LMFDB - Embedded newform 77.4.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,4,Mod(1,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.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:	$4.54314707044$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.509800.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 5x + 15 $ x^4 - x^3 - 10x^2 + 5x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.66444$ of defining polynomial
Character	$\chi$	$=$	77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.76366 q^{2} -7.36360 q^{3} +6.16515 q^{4} -15.4926 q^{5} -27.7141 q^{6} -7.00000 q^{7} -6.90574 q^{8} +27.2227 q^{9} +O(q^{10})$	\(q+3.76366 q^{2} -7.36360 q^{3} +6.16515 q^{4} -15.4926 q^{5} -27.7141 q^{6} -7.00000 q^{7} -6.90574 q^{8} +27.2227 q^{9} -58.3089 q^{10} +11.0000 q^{11} -45.3978 q^{12} +49.0777 q^{13} -26.3456 q^{14} +114.081 q^{15} -75.3121 q^{16} -34.1261 q^{17} +102.457 q^{18} -144.114 q^{19} -95.5142 q^{20} +51.5452 q^{21} +41.4003 q^{22} +118.906 q^{23} +50.8511 q^{24} +115.020 q^{25} +184.712 q^{26} -1.63966 q^{27} -43.1561 q^{28} -63.6830 q^{29} +429.364 q^{30} -212.912 q^{31} -228.203 q^{32} -80.9996 q^{33} -128.439 q^{34} +108.448 q^{35} +167.832 q^{36} -200.224 q^{37} -542.396 q^{38} -361.389 q^{39} +106.988 q^{40} +451.267 q^{41} +193.999 q^{42} -130.664 q^{43} +67.8167 q^{44} -421.750 q^{45} +447.523 q^{46} -176.271 q^{47} +554.569 q^{48} +49.0000 q^{49} +432.898 q^{50} +251.291 q^{51} +302.571 q^{52} -629.988 q^{53} -6.17114 q^{54} -170.419 q^{55} +48.3402 q^{56} +1061.20 q^{57} -239.681 q^{58} -86.9318 q^{59} +703.329 q^{60} +644.248 q^{61} -801.330 q^{62} -190.559 q^{63} -256.384 q^{64} -760.340 q^{65} -304.855 q^{66} -400.974 q^{67} -210.393 q^{68} -875.578 q^{69} +408.162 q^{70} +507.611 q^{71} -187.993 q^{72} +176.392 q^{73} -753.575 q^{74} -846.965 q^{75} -888.485 q^{76} -77.0000 q^{77} -1360.14 q^{78} -701.122 q^{79} +1166.78 q^{80} -722.938 q^{81} +1698.42 q^{82} -1259.27 q^{83} +317.784 q^{84} +528.702 q^{85} -491.775 q^{86} +468.936 q^{87} -75.9631 q^{88} +788.394 q^{89} -1587.32 q^{90} -343.544 q^{91} +733.075 q^{92} +1567.80 q^{93} -663.423 q^{94} +2232.70 q^{95} +1680.40 q^{96} +185.039 q^{97} +184.419 q^{98} +299.449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{3} + 22 q^{4} - 18 q^{5} + 2 q^{6} - 28 q^{7} - 60 q^{8} + 66 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 12 * q^3 + 22 * q^4 - 18 * q^5 + 2 * q^6 - 28 * q^7 - 60 * q^8 + 66 * q^9	\( 4 q - 4 q^{2} - 12 q^{3} + 22 q^{4} - 18 q^{5} + 2 q^{6} - 28 q^{7} - 60 q^{8} + 66 q^{9} - 92 q^{10} + 44 q^{11} - 186 q^{12} - 134 q^{13} + 28 q^{14} - 62 q^{15} - 6 q^{16} - 74 q^{17} - 256 q^{18} - 164 q^{19} + 116 q^{20} + 84 q^{21} - 44 q^{22} + 194 q^{23} + 570 q^{24} + 38 q^{25} + 734 q^{26} - 510 q^{27} - 154 q^{28} - 108 q^{29} + 1252 q^{30} - 412 q^{31} - 4 q^{32} - 132 q^{33} - 346 q^{34} + 126 q^{35} + 1518 q^{36} + 286 q^{37} + 224 q^{38} - 256 q^{39} - 540 q^{40} - 18 q^{41} - 14 q^{42} - 496 q^{43} + 242 q^{44} + 580 q^{45} - 284 q^{46} + 62 q^{47} - 862 q^{48} + 196 q^{49} + 212 q^{50} - 508 q^{51} - 822 q^{52} - 828 q^{53} + 2420 q^{54} - 198 q^{55} + 420 q^{56} + 700 q^{57} + 1388 q^{58} - 1224 q^{59} - 1776 q^{60} - 350 q^{61} - 878 q^{62} - 462 q^{63} - 718 q^{64} - 396 q^{65} + 22 q^{66} - 1498 q^{67} + 1058 q^{68} - 386 q^{69} + 644 q^{70} + 2326 q^{71} - 3000 q^{72} - 1630 q^{73} - 1156 q^{74} - 1362 q^{75} - 3152 q^{76} - 308 q^{77} - 2464 q^{78} - 1020 q^{79} + 3072 q^{80} + 1128 q^{81} + 2118 q^{82} - 1920 q^{83} + 1302 q^{84} + 2008 q^{85} + 1056 q^{86} + 1640 q^{87} - 660 q^{88} + 1550 q^{89} - 5780 q^{90} + 938 q^{91} + 2592 q^{92} + 6046 q^{93} - 1042 q^{94} + 2332 q^{95} + 4082 q^{96} - 2202 q^{97} - 196 q^{98} + 726 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^3 + 22 * q^4 - 18 * q^5 + 2 * q^6 - 28 * q^7 - 60 * q^8 + 66 * q^9 - 92 * q^10 + 44 * q^11 - 186 * q^12 - 134 * q^13 + 28 * q^14 - 62 * q^15 - 6 * q^16 - 74 * q^17 - 256 * q^18 - 164 * q^19 + 116 * q^20 + 84 * q^21 - 44 * q^22 + 194 * q^23 + 570 * q^24 + 38 * q^25 + 734 * q^26 - 510 * q^27 - 154 * q^28 - 108 * q^29 + 1252 * q^30 - 412 * q^31 - 4 * q^32 - 132 * q^33 - 346 * q^34 + 126 * q^35 + 1518 * q^36 + 286 * q^37 + 224 * q^38 - 256 * q^39 - 540 * q^40 - 18 * q^41 - 14 * q^42 - 496 * q^43 + 242 * q^44 + 580 * q^45 - 284 * q^46 + 62 * q^47 - 862 * q^48 + 196 * q^49 + 212 * q^50 - 508 * q^51 - 822 * q^52 - 828 * q^53 + 2420 * q^54 - 198 * q^55 + 420 * q^56 + 700 * q^57 + 1388 * q^58 - 1224 * q^59 - 1776 * q^60 - 350 * q^61 - 878 * q^62 - 462 * q^63 - 718 * q^64 - 396 * q^65 + 22 * q^66 - 1498 * q^67 + 1058 * q^68 - 386 * q^69 + 644 * q^70 + 2326 * q^71 - 3000 * q^72 - 1630 * q^73 - 1156 * q^74 - 1362 * q^75 - 3152 * q^76 - 308 * q^77 - 2464 * q^78 - 1020 * q^79 + 3072 * q^80 + 1128 * q^81 + 2118 * q^82 - 1920 * q^83 + 1302 * q^84 + 2008 * q^85 + 1056 * q^86 + 1640 * q^87 - 660 * q^88 + 1550 * q^89 - 5780 * q^90 + 938 * q^91 + 2592 * q^92 + 6046 * q^93 - 1042 * q^94 + 2332 * q^95 + 4082 * q^96 - 2202 * q^97 - 196 * q^98 + 726 * 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 $

$2$	3.76366	1.33066	0.665328	−	0.746551i	$-0.268292\pi$
$2$	3.76366	1.33066	0.665328	+	0.746551i	$0.268292\pi$
$3$	−7.36360	−1.41713	−0.708563	−	0.705647i	$-0.750656\pi$
$3$	−7.36360	−1.41713	−0.708563	+	0.705647i	$0.750656\pi$
$4$	6.16515	0.770644
$5$	−15.4926	−1.38570	−0.692850	−	0.721082i	$-0.743645\pi$
$5$	−15.4926	−1.38570	−0.692850	+	0.721082i	$0.743645\pi$
$6$	−27.7141	−1.88571
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−6.90574	−0.305193
$9$	27.2227	1.00825
$10$	−58.3089	−1.84389
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−45.3978	−1.09210
$13$	49.0777	1.04705	0.523527	−	0.852009i	$-0.324616\pi$
$13$	49.0777	1.04705	0.523527	+	0.852009i	$0.324616\pi$
$14$	−26.3456	−0.502941
$15$	114.081	1.96371
$16$	−75.3121	−1.17675
$17$	−34.1261	−0.486871	−0.243435	−	0.969917i	$-0.578274\pi$
$17$	−34.1261	−0.486871	−0.243435	+	0.969917i	$0.578274\pi$
$18$	102.457	1.34163
$19$	−144.114	−1.74011	−0.870053	−	0.492958i	$-0.835916\pi$
$19$	−144.114	−1.74011	−0.870053	+	0.492958i	$0.835916\pi$
$20$	−95.5142	−1.06788
$21$	51.5452	0.535623
$22$	41.4003	0.401208
$23$	118.906	1.07798	0.538992	−	0.842311i	$-0.318805\pi$
$23$	118.906	1.07798	0.538992	+	0.842311i	$0.318805\pi$
$24$	50.8511	0.432498
$25$	115.020	0.920164
$26$	184.712	1.39327
$27$	−1.63966	−0.0116872
$28$	−43.1561	−0.291276
$29$	−63.6830	−0.407780	−0.203890	−	0.978994i	$-0.565359\pi$
$29$	−63.6830	−0.407780	−0.203890	+	0.978994i	$0.565359\pi$
$30$	429.364	2.61302
$31$	−212.912	−1.23355	−0.616777	−	0.787138i	$-0.711562\pi$
$31$	−212.912	−1.23355	−0.616777	+	0.787138i	$0.711562\pi$
$32$	−228.203	−1.26066
$33$	−80.9996	−0.427280
$34$	−128.439	−0.647857
$35$	108.448	0.523745
$36$	167.832	0.777000
$37$	−200.224	−0.889638	−0.444819	−	0.895620i	$-0.646732\pi$
$37$	−200.224	−0.889638	−0.444819	+	0.895620i	$0.646732\pi$
$38$	−542.396	−2.31548
$39$	−361.389	−1.48381
$40$	106.988	0.422907
$41$	451.267	1.71893	0.859464	−	0.511197i	$-0.170798\pi$
$41$	451.267	1.71893	0.859464	+	0.511197i	$0.170798\pi$
$42$	193.999	0.712730
$43$	−130.664	−0.463396	−0.231698	−	0.972788i	$-0.574428\pi$
$43$	−130.664	−0.463396	−0.231698	+	0.972788i	$0.574428\pi$
$44$	67.8167	0.232358
$45$	−421.750	−1.39713
$46$	447.523	1.43443
$47$	−176.271	−0.547057	−0.273529	−	0.961864i	$-0.588191\pi$
$47$	−176.271	−0.547057	−0.273529	+	0.961864i	$0.588191\pi$
$48$	554.569	1.66761
$49$	49.0000	0.142857
$50$	432.898	1.22442
$51$	251.291	0.689957
$52$	302.571	0.806906
$53$	−629.988	−1.63274	−0.816372	−	0.577526i	$-0.804018\pi$
$53$	−629.988	−1.63274	−0.816372	+	0.577526i	$0.804018\pi$
$54$	−6.17114	−0.0155516
$55$	−170.419	−0.417804
$56$	48.3402	0.115352
$57$	1061.20	2.46595
$58$	−239.681	−0.542615
$59$	−86.9318	−0.191823	−0.0959115	−	0.995390i	$-0.530577\pi$
$59$	−86.9318	−0.191823	−0.0959115	+	0.995390i	$0.530577\pi$
$60$	703.329	1.51332
$61$	644.248	1.35225	0.676127	−	0.736785i	$-0.263657\pi$
$61$	644.248	1.35225	0.676127	+	0.736785i	$0.263657\pi$
$62$	−801.330	−1.64143
$63$	−190.559	−0.381082
$64$	−256.384	−0.500750
$65$	−760.340	−1.45090
$66$	−304.855	−0.568562
$67$	−400.974	−0.731147	−0.365573	−	0.930783i	$-0.619127\pi$
$67$	−400.974	−0.731147	−0.365573	+	0.930783i	$0.619127\pi$
$68$	−210.393	−0.375204
$69$	−875.578	−1.52764
$70$	408.162	0.696925
$71$	507.611	0.848484	0.424242	−	0.905549i	$-0.360541\pi$
$71$	507.611	0.848484	0.424242	+	0.905549i	$0.360541\pi$
$72$	−187.993	−0.307710
$73$	176.392	0.282811	0.141405	−	0.989952i	$-0.454838\pi$
$73$	176.392	0.282811	0.141405	+	0.989952i	$0.454838\pi$
$74$	−753.575	−1.18380
$75$	−846.965	−1.30399
$76$	−888.485	−1.34100
$77$	−77.0000	−0.113961
$78$	−1360.14	−1.97444
$79$	−701.122	−0.998512	−0.499256	−	0.866455i	$-0.666393\pi$
$79$	−701.122	−0.998512	−0.499256	+	0.866455i	$0.666393\pi$
$80$	1166.78	1.63062
$81$	−722.938	−0.991685
$82$	1698.42	2.28730
$83$	−1259.27	−1.66534	−0.832670	−	0.553770i	$-0.813189\pi$
$83$	−1259.27	−1.66534	−0.832670	+	0.553770i	$0.813189\pi$
$84$	317.784	0.412775
$85$	528.702	0.674656
$86$	−491.775	−0.616621
$87$	468.936	0.577876
$88$	−75.9631	−0.0920193
$89$	788.394	0.938984	0.469492	−	0.882937i	$-0.344437\pi$
$89$	788.394	0.938984	0.469492	+	0.882937i	$0.344437\pi$
$90$	−1587.32	−1.85910
$91$	−343.544	−0.395749
$92$	733.075	0.830743
$93$	1567.80	1.74810
$94$	−663.423	−0.727945
$95$	2232.70	2.41126
$96$	1680.40	1.78651
$97$	185.039	0.193689	0.0968446	−	0.995300i	$-0.469125\pi$
$97$	185.039	0.193689	0.0968446	+	0.995300i	$0.469125\pi$
$98$	184.419	0.190094
$99$	299.449	0.303998
$100$	709.119	0.709119
$101$	1243.55	1.22513	0.612565	−	0.790420i	$-0.290138\pi$
$101$	1243.55	1.22513	0.612565	+	0.790420i	$0.290138\pi$
$102$	945.775	0.918095
$103$	−1555.21	−1.48776	−0.743879	−	0.668315i	$-0.767016\pi$
$103$	−1555.21	−1.48776	−0.743879	+	0.668315i	$0.767016\pi$
$104$	−338.918	−0.319554
$105$	−798.569	−0.742213
$106$	−2371.06	−2.17262
$107$	−247.062	−0.223218	−0.111609	−	0.993752i	$-0.535600\pi$
$107$	−247.062	−0.223218	−0.111609	+	0.993752i	$0.535600\pi$
$108$	−10.1088	−0.00900665
$109$	1160.58	1.01985	0.509923	−	0.860220i	$-0.329674\pi$
$109$	1160.58	1.01985	0.509923	+	0.860220i	$0.329674\pi$
$110$	−641.398	−0.555953
$111$	1474.37	1.26073
$112$	527.185	0.444770
$113$	1738.50	1.44729	0.723646	−	0.690171i	$-0.242465\pi$
$113$	1738.50	1.44729	0.723646	+	0.690171i	$0.242465\pi$
$114$	3993.99	3.28133
$115$	−1842.16	−1.49376
$116$	−392.615	−0.314254
$117$	1336.03	1.05569
$118$	−327.182	−0.255250
$119$	238.883	0.184020
$120$	−787.816	−0.599312
$121$	121.000	0.0909091
$122$	2424.73	1.79938
$123$	−3322.95	−2.43594
$124$	−1312.64	−0.950631
$125$	154.609	0.110629
$126$	−717.199	−0.507088
$127$	−1507.65	−1.05340	−0.526701	−	0.850051i	$-0.676571\pi$
$127$	−1507.65	−1.05340	−0.526701	+	0.850051i	$0.676571\pi$
$128$	860.685	0.594333
$129$	962.157	0.656691
$130$	−2861.66	−1.93065
$131$	1327.55	0.885408	0.442704	−	0.896668i	$-0.354019\pi$
$131$	1327.55	0.885408	0.442704	+	0.896668i	$0.354019\pi$
$132$	−499.375	−0.329281
$133$	1008.80	0.657698
$134$	−1509.13	−0.972904
$135$	25.4026	0.0161949
$136$	235.666	0.148590
$137$	−441.531	−0.275347	−0.137674	−	0.990478i	$-0.543962\pi$
$137$	−441.531	−0.275347	−0.137674	+	0.990478i	$0.543962\pi$
$138$	−3295.38	−2.03276
$139$	179.162	0.109326	0.0546631	−	0.998505i	$-0.482592\pi$
$139$	179.162	0.109326	0.0546631	+	0.998505i	$0.482592\pi$
$140$	668.600	0.403621
$141$	1297.99	0.775250
$142$	1910.48	1.12904
$143$	539.854	0.315698
$144$	−2050.20	−1.18646
$145$	986.615	0.565061
$146$	663.882	0.376324
$147$	−360.817	−0.202447
$148$	−1234.41	−0.685594
$149$	−1147.07	−0.630680	−0.315340	−	0.948979i	$-0.602118\pi$
$149$	−1147.07	−0.630680	−0.315340	+	0.948979i	$0.602118\pi$
$150$	−3187.69	−1.73516
$151$	1873.03	1.00944	0.504719	−	0.863284i	$-0.331596\pi$
$151$	1873.03	1.00944	0.504719	+	0.863284i	$0.331596\pi$
$152$	995.214	0.531069
$153$	−929.004	−0.490886
$154$	−289.802	−0.151642
$155$	3298.56	1.70933
$156$	−2228.02	−1.14349
$157$	−643.927	−0.327331	−0.163665	−	0.986516i	$-0.552332\pi$
$157$	−643.927	−0.327331	−0.163665	+	0.986516i	$0.552332\pi$
$158$	−2638.79	−1.32868
$159$	4638.98	2.31381
$160$	3535.46	1.74689
$161$	−832.343	−0.407440
$162$	−2720.90	−1.31959
$163$	−3044.47	−1.46295	−0.731477	−	0.681866i	$-0.761169\pi$
$163$	−3044.47	−1.46295	−0.731477	+	0.681866i	$0.761169\pi$
$164$	2782.13	1.32468
$165$	1254.89	0.592081
$166$	−4739.48	−2.21599
$167$	−337.038	−0.156172	−0.0780861	−	0.996947i	$-0.524881\pi$
$167$	−337.038	−0.156172	−0.0780861	+	0.996947i	$0.524881\pi$
$168$	−355.958	−0.163469
$169$	211.617	0.0963209
$170$	1989.86	0.897735
$171$	−3923.17	−1.75446
$172$	−805.563	−0.357114
$173$	−3504.80	−1.54026	−0.770131	−	0.637886i	$-0.779809\pi$
$173$	−3504.80	−1.54026	−0.770131	+	0.637886i	$0.779809\pi$
$174$	1764.92	0.768955
$175$	−805.143	−0.347789
$176$	−828.433	−0.354804
$177$	640.132	0.271837
$178$	2967.25	1.24946
$179$	221.078	0.0923135	0.0461568	−	0.998934i	$-0.485303\pi$
$179$	221.078	0.0923135	0.0461568	+	0.998934i	$0.485303\pi$
$180$	−2600.15	−1.07669
$181$	−4561.63	−1.87328	−0.936640	−	0.350295i	$-0.886081\pi$
$181$	−4561.63	−1.87328	−0.936640	+	0.350295i	$0.886081\pi$
$182$	−1292.98	−0.526606
$183$	−4743.99	−1.91631
$184$	−821.135	−0.328994
$185$	3101.99	1.23277
$186$	5900.67	2.32612
$187$	−375.387	−0.146797
$188$	−1086.74	−0.421587
$189$	11.4776	0.00441733
$190$	8403.13	3.20856
$191$	4180.40	1.58368	0.791841	−	0.610727i	$-0.209123\pi$
$191$	4180.40	1.58368	0.791841	+	0.610727i	$0.209123\pi$
$192$	1887.91	0.709625
$193$	−1942.59	−0.724510	−0.362255	−	0.932079i	$-0.617993\pi$
$193$	−1942.59	−0.724510	−0.362255	+	0.932079i	$0.617993\pi$
$194$	696.424	0.257734
$195$	5598.85	2.05611
$196$	302.093	0.110092
$197$	3775.15	1.36532	0.682660	−	0.730736i	$-0.260823\pi$
$197$	3775.15	1.36532	0.682660	+	0.730736i	$0.260823\pi$
$198$	1127.03	0.404517
$199$	−993.760	−0.353999	−0.176999	−	0.984211i	$-0.556639\pi$
$199$	−993.760	−0.353999	−0.176999	+	0.984211i	$0.556639\pi$
$200$	−794.302	−0.280828
$201$	2952.62	1.03613
$202$	4680.31	1.63023
$203$	445.781	0.154127
$204$	1549.25	0.531712
$205$	−6991.29	−2.38192
$206$	−5853.27	−1.97969
$207$	3236.94	1.08687
$208$	−3696.14	−1.23212
$209$	−1585.25	−0.524662
$210$	−3005.55	−0.987630
$211$	−2912.24	−0.950176	−0.475088	−	0.879938i	$-0.657584\pi$
$211$	−2912.24	−0.950176	−0.475088	+	0.879938i	$0.657584\pi$
$212$	−3883.97	−1.25827
$213$	−3737.85	−1.20241
$214$	−929.856	−0.297026
$215$	2024.32	0.642128
$216$	11.3231	0.00356685
$217$	1490.39	0.466239
$218$	4368.02	1.35706
$219$	−1298.88	−0.400778
$220$	−1050.66	−0.321978
$221$	−1674.83	−0.509780
$222$	5549.03	1.67760
$223$	5069.26	1.52225	0.761127	−	0.648603i	$-0.224647\pi$
$223$	5069.26	1.52225	0.761127	+	0.648603i	$0.224647\pi$
$224$	1597.42	0.476484
$225$	3131.16	0.927753
$226$	6543.12	1.92585
$227$	−5653.25	−1.65295	−0.826475	−	0.562974i	$-0.809657\pi$
$227$	−5653.25	−1.65295	−0.826475	+	0.562974i	$0.809657\pi$
$228$	6542.45	1.90037
$229$	−5141.63	−1.48371	−0.741853	−	0.670563i	$-0.766053\pi$
$229$	−5141.63	−1.48371	−0.741853	+	0.670563i	$0.766053\pi$
$230$	−6933.29	−1.98768
$231$	566.998	0.161497
$232$	439.778	0.124452
$233$	312.296	0.0878077	0.0439039	−	0.999036i	$-0.486020\pi$
$233$	312.296	0.0878077	0.0439039	+	0.999036i	$0.486020\pi$
$234$	5028.35	1.40476
$235$	2730.89	0.758057
$236$	−535.948	−0.147827
$237$	5162.79	1.41502
$238$	899.074	0.244867
$239$	−4012.12	−1.08587	−0.542935	−	0.839775i	$-0.682687\pi$
$239$	−4012.12	−1.08587	−0.542935	+	0.839775i	$0.682687\pi$
$240$	−8591.71	−2.31080
$241$	499.662	0.133552	0.0667761	−	0.997768i	$-0.478729\pi$
$241$	499.662	0.133552	0.0667761	+	0.997768i	$0.478729\pi$
$242$	455.403	0.120969
$243$	5367.70	1.41703
$244$	3971.89	1.04211
$245$	−759.137	−0.197957
$246$	−12506.5	−3.24139
$247$	−7072.78	−1.82198
$248$	1470.32	0.376472
$249$	9272.79	2.36000
$250$	581.895	0.147209
$251$	−6112.34	−1.53708	−0.768541	−	0.639801i	$-0.779017\pi$
$251$	−6112.34	−1.53708	−0.768541	+	0.639801i	$0.779017\pi$
$252$	−1174.82	−0.293678
$253$	1307.97	0.325025
$254$	−5674.28	−1.40172
$255$	−3893.15	−0.956073
$256$	5290.40	1.29160
$257$	−1910.22	−0.463642	−0.231821	−	0.972758i	$-0.574468\pi$
$257$	−1910.22	−0.463642	−0.231821	+	0.972758i	$0.574468\pi$
$258$	3621.23	0.873830
$259$	1401.57	0.336252
$260$	−4687.62	−1.11813
$261$	−1733.62	−0.411143
$262$	4996.44	1.17817
$263$	1749.49	0.410184	0.205092	−	0.978743i	$-0.434251\pi$
$263$	1749.49	0.410184	0.205092	+	0.978743i	$0.434251\pi$
$264$	559.363	0.130403
$265$	9760.14	2.26249
$266$	3796.77	0.875170
$267$	−5805.42	−1.33066
$268$	−2472.07	−0.563454
$269$	−2884.89	−0.653883	−0.326942	−	0.945045i	$-0.606018\pi$
$269$	−2884.89	−0.653883	−0.326942	+	0.945045i	$0.606018\pi$
$270$	95.6070	0.0215498
$271$	6065.04	1.35950	0.679751	−	0.733443i	$-0.262088\pi$
$271$	6065.04	1.35950	0.679751	+	0.733443i	$0.262088\pi$
$272$	2570.11	0.572926
$273$	2529.72	0.560826
$274$	−1661.77	−0.366392
$275$	1265.23	0.277440
$276$	−5398.07	−1.17727
$277$	−3331.31	−0.722595	−0.361297	−	0.932451i	$-0.617666\pi$
$277$	−3331.31	−0.722595	−0.361297	+	0.932451i	$0.617666\pi$
$278$	674.307	0.145476
$279$	−5796.04	−1.24373
$280$	−748.915	−0.159844
$281$	−384.608	−0.0816505	−0.0408252	−	0.999166i	$-0.512999\pi$
$281$	−384.608	−0.0816505	−0.0408252	+	0.999166i	$0.512999\pi$
$282$	4885.18	1.03159
$283$	1768.02	0.371371	0.185685	−	0.982609i	$-0.440549\pi$
$283$	1768.02	0.371371	0.185685	+	0.982609i	$0.440549\pi$
$284$	3129.50	0.653879
$285$	−16440.7	−3.41707
$286$	2031.83	0.420086
$287$	−3158.87	−0.649693
$288$	−6212.31	−1.27105
$289$	−3748.41	−0.762957
$290$	3713.28	0.751902
$291$	−1362.55	−0.274482
$292$	1087.49	0.217946
$293$	3801.87	0.758047	0.379023	−	0.925387i	$-0.376260\pi$
$293$	3801.87	0.758047	0.379023	+	0.925387i	$0.376260\pi$
$294$	−1357.99	−0.269387
$295$	1346.80	0.265809
$296$	1382.69	0.271512
$297$	−18.0363	−0.00352381
$298$	−4317.17	−0.839217
$299$	5835.64	1.12871
$300$	−5221.67	−1.00491
$301$	914.647	0.175147
$302$	7049.46	1.34321
$303$	−9157.03	−1.73616
$304$	10853.5	2.04767
$305$	−9981.07	−1.87382
$306$	−3496.46	−0.653200
$307$	−687.619	−0.127832	−0.0639161	−	0.997955i	$-0.520359\pi$
$307$	−687.619	−0.127832	−0.0639161	+	0.997955i	$0.520359\pi$
$308$	−474.717	−0.0878231
$309$	11451.9	2.10834
$310$	12414.7	2.27454
$311$	−2517.73	−0.459059	−0.229530	−	0.973302i	$-0.573719\pi$
$311$	−2517.73	−0.459059	−0.229530	+	0.973302i	$0.573719\pi$
$312$	2495.66	0.452848
$313$	−4725.03	−0.853274	−0.426637	−	0.904423i	$-0.640302\pi$
$313$	−4725.03	−0.853274	−0.426637	+	0.904423i	$0.640302\pi$
$314$	−2423.52	−0.435565
$315$	2952.25	0.528065
$316$	−4322.53	−0.769497
$317$	2870.09	0.508519	0.254259	−	0.967136i	$-0.418168\pi$
$317$	2870.09	0.508519	0.254259	+	0.967136i	$0.418168\pi$
$318$	17459.6	3.07888
$319$	−700.513	−0.122950
$320$	3972.05	0.693888
$321$	1819.26	0.316328
$322$	−3132.66	−0.542162
$323$	4918.05	0.847207
$324$	−4457.03	−0.764236
$325$	5644.94	0.963461
$326$	−11458.4	−1.94669
$327$	−8546.03	−1.44525
$328$	−3116.33	−0.524605
$329$	1233.89	0.206768
$330$	4723.00	0.787856
$331$	365.467	0.0606885	0.0303443	−	0.999540i	$-0.490340\pi$
$331$	365.467	0.0606885	0.0303443	+	0.999540i	$0.490340\pi$
$332$	−7763.61	−1.28338
$333$	−5450.63	−0.896975
$334$	−1268.50	−0.207811
$335$	6212.13	1.01315
$336$	−3881.98	−0.630296
$337$	−4292.33	−0.693822	−0.346911	−	0.937898i	$-0.612769\pi$
$337$	−4292.33	−0.693822	−0.346911	+	0.937898i	$0.612769\pi$
$338$	796.455	0.128170
$339$	−12801.6	−2.05100
$340$	3259.53	0.519920
$341$	−2342.03	−0.371930
$342$	−14765.5	−2.33458
$343$	−343.000	−0.0539949
$344$	902.330	0.141426
$345$	13565.0	2.11685
$346$	−13190.9	−2.04956
$347$	−6090.40	−0.942218	−0.471109	−	0.882075i	$-0.656146\pi$
$347$	−6090.40	−0.942218	−0.471109	+	0.882075i	$0.656146\pi$
$348$	2891.06	0.445337
$349$	6338.89	0.972244	0.486122	−	0.873891i	$-0.338411\pi$
$349$	6338.89	0.972244	0.486122	+	0.873891i	$0.338411\pi$
$350$	−3030.29	−0.462788
$351$	−80.4709	−0.0122371
$352$	−2510.24	−0.380103
$353$	5754.44	0.867643	0.433821	−	0.900999i	$-0.357165\pi$
$353$	5754.44	0.867643	0.433821	+	0.900999i	$0.357165\pi$
$354$	2409.24	0.361722
$355$	−7864.21	−1.17574
$356$	4860.57	0.723622
$357$	−1759.04	−0.260779
$358$	832.062	0.122838
$359$	7396.98	1.08746	0.543729	−	0.839261i	$-0.317012\pi$
$359$	7396.98	1.08746	0.543729	+	0.839261i	$0.317012\pi$
$360$	2912.49	0.426394
$361$	13909.8	2.02797
$362$	−17168.4	−2.49269
$363$	−890.996	−0.128830
$364$	−2118.00	−0.304982
$365$	−2732.78	−0.391891
$366$	−17854.8	−2.54996
$367$	−4613.59	−0.656205	−0.328102	−	0.944642i	$-0.606409\pi$
$367$	−4613.59	−0.656205	−0.328102	+	0.944642i	$0.606409\pi$
$368$	−8955.07	−1.26852
$369$	12284.7	1.73310
$370$	11674.8	1.64039
$371$	4409.91	0.617119
$372$	9665.73	1.34716
$373$	4603.15	0.638986	0.319493	−	0.947589i	$-0.396487\pi$
$373$	4603.15	0.638986	0.319493	+	0.947589i	$0.396487\pi$
$374$	−1412.83	−0.195336
$375$	−1138.48	−0.156775
$376$	1217.28	0.166958
$377$	−3125.41	−0.426968
$378$	43.1980	0.00587795
$379$	6982.50	0.946350	0.473175	−	0.880968i	$-0.343108\pi$
$379$	6982.50	0.946350	0.473175	+	0.880968i	$0.343108\pi$
$380$	13764.9	1.85823
$381$	11101.7	1.49280
$382$	15733.6	2.10734
$383$	12743.5	1.70016	0.850079	−	0.526655i	$-0.176554\pi$
$383$	12743.5	1.70016	0.850079	+	0.526655i	$0.176554\pi$
$384$	−6337.75	−0.842244
$385$	1192.93	0.157915
$386$	−7311.24	−0.964073
$387$	−3557.02	−0.467218
$388$	1140.79	0.149265
$389$	1568.76	0.204471	0.102235	−	0.994760i	$-0.467400\pi$
$389$	1568.76	0.204471	0.102235	+	0.994760i	$0.467400\pi$
$390$	21072.2	2.73598
$391$	−4057.81	−0.524839
$392$	−338.381	−0.0435991
$393$	−9775.54	−1.25474
$394$	14208.4	1.81677
$395$	10862.2	1.38364
$396$	1846.15	0.234274
$397$	9841.87	1.24420	0.622102	−	0.782936i	$-0.286279\pi$
$397$	9841.87	1.24420	0.622102	+	0.782936i	$0.286279\pi$
$398$	−3740.18	−0.471050
$399$	−7428.39	−0.932042
$400$	−8662.43	−1.08280
$401$	5128.60	0.638679	0.319339	−	0.947640i	$-0.396539\pi$
$401$	5128.60	0.638679	0.319339	+	0.947640i	$0.396539\pi$
$402$	11112.7	1.37873
$403$	−10449.2	−1.29160
$404$	7666.69	0.944139
$405$	11200.2	1.37418
$406$	1677.77	0.205089
$407$	−2202.46	−0.268236
$408$	−1735.35	−0.210570
$409$	−87.6006	−0.0105906	−0.00529532	−	0.999986i	$-0.501686\pi$
$409$	−87.6006	−0.0105906	−0.00529532	+	0.999986i	$0.501686\pi$
$410$	−26312.9	−3.16951
$411$	3251.26	0.390202
$412$	−9588.08	−1.14653
$413$	608.523	0.0725023
$414$	12182.8	1.44626
$415$	19509.4	2.30766
$416$	−11199.7	−1.31998
$417$	−1319.28	−0.154929
$418$	−5966.36	−0.698144
$419$	−7130.86	−0.831420	−0.415710	−	0.909497i	$-0.636467\pi$
$419$	−7130.86	−0.831420	−0.415710	+	0.909497i	$0.636467\pi$
$420$	−4923.30	−0.571982
$421$	6159.77	0.713085	0.356543	−	0.934279i	$-0.383955\pi$
$421$	6159.77	0.713085	0.356543	+	0.934279i	$0.383955\pi$
$422$	−10960.7	−1.26436
$423$	−4798.55	−0.551569
$424$	4350.53	0.498303
$425$	−3925.20	−0.448001
$426$	−14068.0	−1.59999
$427$	−4509.74	−0.511104
$428$	−1523.17	−0.172022
$429$	−3975.27	−0.447385
$430$	7618.86	0.854452
$431$	12044.1	1.34604	0.673019	−	0.739625i	$-0.264997\pi$
$431$	12044.1	1.34604	0.673019	+	0.739625i	$0.264997\pi$
$432$	123.487	0.0137529
$433$	−9609.67	−1.06654	−0.533270	−	0.845945i	$-0.679037\pi$
$433$	−9609.67	−1.06654	−0.533270	+	0.845945i	$0.679037\pi$
$434$	5609.31	0.620404
$435$	−7265.04	−0.800763
$436$	7155.14	0.785938
$437$	−17136.0	−1.87581
$438$	−4888.56	−0.533298
$439$	−3122.62	−0.339486	−0.169743	−	0.985488i	$-0.554294\pi$
$439$	−3122.62	−0.339486	−0.169743	+	0.985488i	$0.554294\pi$
$440$	1176.87	0.127511
$441$	1333.91	0.144035
$442$	−6303.50	−0.678341
$443$	9381.76	1.00619	0.503093	−	0.864232i	$-0.332195\pi$
$443$	9381.76	1.00619	0.503093	+	0.864232i	$0.332195\pi$
$444$	9089.72	0.971574
$445$	−12214.3	−1.30115
$446$	19079.0	2.02559
$447$	8446.54	0.893753
$448$	1794.69	0.189266
$449$	3407.36	0.358136	0.179068	−	0.983837i	$-0.442692\pi$
$449$	3407.36	0.358136	0.179068	+	0.983837i	$0.442692\pi$
$450$	11784.6	1.23452
$451$	4963.93	0.518276
$452$	10718.1	1.11535
$453$	−13792.3	−1.43050
$454$	−21276.9	−2.19951
$455$	5322.38	0.548389
$456$	−7328.36	−0.752592
$457$	−13714.0	−1.40375	−0.701876	−	0.712299i	$-0.747654\pi$
$457$	−13714.0	−1.40375	−0.701876	+	0.712299i	$0.747654\pi$
$458$	−19351.4	−1.97430
$459$	55.9554	0.00569014
$460$	−11357.2	−1.15116
$461$	−8864.54	−0.895581	−0.447790	−	0.894139i	$-0.647789\pi$
$461$	−8864.54	−0.895581	−0.447790	+	0.894139i	$0.647789\pi$
$462$	2133.99	0.214896
$463$	−14753.3	−1.48087	−0.740437	−	0.672126i	$-0.765381\pi$
$463$	−14753.3	−1.48087	−0.740437	+	0.672126i	$0.765381\pi$
$464$	4796.10	0.479856
$465$	−24289.3	−2.42234
$466$	1175.38	0.116842
$467$	488.428	0.0483977	0.0241989	−	0.999707i	$-0.492297\pi$
$467$	488.428	0.0483977	0.0241989	+	0.999707i	$0.492297\pi$
$468$	8236.80	0.813560
$469$	2806.82	0.276347
$470$	10278.1	1.00871
$471$	4741.62	0.463869
$472$	600.329	0.0585431
$473$	−1437.30	−0.139719
$474$	19431.0	1.88290
$475$	−16576.1	−1.60118
$476$	1472.75	0.141814
$477$	−17149.9	−1.64621
$478$	−15100.3	−1.44492
$479$	−1233.56	−0.117668	−0.0588338	−	0.998268i	$-0.518738\pi$
$479$	−1233.56	−0.117668	−0.0588338	+	0.998268i	$0.518738\pi$
$480$	−26033.8	−2.47557
$481$	−9826.52	−0.931499
$482$	1880.56	0.177712
$483$	6129.04	0.577394
$484$	745.984	0.0700586
$485$	−2866.73	−0.268395
$486$	20202.2	1.88558
$487$	16700.6	1.55395	0.776977	−	0.629529i	$-0.216752\pi$
$487$	16700.6	1.55395	0.776977	+	0.629529i	$0.216752\pi$
$488$	−4449.01	−0.412699
$489$	22418.3	2.07319
$490$	−2857.14	−0.263413
$491$	−2127.96	−0.195587	−0.0977937	−	0.995207i	$-0.531179\pi$
$491$	−2127.96	−0.195587	−0.0977937	+	0.995207i	$0.531179\pi$
$492$	−20486.5	−1.87724
$493$	2173.25	0.198536
$494$	−26619.5	−2.42443
$495$	−4639.25	−0.421250
$496$	16034.9	1.45159
$497$	−3553.28	−0.320697
$498$	34899.7	3.14034
$499$	12341.5	1.10718	0.553590	−	0.832789i	$-0.313258\pi$
$499$	12341.5	1.10718	0.553590	+	0.832789i	$0.313258\pi$
$500$	953.186	0.0852556
$501$	2481.81	0.221316
$502$	−23004.8	−2.04533
$503$	−3433.67	−0.304374	−0.152187	−	0.988352i	$-0.548632\pi$
$503$	−3433.67	−0.304374	−0.152187	+	0.988352i	$0.548632\pi$
$504$	1315.95	0.116304
$505$	−19265.9	−1.69766
$506$	4922.75	0.432496
$507$	−1558.26	−0.136499
$508$	−9294.88	−0.811798
$509$	−1842.48	−0.160445	−0.0802223	−	0.996777i	$-0.525563\pi$
$509$	−1842.48	−0.160445	−0.0802223	+	0.996777i	$0.525563\pi$
$510$	−14652.5	−1.27220
$511$	−1234.75	−0.106892
$512$	13025.8	1.12434
$513$	236.298	0.0203369
$514$	−7189.41	−0.616948
$515$	24094.2	2.06158
$516$	5931.84	0.506075
$517$	−1938.98	−0.164944
$518$	5275.03	0.447435
$519$	25808.0	2.18275
$520$	5250.71	0.442806
$521$	3532.65	0.297060	0.148530	−	0.988908i	$-0.452546\pi$
$521$	3532.65	0.297060	0.148530	+	0.988908i	$0.452546\pi$
$522$	−6524.76	−0.547090
$523$	−4497.20	−0.376001	−0.188001	−	0.982169i	$-0.560201\pi$
$523$	−4497.20	−0.376001	−0.188001	+	0.982169i	$0.560201\pi$
$524$	8184.54	0.682335
$525$	5928.76	0.492861
$526$	6584.50	0.545814
$527$	7265.87	0.600581
$528$	6100.25	0.502802
$529$	1971.67	0.162050
$530$	36733.9	3.01060
$531$	−2366.52	−0.193405
$532$	6219.39	0.506851
$533$	22147.1	1.79981
$534$	−21849.6	−1.77065
$535$	3827.62	0.309313
$536$	2769.02	0.223141
$537$	−1627.93	−0.130820
$538$	−10857.7	−0.870093
$539$	539.000	0.0430730
$540$	156.611	0.0124805
$541$	−11426.0	−0.908023	−0.454011	−	0.890996i	$-0.650007\pi$
$541$	−11426.0	−0.908023	−0.454011	+	0.890996i	$0.650007\pi$
$542$	22826.8	1.80903
$543$	33590.1	2.65467
$544$	7787.70	0.613777
$545$	−17980.4	−1.41320
$546$	9521.01	0.746267
$547$	17875.3	1.39725	0.698623	−	0.715490i	$-0.253796\pi$
$547$	17875.3	1.39725	0.698623	+	0.715490i	$0.253796\pi$
$548$	−2722.11	−0.212195
$549$	17538.2	1.36341
$550$	4761.88	0.369177
$551$	9177.61	0.709581
$552$	6046.51	0.466226
$553$	4907.86	0.377402
$554$	−12537.9	−0.961525
$555$	−22841.8	−1.74699
$556$	1104.56	0.0842517
$557$	25343.4	1.92789	0.963946	−	0.266097i	$-0.0857341\pi$
$557$	25343.4	1.92789	0.963946	+	0.266097i	$0.0857341\pi$
$558$	−21814.3	−1.65497
$559$	−6412.68	−0.485201
$560$	−8167.46	−0.616318
$561$	2764.20	0.208030
$562$	−1447.53	−0.108649
$563$	−1597.92	−0.119617	−0.0598084	−	0.998210i	$-0.519049\pi$
$563$	−1597.92	−0.119617	−0.0598084	+	0.998210i	$0.519049\pi$
$564$	8002.29	0.597442
$565$	−26933.8	−2.00551
$566$	6654.23	0.494166
$567$	5060.57	0.374822
$568$	−3505.43	−0.258952
$569$	−11487.7	−0.846377	−0.423188	−	0.906042i	$-0.639089\pi$
$569$	−11487.7	−0.846377	−0.423188	+	0.906042i	$0.639089\pi$
$570$	−61877.3	−4.54694
$571$	17027.0	1.24791	0.623957	−	0.781459i	$-0.285524\pi$
$571$	17027.0	1.24791	0.623957	+	0.781459i	$0.285524\pi$
$572$	3328.28	0.243291
$573$	−30782.8	−2.24428
$574$	−11888.9	−0.864518
$575$	13676.6	0.991922
$576$	−6979.45	−0.504879
$577$	19368.0	1.39740	0.698701	−	0.715414i	$-0.253762\pi$
$577$	19368.0	1.39740	0.698701	+	0.715414i	$0.253762\pi$
$578$	−14107.7	−1.01523
$579$	14304.4	1.02672
$580$	6082.63	0.435461
$581$	8814.91	0.629439
$582$	−5128.19	−0.365241
$583$	−6929.86	−0.492291
$584$	−1218.12	−0.0863120
$585$	−20698.5	−1.46287
$586$	14309.0	1.00870
$587$	−27035.0	−1.90094	−0.950472	−	0.310809i	$-0.899400\pi$
$587$	−27035.0	−1.90094	−0.950472	+	0.310809i	$0.899400\pi$
$588$	−2224.49	−0.156014
$589$	30683.6	2.14651
$590$	5068.90	0.353700
$591$	−27798.7	−1.93483
$592$	15079.3	1.04688
$593$	−9717.62	−0.672943	−0.336471	−	0.941694i	$-0.609234\pi$
$593$	−9717.62	−0.672943	−0.336471	+	0.941694i	$0.609234\pi$
$594$	−67.8825	−0.00468898
$595$	−3700.92	−0.254996
$596$	−7071.83	−0.486030
$597$	7317.65	0.501661
$598$	21963.4	1.50192
$599$	−18386.6	−1.25418	−0.627092	−	0.778945i	$-0.715755\pi$
$599$	−18386.6	−1.25418	−0.627092	+	0.778945i	$0.715755\pi$
$600$	5848.92	0.397969
$601$	−3288.31	−0.223183	−0.111591	−	0.993754i	$-0.535595\pi$
$601$	−3288.31	−0.223183	−0.111591	+	0.993754i	$0.535595\pi$
$602$	3442.42	0.233061
$603$	−10915.6	−0.737176
$604$	11547.5	0.777918
$605$	−1874.60	−0.125973
$606$	−34464.0	−2.31024
$607$	−27356.2	−1.82925	−0.914623	−	0.404307i	$-0.867513\pi$
$607$	−27356.2	−1.82925	−0.914623	+	0.404307i	$0.867513\pi$
$608$	32887.3	2.19368
$609$	−3282.55	−0.218417
$610$	−37565.4	−2.49341
$611$	−8650.95	−0.572798
$612$	−5727.45	−0.378298
$613$	−9573.59	−0.630789	−0.315395	−	0.948961i	$-0.602137\pi$
$613$	−9573.59	−0.630789	−0.315395	+	0.948961i	$0.602137\pi$
$614$	−2587.97	−0.170101
$615$	51481.1	3.37548
$616$	531.742	0.0347800
$617$	−7506.76	−0.489807	−0.244903	−	0.969547i	$-0.578756\pi$
$617$	−7506.76	−0.489807	−0.244903	+	0.969547i	$0.578756\pi$
$618$	43101.2	2.80547
$619$	−9294.64	−0.603527	−0.301763	−	0.953383i	$-0.597575\pi$
$619$	−9294.64	−0.603527	−0.301763	+	0.953383i	$0.597575\pi$
$620$	20336.1	1.31729
$621$	−194.966	−0.0125986
$622$	−9475.89	−0.610850
$623$	−5518.75	−0.354902
$624$	27216.9	1.74607
$625$	−16772.8	−1.07346
$626$	−17783.4	−1.13541
$627$	11673.2	0.743512
$628$	−3969.91	−0.252256
$629$	6832.87	0.433139
$630$	11111.3	0.702672
$631$	4254.20	0.268395	0.134197	−	0.990955i	$-0.457154\pi$
$631$	4254.20	0.268395	0.134197	+	0.990955i	$0.457154\pi$
$632$	4841.77	0.304739
$633$	21444.6	1.34652
$634$	10802.1	0.676663
$635$	23357.4	1.45970
$636$	28600.0	1.78312
$637$	2404.81	0.149579
$638$	−2636.49	−0.163605
$639$	13818.5	0.855482
$640$	−13334.3	−0.823566
$641$	5112.91	0.315051	0.157526	−	0.987515i	$-0.449648\pi$
$641$	5112.91	0.315051	0.157526	+	0.987515i	$0.449648\pi$
$642$	6847.09	0.420924
$643$	7296.68	0.447516	0.223758	−	0.974645i	$-0.428167\pi$
$643$	7296.68	0.447516	0.223758	+	0.974645i	$0.428167\pi$
$644$	−5131.52	−0.313991
$645$	−14906.3	−0.909977
$646$	18509.9	1.12734
$647$	15612.1	0.948649	0.474324	−	0.880350i	$-0.342692\pi$
$647$	15612.1	0.948649	0.474324	+	0.880350i	$0.342692\pi$
$648$	4992.42	0.302656
$649$	−956.250	−0.0578368
$650$	21245.6	1.28203
$651$	−10974.6	−0.660720
$652$	−18769.6	−1.12742
$653$	−23160.6	−1.38797	−0.693986	−	0.719988i	$-0.744147\pi$
$653$	−23160.6	−1.38797	−0.693986	+	0.719988i	$0.744147\pi$
$654$	−32164.4	−1.92313
$655$	−20567.2	−1.22691
$656$	−33985.8	−2.02275
$657$	4801.87	0.285143
$658$	4643.96	0.275137
$659$	−5707.65	−0.337388	−0.168694	−	0.985668i	$-0.553955\pi$
$659$	−5707.65	−0.337388	−0.168694	+	0.985668i	$0.553955\pi$
$660$	7736.62	0.456284
$661$	−16202.5	−0.953411	−0.476706	−	0.879063i	$-0.658169\pi$
$661$	−16202.5	−0.953411	−0.476706	+	0.879063i	$0.658169\pi$
$662$	1375.50	0.0807555
$663$	12332.8	0.722422
$664$	8696.21	0.508251
$665$	−15628.9	−0.911372
$666$	−20514.3	−1.19356
$667$	−7572.30	−0.439581
$668$	−2077.89	−0.120353
$669$	−37328.0	−2.15723
$670$	23380.4	1.34815
$671$	7086.73	0.407720
$672$	−11762.8	−0.675238
$673$	−16956.2	−0.971192	−0.485596	−	0.874183i	$-0.661397\pi$
$673$	−16956.2	−0.971192	−0.485596	+	0.874183i	$0.661397\pi$
$674$	−16154.9	−0.923239
$675$	−188.595	−0.0107541
$676$	1304.65	0.0742292
$677$	21259.0	1.20687	0.603433	−	0.797414i	$-0.293799\pi$
$677$	21259.0	1.20687	0.603433	+	0.797414i	$0.293799\pi$
$678$	−48180.9	−2.72917
$679$	−1295.27	−0.0732076
$680$	−3651.08	−0.205901
$681$	41628.3	2.34244
$682$	−8814.62	−0.494911
$683$	5867.98	0.328744	0.164372	−	0.986398i	$-0.447440\pi$
$683$	5867.98	0.328744	0.164372	+	0.986398i	$0.447440\pi$
$684$	−24186.9	−1.35206
$685$	6840.46	0.381548
$686$	−1290.94	−0.0718486
$687$	37860.9	2.10260
$688$	9840.57	0.545303
$689$	−30918.3	−1.70957
$690$	51054.0	2.81680
$691$	15583.0	0.857892	0.428946	−	0.903330i	$-0.358885\pi$
$691$	15583.0	0.857892	0.428946	+	0.903330i	$0.358885\pi$
$692$	−21607.7	−1.18699
$693$	−2096.15	−0.114900
$694$	−22922.2	−1.25377
$695$	−2775.69	−0.151493
$696$	−3238.35	−0.176364
$697$	−15400.0	−0.836895
$698$	23857.4	1.29372
$699$	−2299.63	−0.124435
$700$	−4963.83	−0.268022
$701$	−19210.5	−1.03505	−0.517525	−	0.855668i	$-0.673147\pi$
$701$	−19210.5	−1.03505	−0.517525	+	0.855668i	$0.673147\pi$
$702$	−302.865	−0.0162833
$703$	28855.1	1.54806
$704$	−2820.22	−0.150982
$705$	−20109.2	−1.07426
$706$	21657.8	1.15453
$707$	−8704.87	−0.463055
$708$	3946.51	0.209490
$709$	−1760.77	−0.0932683	−0.0466342	−	0.998912i	$-0.514850\pi$
$709$	−1760.77	−0.0932683	−0.0466342	+	0.998912i	$0.514850\pi$
$710$	−29598.2	−1.56451
$711$	−19086.4	−1.00675
$712$	−5444.44	−0.286572
$713$	−25316.6	−1.32975
$714$	−6620.43	−0.347007
$715$	−8363.74	−0.437463
$716$	1362.98	0.0711409
$717$	29543.7	1.53881
$718$	27839.7	1.44703
$719$	10517.7	0.545541	0.272770	−	0.962079i	$-0.412060\pi$
$719$	10517.7	0.545541	0.272770	+	0.962079i	$0.412060\pi$
$720$	31762.9	1.64407
$721$	10886.4	0.562319
$722$	52352.0	2.69853
$723$	−3679.31	−0.189260
$724$	−28123.2	−1.44363
$725$	−7324.85	−0.375225
$726$	−3353.41	−0.171428
$727$	−10483.4	−0.534814	−0.267407	−	0.963584i	$-0.586167\pi$
$727$	−10483.4	−0.534814	−0.267407	+	0.963584i	$0.586167\pi$
$728$	2372.42	0.120780
$729$	−20006.3	−1.01643
$730$	−10285.2	−0.521471
$731$	4459.05	0.225614
$732$	−29247.4	−1.47680
$733$	−8568.83	−0.431783	−0.215892	−	0.976417i	$-0.569266\pi$
$733$	−8568.83	−0.431783	−0.215892	+	0.976417i	$0.569266\pi$
$734$	−17364.0	−0.873183
$735$	5589.99	0.280530
$736$	−27134.8	−1.35897
$737$	−4410.72	−0.220449
$738$	46235.4	2.30616
$739$	−3089.07	−0.153766	−0.0768832	−	0.997040i	$-0.524497\pi$
$739$	−3089.07	−0.153766	−0.0768832	+	0.997040i	$0.524497\pi$
$740$	19124.2	0.950028
$741$	52081.1	2.58198
$742$	16597.4	0.821173
$743$	−28558.8	−1.41012	−0.705060	−	0.709148i	$-0.749080\pi$
$743$	−28558.8	−1.41012	−0.705060	+	0.709148i	$0.749080\pi$
$744$	−10826.8	−0.533509
$745$	17771.0	0.873933
$746$	17324.7	0.850270
$747$	−34280.8	−1.67907
$748$	−2314.32	−0.113128
$749$	1729.43	0.0843685
$750$	−4284.84	−0.208614
$751$	−2062.51	−0.100216	−0.0501078	−	0.998744i	$-0.515956\pi$
$751$	−2062.51	−0.100216	−0.0501078	+	0.998744i	$0.515956\pi$
$752$	13275.3	0.643751
$753$	45008.9	2.17824
$754$	−11763.0	−0.568147
$755$	−29018.1	−1.39878
$756$	70.7615	0.00340419
$757$	39089.1	1.87678	0.938388	−	0.345584i	$-0.112319\pi$
$757$	39089.1	1.87678	0.938388	+	0.345584i	$0.112319\pi$
$758$	26279.8	1.25927
$759$	−9631.35	−0.460601
$760$	−15418.4	−0.735902
$761$	−13820.5	−0.658337	−0.329169	−	0.944271i	$-0.606768\pi$
$761$	−13820.5	−0.658337	−0.329169	+	0.944271i	$0.606768\pi$
$762$	41783.1	1.98641
$763$	−8124.04	−0.385465
$764$	25772.8	1.22046
$765$	14392.7	0.680220
$766$	47962.1	2.26233
$767$	−4266.41	−0.200849
$768$	−38956.4	−1.83036
$769$	−28495.1	−1.33623	−0.668115	−	0.744058i	$-0.732899\pi$
$769$	−28495.1	−1.33623	−0.668115	+	0.744058i	$0.732899\pi$
$770$	4489.78	0.210131
$771$	14066.1	0.657040
$772$	−11976.3	−0.558339
$773$	1874.14	0.0872032	0.0436016	−	0.999049i	$-0.486117\pi$
$773$	1874.14	0.0872032	0.0436016	+	0.999049i	$0.486117\pi$
$774$	−13387.4	−0.621706
$775$	−24489.3	−1.13507
$776$	−1277.83	−0.0591127
$777$	−10320.6	−0.476511
$778$	5904.28	0.272080
$779$	−65033.8	−2.99112
$780$	34517.7	1.58453
$781$	5583.72	0.255828
$782$	−15272.2	−0.698380
$783$	104.419	0.00476580
$784$	−3690.29	−0.168107
$785$	9976.10	0.453582
$786$	−36791.8	−1.66962
$787$	16614.9	0.752551	0.376275	−	0.926508i	$-0.377205\pi$
$787$	16614.9	0.752551	0.376275	+	0.926508i	$0.377205\pi$
$788$	23274.4	1.05218
$789$	−12882.6	−0.581282
$790$	40881.7	1.84114
$791$	−12169.5	−0.547025
$792$	−2067.92	−0.0927782
$793$	31618.2	1.41588
$794$	37041.5	1.65561
$795$	−71869.8	−3.20624
$796$	−6126.68	−0.272807
$797$	19323.7	0.858823	0.429411	−	0.903109i	$-0.358721\pi$
$797$	19323.7	0.858823	0.429411	+	0.903109i	$0.358721\pi$
$798$	−27957.9	−1.24023
$799$	6015.43	0.266346
$800$	−26248.1	−1.16001
$801$	21462.2	0.946728
$802$	19302.3	0.849861
$803$	1940.32	0.0852706
$804$	18203.3	0.798485
$805$	12895.2	0.564589
$806$	−39327.4	−1.71867
$807$	21243.2	0.926635
$808$	−8587.65	−0.373902
$809$	−15363.0	−0.667657	−0.333829	−	0.942634i	$-0.608341\pi$
$809$	−15363.0	−0.667657	−0.333829	+	0.942634i	$0.608341\pi$
$810$	42153.7	1.82856
$811$	11404.0	0.493771	0.246886	−	0.969045i	$-0.420593\pi$
$811$	11404.0	0.493771	0.246886	+	0.969045i	$0.420593\pi$
$812$	2748.31	0.118777
$813$	−44660.6	−1.92659
$814$	−8289.33	−0.356930
$815$	47166.8	2.02722
$816$	−18925.3	−0.811908
$817$	18830.5	0.806359
$818$	−329.699	−0.0140925
$819$	−9352.18	−0.399013
$820$	−43102.4	−1.83561
$821$	5529.00	0.235035	0.117517	−	0.993071i	$-0.462506\pi$
$821$	5529.00	0.235035	0.117517	+	0.993071i	$0.462506\pi$
$822$	12236.6	0.519224
$823$	−12216.1	−0.517407	−0.258704	−	0.965957i	$-0.583295\pi$
$823$	−12216.1	−0.517407	−0.258704	+	0.965957i	$0.583295\pi$
$824$	10739.8	0.454054
$825$	−9316.62	−0.393167
$826$	2290.27	0.0964756
$827$	−29123.0	−1.22455	−0.612277	−	0.790643i	$-0.709746\pi$
$827$	−29123.0	−1.22455	−0.612277	+	0.790643i	$0.709746\pi$
$828$	19956.2	0.837594
$829$	25679.6	1.07586	0.537930	−	0.842990i	$-0.319207\pi$
$829$	25679.6	1.07586	0.537930	+	0.842990i	$0.319207\pi$
$830$	73426.8	3.07070
$831$	24530.4	1.02401
$832$	−12582.7	−0.524312
$833$	−1672.18	−0.0695529
$834$	−4965.33	−0.206157
$835$	5221.59	0.216408
$836$	−9773.33	−0.404328
$837$	349.104	0.0144167
$838$	−26838.1	−1.10633
$839$	−7009.97	−0.288452	−0.144226	−	0.989545i	$-0.546069\pi$
$839$	−7009.97	−0.288452	−0.144226	+	0.989545i	$0.546069\pi$
$840$	5514.71	0.226519
$841$	−20333.5	−0.833715
$842$	23183.3	0.948871
$843$	2832.10	0.115709
$844$	−17954.4	−0.732247
$845$	−3278.50	−0.133472
$846$	−18060.1	−0.733948
$847$	−847.000	−0.0343604
$848$	47445.7	1.92133
$849$	−13019.0	−0.526279
$850$	−14773.1	−0.596135
$851$	−23807.9	−0.959016
$852$	−23044.4	−0.926630
$853$	7430.54	0.298261	0.149131	−	0.988818i	$-0.452353\pi$
$853$	7430.54	0.298261	0.149131	+	0.988818i	$0.452353\pi$
$854$	−16973.1	−0.680103
$855$	60780.0	2.43115
$856$	1706.14	0.0681247
$857$	−16112.3	−0.642225	−0.321113	−	0.947041i	$-0.604057\pi$
$857$	−16112.3	−0.642225	−0.321113	+	0.947041i	$0.604057\pi$
$858$	−14961.6	−0.595315
$859$	46836.9	1.86037	0.930183	−	0.367097i	$-0.119648\pi$
$859$	46836.9	1.86037	0.930183	+	0.367097i	$0.119648\pi$
$860$	12480.3	0.494853
$861$	23260.6	0.920698
$862$	45329.8	1.79111
$863$	−2453.00	−0.0967568	−0.0483784	−	0.998829i	$-0.515405\pi$
$863$	−2453.00	−0.0967568	−0.0483784	+	0.998829i	$0.515405\pi$
$864$	374.177	0.0147335
$865$	54298.5	2.13434
$866$	−36167.6	−1.41920
$867$	27601.8	1.08121
$868$	9188.45	0.359305
$869$	−7712.34	−0.301063
$870$	−27343.2	−1.06554
$871$	−19678.9	−0.765549
$872$	−8014.65	−0.311250
$873$	5037.25	0.195287
$874$	−64494.3	−2.49605
$875$	−1082.26	−0.0418138
$876$	−8007.82	−0.308858
$877$	23733.6	0.913829	0.456914	−	0.889511i	$-0.348955\pi$
$877$	23733.6	0.913829	0.456914	+	0.889511i	$0.348955\pi$
$878$	−11752.5	−0.451740
$879$	−27995.5	−1.07425
$880$	12834.6	0.491652
$881$	10868.6	0.415634	0.207817	−	0.978168i	$-0.433364\pi$
$881$	10868.6	0.415634	0.207817	+	0.978168i	$0.433364\pi$
$882$	5020.39	0.191661
$883$	−43075.4	−1.64168	−0.820840	−	0.571158i	$-0.806495\pi$
$883$	−43075.4	−1.64168	−0.820840	+	0.571158i	$0.806495\pi$
$884$	−10325.6	−0.392859
$885$	−9917.30	−0.376685
$886$	35309.8	1.33889
$887$	−16224.0	−0.614149	−0.307075	−	0.951685i	$-0.599350\pi$
$887$	−16224.0	−0.614149	−0.307075	+	0.951685i	$0.599350\pi$
$888$	−10181.6	−0.384766
$889$	10553.5	0.398149
$890$	−45970.4	−1.73138
$891$	−7952.32	−0.299004
$892$	31252.7	1.17312
$893$	25403.1	0.951938
$894$	31789.9	1.18928
$895$	−3425.07	−0.127919
$896$	−6024.80	−0.224637
$897$	−42971.3	−1.59952
$898$	12824.1	0.476556
$899$	13558.9	0.503019
$900$	19304.1	0.714967
$901$	21499.0	0.794935
$902$	18682.6	0.689647
$903$	−6735.10	−0.248206
$904$	−12005.6	−0.441704
$905$	70671.5	2.59580
$906$	−51909.4	−1.90351
$907$	39985.6	1.46384	0.731918	−	0.681392i	$-0.238625\pi$
$907$	39985.6	1.46384	0.731918	+	0.681392i	$0.238625\pi$
$908$	−34853.2	−1.27384
$909$	33852.8	1.23523
$910$	20031.7	0.729717
$911$	20330.9	0.739398	0.369699	−	0.929152i	$-0.379461\pi$
$911$	20330.9	0.739398	0.369699	+	0.929152i	$0.379461\pi$
$912$	−79921.1	−2.90181
$913$	−13852.0	−0.502119
$914$	−51614.9	−1.86791
$915$	73496.7	2.65544
$916$	−31699.0	−1.14341
$917$	−9292.84	−0.334653
$918$	210.597	0.00757161
$919$	−3734.71	−0.134055	−0.0670275	−	0.997751i	$-0.521352\pi$
$919$	−3734.71	−0.134055	−0.0670275	+	0.997751i	$0.521352\pi$
$920$	12721.5	0.455887
$921$	5063.36	0.181154
$922$	−33363.1	−1.19171
$923$	24912.4	0.888408
$924$	3495.63	0.124456
$925$	−23029.9	−0.818613
$926$	−55526.5	−1.97053
$927$	−42336.9	−1.50003
$928$	14532.7	0.514072
$929$	30122.2	1.06381	0.531904	−	0.846805i	$-0.321477\pi$
$929$	30122.2	1.06381	0.531904	+	0.846805i	$0.321477\pi$
$930$	−91416.7	−3.22330
$931$	−7061.59	−0.248587
$932$	1925.35	0.0676685
$933$	18539.6	0.650545
$934$	1838.28	0.0644007
$935$	5815.72	0.203417
$936$	−9226.24	−0.322189
$937$	−33701.9	−1.17502	−0.587509	−	0.809217i	$-0.699891\pi$
$937$	−33701.9	−1.17502	−0.587509	+	0.809217i	$0.699891\pi$
$938$	10563.9	0.367723
$939$	34793.3	1.20920
$940$	16836.3	0.584193
$941$	20897.3	0.723944	0.361972	−	0.932189i	$-0.382104\pi$
$941$	20897.3	0.723944	0.361972	+	0.932189i	$0.382104\pi$
$942$	17845.9	0.617250
$943$	53658.4	1.85298
$944$	6547.02	0.225728
$945$	−177.819	−0.00612110
$946$	−5409.52	−0.185918
$947$	−43378.9	−1.48852	−0.744258	−	0.667892i	$-0.767197\pi$
$947$	−43378.9	−1.48852	−0.744258	+	0.667892i	$0.767197\pi$
$948$	31829.4	1.09047
$949$	8656.93	0.296118
$950$	−62386.7	−2.13062
$951$	−21134.2	−0.720635
$952$	−1649.66	−0.0561616
$953$	−36362.5	−1.23599	−0.617994	−	0.786183i	$-0.712054\pi$
$953$	−36362.5	−1.23599	−0.617994	+	0.786183i	$0.712054\pi$
$954$	−64546.6	−2.19054
$955$	−64765.3	−2.19451
$956$	−24735.4	−0.836819
$957$	5158.30	0.174236
$958$	−4642.70	−0.156575
$959$	3090.72	0.104071
$960$	−29248.6	−0.983328
$961$	15540.6	0.521654
$962$	−36983.7	−1.23950
$963$	−6725.67	−0.225059
$964$	3080.49	0.102921
$965$	30095.7	1.00395
$966$	23067.7	0.768312
$967$	23769.2	0.790451	0.395225	−	0.918584i	$-0.370667\pi$
$967$	23769.2	0.790451	0.395225	+	0.918584i	$0.370667\pi$
$968$	−835.595	−0.0277449
$969$	−36214.6	−1.20060
$970$	−10789.4	−0.357141
$971$	−27125.4	−0.896494	−0.448247	−	0.893910i	$-0.647952\pi$
$971$	−27125.4	−0.896494	−0.448247	+	0.893910i	$0.647952\pi$
$972$	33092.7	1.09203
$973$	−1254.14	−0.0413214
$974$	62855.3	2.06778
$975$	−41567.1	−1.36535
$976$	−48519.7	−1.59127
$977$	−30145.5	−0.987146	−0.493573	−	0.869704i	$-0.664309\pi$
$977$	−30145.5	−0.987146	−0.493573	+	0.869704i	$0.664309\pi$
$978$	84374.9	2.75870
$979$	8672.33	0.283114
$980$	−4680.20	−0.152555
$981$	31594.0	1.02826
$982$	−8008.92	−0.260259
$983$	23037.5	0.747489	0.373745	−	0.927532i	$-0.378074\pi$
$983$	23037.5	0.747489	0.373745	+	0.927532i	$0.378074\pi$
$984$	22947.4	0.743432
$985$	−58486.8	−1.89192
$986$	8179.39	0.264183
$987$	−9085.91	−0.293017
$988$	−43604.8	−1.40410
$989$	−15536.7	−0.499534
$990$	−17460.6	−0.560538
$991$	13580.1	0.435303	0.217651	−	0.976027i	$-0.430160\pi$
$991$	13580.1	0.435303	0.217651	+	0.976027i	$0.430160\pi$
$992$	48587.3	1.55509
$993$	−2691.16	−0.0860033
$994$	−13373.3	−0.426737
$995$	15395.9	0.490536
$996$	57168.2	1.81872
$997$	−26627.3	−0.845832	−0.422916	−	0.906169i	$-0.638993\pi$
$997$	−26627.3	−0.845832	−0.422916	+	0.906169i	$0.638993\pi$
$998$	46449.3	1.47327
$999$	328.300	0.0103973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.a.c.1.4	✓	4
3.2	odd	2		693.4.a.m.1.1		4
4.3	odd	2		1232.4.a.w.1.3		4
5.4	even	2		1925.4.a.q.1.1		4
7.6	odd	2		539.4.a.f.1.4		4
11.10	odd	2		847.4.a.e.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.a.c.1.4	✓	4	1.1	even	1	trivial
539.4.a.f.1.4		4	7.6	odd	2
693.4.a.m.1.1		4	3.2	odd	2
847.4.a.e.1.1		4	11.10	odd	2
1232.4.a.w.1.3		4	4.3	odd	2
1925.4.a.q.1.1		4	5.4	even	2

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.a (trivial)

\(f(q)\)	\(=\)	\(q+3.76366 q^{2} -7.36360 q^{3} +6.16515 q^{4} -15.4926 q^{5} -27.7141 q^{6} -7.00000 q^{7} -6.90574 q^{8} +27.2227 q^{9} +O(q^{10})\)	\(q+3.76366 q^{2} -7.36360 q^{3} +6.16515 q^{4} -15.4926 q^{5} -27.7141 q^{6} -7.00000 q^{7} -6.90574 q^{8} +27.2227 q^{9} -58.3089 q^{10} +11.0000 q^{11} -45.3978 q^{12} +49.0777 q^{13} -26.3456 q^{14} +114.081 q^{15} -75.3121 q^{16} -34.1261 q^{17} +102.457 q^{18} -144.114 q^{19} -95.5142 q^{20} +51.5452 q^{21} +41.4003 q^{22} +118.906 q^{23} +50.8511 q^{24} +115.020 q^{25} +184.712 q^{26} -1.63966 q^{27} -43.1561 q^{28} -63.6830 q^{29} +429.364 q^{30} -212.912 q^{31} -228.203 q^{32} -80.9996 q^{33} -128.439 q^{34} +108.448 q^{35} +167.832 q^{36} -200.224 q^{37} -542.396 q^{38} -361.389 q^{39} +106.988 q^{40} +451.267 q^{41} +193.999 q^{42} -130.664 q^{43} +67.8167 q^{44} -421.750 q^{45} +447.523 q^{46} -176.271 q^{47} +554.569 q^{48} +49.0000 q^{49} +432.898 q^{50} +251.291 q^{51} +302.571 q^{52} -629.988 q^{53} -6.17114 q^{54} -170.419 q^{55} +48.3402 q^{56} +1061.20 q^{57} -239.681 q^{58} -86.9318 q^{59} +703.329 q^{60} +644.248 q^{61} -801.330 q^{62} -190.559 q^{63} -256.384 q^{64} -760.340 q^{65} -304.855 q^{66} -400.974 q^{67} -210.393 q^{68} -875.578 q^{69} +408.162 q^{70} +507.611 q^{71} -187.993 q^{72} +176.392 q^{73} -753.575 q^{74} -846.965 q^{75} -888.485 q^{76} -77.0000 q^{77} -1360.14 q^{78} -701.122 q^{79} +1166.78 q^{80} -722.938 q^{81} +1698.42 q^{82} -1259.27 q^{83} +317.784 q^{84} +528.702 q^{85} -491.775 q^{86} +468.936 q^{87} -75.9631 q^{88} +788.394 q^{89} -1587.32 q^{90} -343.544 q^{91} +733.075 q^{92} +1567.80 q^{93} -663.423 q^{94} +2232.70 q^{95} +1680.40 q^{96} +185.039 q^{97} +184.419 q^{98} +299.449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{3} + 22 q^{4} - 18 q^{5} + 2 q^{6} - 28 q^{7} - 60 q^{8} + 66 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 12 * q^3 + 22 * q^4 - 18 * q^5 + 2 * q^6 - 28 * q^7 - 60 * q^8 + 66 * q^9	\( 4 q - 4 q^{2} - 12 q^{3} + 22 q^{4} - 18 q^{5} + 2 q^{6} - 28 q^{7} - 60 q^{8} + 66 q^{9} - 92 q^{10} + 44 q^{11} - 186 q^{12} - 134 q^{13} + 28 q^{14} - 62 q^{15} - 6 q^{16} - 74 q^{17} - 256 q^{18} - 164 q^{19} + 116 q^{20} + 84 q^{21} - 44 q^{22} + 194 q^{23} + 570 q^{24} + 38 q^{25} + 734 q^{26} - 510 q^{27} - 154 q^{28} - 108 q^{29} + 1252 q^{30} - 412 q^{31} - 4 q^{32} - 132 q^{33} - 346 q^{34} + 126 q^{35} + 1518 q^{36} + 286 q^{37} + 224 q^{38} - 256 q^{39} - 540 q^{40} - 18 q^{41} - 14 q^{42} - 496 q^{43} + 242 q^{44} + 580 q^{45} - 284 q^{46} + 62 q^{47} - 862 q^{48} + 196 q^{49} + 212 q^{50} - 508 q^{51} - 822 q^{52} - 828 q^{53} + 2420 q^{54} - 198 q^{55} + 420 q^{56} + 700 q^{57} + 1388 q^{58} - 1224 q^{59} - 1776 q^{60} - 350 q^{61} - 878 q^{62} - 462 q^{63} - 718 q^{64} - 396 q^{65} + 22 q^{66} - 1498 q^{67} + 1058 q^{68} - 386 q^{69} + 644 q^{70} + 2326 q^{71} - 3000 q^{72} - 1630 q^{73} - 1156 q^{74} - 1362 q^{75} - 3152 q^{76} - 308 q^{77} - 2464 q^{78} - 1020 q^{79} + 3072 q^{80} + 1128 q^{81} + 2118 q^{82} - 1920 q^{83} + 1302 q^{84} + 2008 q^{85} + 1056 q^{86} + 1640 q^{87} - 660 q^{88} + 1550 q^{89} - 5780 q^{90} + 938 q^{91} + 2592 q^{92} + 6046 q^{93} - 1042 q^{94} + 2332 q^{95} + 4082 q^{96} - 2202 q^{97} - 196 q^{98} + 726 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^3 + 22 * q^4 - 18 * q^5 + 2 * q^6 - 28 * q^7 - 60 * q^8 + 66 * q^9 - 92 * q^10 + 44 * q^11 - 186 * q^12 - 134 * q^13 + 28 * q^14 - 62 * q^15 - 6 * q^16 - 74 * q^17 - 256 * q^18 - 164 * q^19 + 116 * q^20 + 84 * q^21 - 44 * q^22 + 194 * q^23 + 570 * q^24 + 38 * q^25 + 734 * q^26 - 510 * q^27 - 154 * q^28 - 108 * q^29 + 1252 * q^30 - 412 * q^31 - 4 * q^32 - 132 * q^33 - 346 * q^34 + 126 * q^35 + 1518 * q^36 + 286 * q^37 + 224 * q^38 - 256 * q^39 - 540 * q^40 - 18 * q^41 - 14 * q^42 - 496 * q^43 + 242 * q^44 + 580 * q^45 - 284 * q^46 + 62 * q^47 - 862 * q^48 + 196 * q^49 + 212 * q^50 - 508 * q^51 - 822 * q^52 - 828 * q^53 + 2420 * q^54 - 198 * q^55 + 420 * q^56 + 700 * q^57 + 1388 * q^58 - 1224 * q^59 - 1776 * q^60 - 350 * q^61 - 878 * q^62 - 462 * q^63 - 718 * q^64 - 396 * q^65 + 22 * q^66 - 1498 * q^67 + 1058 * q^68 - 386 * q^69 + 644 * q^70 + 2326 * q^71 - 3000 * q^72 - 1630 * q^73 - 1156 * q^74 - 1362 * q^75 - 3152 * q^76 - 308 * q^77 - 2464 * q^78 - 1020 * q^79 + 3072 * q^80 + 1128 * q^81 + 2118 * q^82 - 1920 * q^83 + 1302 * q^84 + 2008 * q^85 + 1056 * q^86 + 1640 * q^87 - 660 * q^88 + 1550 * q^89 - 5780 * q^90 + 938 * q^91 + 2592 * q^92 + 6046 * q^93 - 1042 * q^94 + 2332 * q^95 + 4082 * q^96 - 2202 * q^97 - 196 * q^98 + 726 * q^99

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