
$997$	−2845.36	−0.0903846	−0.0451923	−	0.998978i	$-0.514390\pi$
$997$	−2845.36	−0.0903846	−0.0451923	+	0.998978i	$0.514390\pi$
$998$	33325.1	1.05700
$999$	−6299.57	−0.199509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.12	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-4.48446 q^{2} -6.75386 q^{3} +12.1104 q^{4} -4.87147 q^{5} +30.2874 q^{6} -3.19104 q^{7} -18.4329 q^{8} +18.6146 q^{9} +O(q^{10})\)	\(q-4.48446 q^{2} -6.75386 q^{3} +12.1104 q^{4} -4.87147 q^{5} +30.2874 q^{6} -3.19104 q^{7} -18.4329 q^{8} +18.6146 q^{9} +21.8459 q^{10} -11.0000 q^{11} -81.7919 q^{12} -54.9098 q^{13} +14.3101 q^{14} +32.9012 q^{15} -14.2214 q^{16} -19.9576 q^{17} -83.4763 q^{18} +158.702 q^{19} -58.9955 q^{20} +21.5518 q^{21} +49.3291 q^{22} +84.2889 q^{23} +124.493 q^{24} -101.269 q^{25} +246.241 q^{26} +56.6341 q^{27} -38.6448 q^{28} -185.819 q^{29} -147.544 q^{30} -81.4787 q^{31} +211.239 q^{32} +74.2924 q^{33} +89.4991 q^{34} +15.5451 q^{35} +225.430 q^{36} -111.233 q^{37} -711.693 q^{38} +370.853 q^{39} +89.7955 q^{40} -245.243 q^{41} -96.6484 q^{42} -256.718 q^{43} -133.214 q^{44} -90.6803 q^{45} -377.990 q^{46} -13.5048 q^{47} +96.0495 q^{48} -332.817 q^{49} +454.136 q^{50} +134.791 q^{51} -664.979 q^{52} +471.427 q^{53} -253.973 q^{54} +53.5862 q^{55} +58.8203 q^{56} -1071.85 q^{57} +833.298 q^{58} -188.400 q^{59} +398.447 q^{60} +285.419 q^{61} +365.388 q^{62} -59.3999 q^{63} -833.521 q^{64} +267.491 q^{65} -333.161 q^{66} +816.361 q^{67} -241.695 q^{68} -569.275 q^{69} -69.7114 q^{70} -123.672 q^{71} -343.121 q^{72} +612.096 q^{73} +498.820 q^{74} +683.954 q^{75} +1921.94 q^{76} +35.1015 q^{77} -1663.07 q^{78} +977.443 q^{79} +69.2793 q^{80} -885.091 q^{81} +1099.78 q^{82} -207.296 q^{83} +261.001 q^{84} +97.2230 q^{85} +1151.24 q^{86} +1254.99 q^{87} +202.762 q^{88} -277.513 q^{89} +406.653 q^{90} +175.219 q^{91} +1020.77 q^{92} +550.295 q^{93} +60.5619 q^{94} -773.113 q^{95} -1426.68 q^{96} +1379.41 q^{97} +1492.51 q^{98} -204.760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 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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