LMFDB - Embedded newform 230.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 60x^{2} - 45x + 108 $ x^4 - 2x^3 - 60x^2 - 45*x + 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$9.04090$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -5.04090 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.0818 q^{6} +5.03071 q^{7} +8.00000 q^{8} -1.58932 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -5.04090 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.0818 q^{6} +5.03071 q^{7} +8.00000 q^{8} -1.58932 q^{9} +10.0000 q^{10} -5.58219 q^{11} -20.1636 q^{12} +62.7277 q^{13} +10.0614 q^{14} -25.2045 q^{15} +16.0000 q^{16} -19.7435 q^{17} -3.17864 q^{18} +158.545 q^{19} +20.0000 q^{20} -25.3593 q^{21} -11.1644 q^{22} -23.0000 q^{23} -40.3272 q^{24} +25.0000 q^{25} +125.455 q^{26} +144.116 q^{27} +20.1228 q^{28} -35.5033 q^{29} -50.4090 q^{30} +282.041 q^{31} +32.0000 q^{32} +28.1393 q^{33} -39.4870 q^{34} +25.1536 q^{35} -6.35728 q^{36} -139.981 q^{37} +317.090 q^{38} -316.204 q^{39} +40.0000 q^{40} +227.680 q^{41} -50.7186 q^{42} +436.962 q^{43} -22.3288 q^{44} -7.94660 q^{45} -46.0000 q^{46} +90.2701 q^{47} -80.6544 q^{48} -317.692 q^{49} +50.0000 q^{50} +99.5250 q^{51} +250.911 q^{52} +330.183 q^{53} +288.232 q^{54} -27.9109 q^{55} +40.2457 q^{56} -799.209 q^{57} -71.0066 q^{58} -796.203 q^{59} -100.818 q^{60} -568.580 q^{61} +564.081 q^{62} -7.99541 q^{63} +64.0000 q^{64} +313.638 q^{65} +56.2785 q^{66} +85.1419 q^{67} -78.9740 q^{68} +115.941 q^{69} +50.3071 q^{70} -369.578 q^{71} -12.7146 q^{72} -310.188 q^{73} -279.963 q^{74} -126.023 q^{75} +634.180 q^{76} -28.0824 q^{77} -632.408 q^{78} -1325.46 q^{79} +80.0000 q^{80} -683.562 q^{81} +455.360 q^{82} -158.806 q^{83} -101.437 q^{84} -98.7175 q^{85} +873.924 q^{86} +178.969 q^{87} -44.6575 q^{88} -1233.89 q^{89} -15.8932 q^{90} +315.565 q^{91} -92.0000 q^{92} -1421.74 q^{93} +180.540 q^{94} +792.725 q^{95} -161.309 q^{96} -106.389 q^{97} -635.384 q^{98} +8.87189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9} + 40 q^{10} + 21 q^{11} + 56 q^{12} + 70 q^{13} + 16 q^{14} + 70 q^{15} + 64 q^{16} + 56 q^{17} + 128 q^{18} + 173 q^{19} + 80 q^{20} - 120 q^{21} + 42 q^{22} - 92 q^{23} + 112 q^{24} + 100 q^{25} + 140 q^{26} + 389 q^{27} + 32 q^{28} - 118 q^{29} + 140 q^{30} + 17 q^{31} + 128 q^{32} - 89 q^{33} + 112 q^{34} + 40 q^{35} + 256 q^{36} - 343 q^{37} + 346 q^{38} - 221 q^{39} + 160 q^{40} + 139 q^{41} - 240 q^{42} - 50 q^{43} + 84 q^{44} + 320 q^{45} - 184 q^{46} + 367 q^{47} + 224 q^{48} - 124 q^{49} + 200 q^{50} + 439 q^{51} + 280 q^{52} - 353 q^{53} + 778 q^{54} + 105 q^{55} + 64 q^{56} - 238 q^{57} - 236 q^{58} - 453 q^{59} + 280 q^{60} - 327 q^{61} + 34 q^{62} - 1723 q^{63} + 256 q^{64} + 350 q^{65} - 178 q^{66} - 455 q^{67} + 224 q^{68} - 322 q^{69} + 80 q^{70} + 195 q^{71} + 512 q^{72} - 633 q^{73} - 686 q^{74} + 350 q^{75} + 692 q^{76} - 2 q^{77} - 442 q^{78} - 1140 q^{79} + 320 q^{80} + 1456 q^{81} + 278 q^{82} - 1199 q^{83} - 480 q^{84} + 280 q^{85} - 100 q^{86} - 1775 q^{87} + 168 q^{88} - 2170 q^{89} + 640 q^{90} + 557 q^{91} - 368 q^{92} - 3241 q^{93} + 734 q^{94} + 865 q^{95} + 448 q^{96} - 703 q^{97} - 248 q^{98} - 2745 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9 + 40 * q^10 + 21 * q^11 + 56 * q^12 + 70 * q^13 + 16 * q^14 + 70 * q^15 + 64 * q^16 + 56 * q^17 + 128 * q^18 + 173 * q^19 + 80 * q^20 - 120 * q^21 + 42 * q^22 - 92 * q^23 + 112 * q^24 + 100 * q^25 + 140 * q^26 + 389 * q^27 + 32 * q^28 - 118 * q^29 + 140 * q^30 + 17 * q^31 + 128 * q^32 - 89 * q^33 + 112 * q^34 + 40 * q^35 + 256 * q^36 - 343 * q^37 + 346 * q^38 - 221 * q^39 + 160 * q^40 + 139 * q^41 - 240 * q^42 - 50 * q^43 + 84 * q^44 + 320 * q^45 - 184 * q^46 + 367 * q^47 + 224 * q^48 - 124 * q^49 + 200 * q^50 + 439 * q^51 + 280 * q^52 - 353 * q^53 + 778 * q^54 + 105 * q^55 + 64 * q^56 - 238 * q^57 - 236 * q^58 - 453 * q^59 + 280 * q^60 - 327 * q^61 + 34 * q^62 - 1723 * q^63 + 256 * q^64 + 350 * q^65 - 178 * q^66 - 455 * q^67 + 224 * q^68 - 322 * q^69 + 80 * q^70 + 195 * q^71 + 512 * q^72 - 633 * q^73 - 686 * q^74 + 350 * q^75 + 692 * q^76 - 2 * q^77 - 442 * q^78 - 1140 * q^79 + 320 * q^80 + 1456 * q^81 + 278 * q^82 - 1199 * q^83 - 480 * q^84 + 280 * q^85 - 100 * q^86 - 1775 * q^87 + 168 * q^88 - 2170 * q^89 + 640 * q^90 + 557 * q^91 - 368 * q^92 - 3241 * q^93 + 734 * q^94 + 865 * q^95 + 448 * q^96 - 703 * q^97 - 248 * q^98 - 2745 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−5.04090	−0.970122	−0.485061	−	0.874480i	$-0.661203\pi$
$3$	−5.04090	−0.970122	−0.485061	+	0.874480i	$0.661203\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−10.0818	−0.685980
$7$	5.03071	0.271633	0.135816	−	0.990734i	$-0.456634\pi$
$7$	5.03071	0.271633	0.135816	+	0.990734i	$0.456634\pi$
$8$	8.00000	0.353553
$9$	−1.58932	−0.0588637
$10$	10.0000	0.316228
$11$	−5.58219	−0.153008	−0.0765042	−	0.997069i	$-0.524376\pi$
$11$	−5.58219	−0.153008	−0.0765042	+	0.997069i	$0.524376\pi$
$12$	−20.1636	−0.485061
$13$	62.7277	1.33827	0.669136	−	0.743140i	$-0.266664\pi$
$13$	62.7277	1.33827	0.669136	+	0.743140i	$0.266664\pi$
$14$	10.0614	0.192073
$15$	−25.2045	−0.433852
$16$	16.0000	0.250000
$17$	−19.7435	−0.281677	−0.140838	−	0.990033i	$-0.544980\pi$
$17$	−19.7435	−0.281677	−0.140838	+	0.990033i	$0.544980\pi$
$18$	−3.17864	−0.0416229
$19$	158.545	1.91435	0.957177	−	0.289505i	$-0.0934907\pi$
$19$	158.545	1.91435	0.957177	+	0.289505i	$0.0934907\pi$
$20$	20.0000	0.223607
$21$	−25.3593	−0.263517
$22$	−11.1644	−0.108193
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−40.3272	−0.342990
$25$	25.0000	0.200000
$26$	125.455	0.946301
$27$	144.116	1.02723
$28$	20.1228	0.135816
$29$	−35.5033	−0.227338	−0.113669	−	0.993519i	$-0.536260\pi$
$29$	−35.5033	−0.227338	−0.113669	+	0.993519i	$0.536260\pi$
$30$	−50.4090	−0.306779
$31$	282.041	1.63406	0.817032	−	0.576592i	$-0.195618\pi$
$31$	282.041	1.63406	0.817032	+	0.576592i	$0.195618\pi$
$32$	32.0000	0.176777
$33$	28.1393	0.148437
$34$	−39.4870	−0.199175
$35$	25.1536	0.121478
$36$	−6.35728	−0.0294319
$37$	−139.981	−0.621967	−0.310984	−	0.950415i	$-0.600658\pi$
$37$	−139.981	−0.621967	−0.310984	+	0.950415i	$0.600658\pi$
$38$	317.090	1.35365
$39$	−316.204	−1.29829
$40$	40.0000	0.158114
$41$	227.680	0.867260	0.433630	−	0.901091i	$-0.357232\pi$
$41$	227.680	0.867260	0.433630	+	0.901091i	$0.357232\pi$
$42$	−50.7186	−0.186335
$43$	436.962	1.54968	0.774838	−	0.632159i	$-0.217831\pi$
$43$	436.962	1.54968	0.774838	+	0.632159i	$0.217831\pi$
$44$	−22.3288	−0.0765042
$45$	−7.94660	−0.0263247
$46$	−46.0000	−0.147442
$47$	90.2701	0.280154	0.140077	−	0.990141i	$-0.455265\pi$
$47$	90.2701	0.280154	0.140077	+	0.990141i	$0.455265\pi$
$48$	−80.6544	−0.242530
$49$	−317.692	−0.926216
$50$	50.0000	0.141421
$51$	99.5250	0.273261
$52$	250.911	0.669136
$53$	330.183	0.855737	0.427869	−	0.903841i	$-0.359265\pi$
$53$	330.183	0.855737	0.427869	+	0.903841i	$0.359265\pi$
$54$	288.232	0.726359
$55$	−27.9109	−0.0684275
$56$	40.2457	0.0960367
$57$	−799.209	−1.85716
$58$	−71.0066	−0.160752
$59$	−796.203	−1.75689	−0.878447	−	0.477839i	$-0.841420\pi$
$59$	−796.203	−1.75689	−0.878447	+	0.477839i	$0.841420\pi$
$60$	−100.818	−0.216926
$61$	−568.580	−1.19343	−0.596715	−	0.802453i	$-0.703528\pi$
$61$	−568.580	−1.19343	−0.596715	+	0.802453i	$0.703528\pi$
$62$	564.081	1.15546
$63$	−7.99541	−0.0159893
$64$	64.0000	0.125000
$65$	313.638	0.598493
$66$	56.2785	0.104961
$67$	85.1419	0.155250	0.0776250	−	0.996983i	$-0.475266\pi$
$67$	85.1419	0.155250	0.0776250	+	0.996983i	$0.475266\pi$
$68$	−78.9740	−0.140838
$69$	115.941	0.202284
$70$	50.3071	0.0858978
$71$	−369.578	−0.617758	−0.308879	−	0.951101i	$-0.599954\pi$
$71$	−369.578	−0.617758	−0.308879	+	0.951101i	$0.599954\pi$
$72$	−12.7146	−0.0208115
$73$	−310.188	−0.497325	−0.248662	−	0.968590i	$-0.579991\pi$
$73$	−310.188	−0.497325	−0.248662	+	0.968590i	$0.579991\pi$
$74$	−279.963	−0.439797
$75$	−126.023	−0.194024
$76$	634.180	0.957177
$77$	−28.0824	−0.0415621
$78$	−632.408	−0.918027
$79$	−1325.46	−1.88766	−0.943832	−	0.330427i	$-0.892807\pi$
$79$	−1325.46	−1.88766	−0.943832	+	0.330427i	$0.892807\pi$
$80$	80.0000	0.111803
$81$	−683.562	−0.937671
$82$	455.360	0.613246
$83$	−158.806	−0.210014	−0.105007	−	0.994471i	$-0.533487\pi$
$83$	−158.806	−0.210014	−0.105007	+	0.994471i	$0.533487\pi$
$84$	−101.437	−0.131758
$85$	−98.7175	−0.125970
$86$	873.924	1.09579
$87$	178.969	0.220545
$88$	−44.6575	−0.0540967
$89$	−1233.89	−1.46957	−0.734787	−	0.678298i	$-0.762718\pi$
$89$	−1233.89	−1.46957	−0.734787	+	0.678298i	$0.762718\pi$
$90$	−15.8932	−0.0186143
$91$	315.565	0.363519
$92$	−92.0000	−0.104257
$93$	−1421.74	−1.58524
$94$	180.540	0.198099
$95$	792.725	0.856125
$96$	−161.309	−0.171495
$97$	−106.389	−0.111363	−0.0556814	−	0.998449i	$-0.517733\pi$
$97$	−106.389	−0.111363	−0.0556814	+	0.998449i	$0.517733\pi$
$98$	−635.384	−0.654933
$99$	8.87189	0.00900665
$100$	100.000	0.100000
$101$	642.676	0.633155	0.316578	−	0.948567i	$-0.397466\pi$
$101$	642.676	0.633155	0.316578	+	0.948567i	$0.397466\pi$
$102$	199.050	0.193224
$103$	1621.99	1.55165	0.775823	−	0.630951i	$-0.217335\pi$
$103$	1621.99	1.55165	0.775823	+	0.630951i	$0.217335\pi$
$104$	501.822	0.473150
$105$	−126.797	−0.117848
$106$	660.365	0.605098
$107$	1490.86	1.34698	0.673490	−	0.739196i	$-0.264795\pi$
$107$	1490.86	1.34698	0.673490	+	0.739196i	$0.264795\pi$
$108$	576.464	0.513613
$109$	1204.00	1.05800	0.529001	−	0.848621i	$-0.322567\pi$
$109$	1204.00	1.05800	0.529001	+	0.848621i	$0.322567\pi$
$110$	−55.8219	−0.0483855
$111$	705.632	0.603384
$112$	80.4914	0.0679082
$113$	276.771	0.230411	0.115206	−	0.993342i	$-0.463247\pi$
$113$	276.771	0.230411	0.115206	+	0.993342i	$0.463247\pi$
$114$	−1598.42	−1.31321
$115$	−115.000	−0.0932505
$116$	−142.013	−0.113669
$117$	−99.6944	−0.0787757
$118$	−1592.41	−1.24231
$119$	−99.3239	−0.0765126
$120$	−201.636	−0.153390
$121$	−1299.84	−0.976588
$122$	−1137.16	−0.843883
$123$	−1147.71	−0.841348
$124$	1128.16	0.817032
$125$	125.000	0.0894427
$126$	−15.9908	−0.0113062
$127$	1552.79	1.08494	0.542471	−	0.840075i	$-0.317489\pi$
$127$	1552.79	1.08494	0.542471	+	0.840075i	$0.317489\pi$
$128$	128.000	0.0883883
$129$	−2202.68	−1.50338
$130$	627.277	0.423199
$131$	−313.873	−0.209337	−0.104669	−	0.994507i	$-0.533378\pi$
$131$	−313.873	−0.209337	−0.104669	+	0.994507i	$0.533378\pi$
$132$	112.557	0.0742184
$133$	797.594	0.520001
$134$	170.284	0.109778
$135$	720.580	0.459390
$136$	−157.948	−0.0995877
$137$	−1066.09	−0.664835	−0.332417	−	0.943132i	$-0.607864\pi$
$137$	−1066.09	−0.664835	−0.332417	+	0.943132i	$0.607864\pi$
$138$	231.881	0.143037
$139$	−1594.79	−0.973152	−0.486576	−	0.873638i	$-0.661754\pi$
$139$	−1594.79	−0.973152	−0.486576	+	0.873638i	$0.661754\pi$
$140$	100.614	0.0607389
$141$	−455.043	−0.271784
$142$	−739.155	−0.436821
$143$	−350.158	−0.204767
$144$	−25.4291	−0.0147159
$145$	−177.517	−0.101669
$146$	−620.375	−0.351662
$147$	1601.45	0.898542
$148$	−559.925	−0.310984
$149$	−1096.91	−0.603102	−0.301551	−	0.953450i	$-0.597504\pi$
$149$	−1096.91	−0.603102	−0.301551	+	0.953450i	$0.597504\pi$
$150$	−252.045	−0.137196
$151$	2734.41	1.47366	0.736832	−	0.676076i	$-0.236321\pi$
$151$	2734.41	1.47366	0.736832	+	0.676076i	$0.236321\pi$
$152$	1268.36	0.676826
$153$	31.3788	0.0165805
$154$	−56.1647	−0.0293889
$155$	1410.20	0.730776
$156$	−1264.82	−0.649143
$157$	−1439.63	−0.731813	−0.365907	−	0.930652i	$-0.619241\pi$
$157$	−1439.63	−0.731813	−0.365907	+	0.930652i	$0.619241\pi$
$158$	−2650.91	−1.33478
$159$	−1664.42	−0.830169
$160$	160.000	0.0790569
$161$	−115.706	−0.0566394
$162$	−1367.12	−0.663034
$163$	−2995.82	−1.43957	−0.719787	−	0.694195i	$-0.755760\pi$
$163$	−2995.82	−1.43957	−0.719787	+	0.694195i	$0.755760\pi$
$164$	910.721	0.433630
$165$	140.696	0.0663830
$166$	−317.611	−0.148503
$167$	−351.532	−0.162888	−0.0814442	−	0.996678i	$-0.525953\pi$
$167$	−351.532	−0.162888	−0.0814442	+	0.996678i	$0.525953\pi$
$168$	−202.874	−0.0931673
$169$	1737.76	0.790971
$170$	−197.435	−0.0890740
$171$	−251.979	−0.112686
$172$	1747.85	0.774838
$173$	−3701.77	−1.62682	−0.813411	−	0.581690i	$-0.802392\pi$
$173$	−3701.77	−1.62682	−0.813411	+	0.581690i	$0.802392\pi$
$174$	357.937	0.155949
$175$	125.768	0.0543266
$176$	−89.3150	−0.0382521
$177$	4013.58	1.70440
$178$	−2467.78	−1.03915
$179$	3584.09	1.49658	0.748290	−	0.663372i	$-0.230875\pi$
$179$	3584.09	1.49658	0.748290	+	0.663372i	$0.230875\pi$
$180$	−31.7864	−0.0131623
$181$	783.672	0.321822	0.160911	−	0.986969i	$-0.448557\pi$
$181$	783.672	0.321822	0.160911	+	0.986969i	$0.448557\pi$
$182$	631.130	0.257046
$183$	2866.16	1.15777
$184$	−184.000	−0.0737210
$185$	−699.907	−0.278152
$186$	−2843.48	−1.12093
$187$	110.212	0.0430989
$188$	361.080	0.140077
$189$	725.005	0.279029
$190$	1585.45	0.605372
$191$	1491.95	0.565201	0.282601	−	0.959238i	$-0.408803\pi$
$191$	1491.95	0.565201	0.282601	+	0.959238i	$0.408803\pi$
$192$	−322.618	−0.121265
$193$	3091.09	1.15286	0.576430	−	0.817147i	$-0.304446\pi$
$193$	3091.09	1.15286	0.576430	+	0.817147i	$0.304446\pi$
$194$	−212.778	−0.0787454
$195$	−1581.02	−0.580611
$196$	−1270.77	−0.463108
$197$	2820.30	1.01999	0.509995	−	0.860178i	$-0.329647\pi$
$197$	2820.30	1.01999	0.509995	+	0.860178i	$0.329647\pi$
$198$	17.7438	0.00636866
$199$	1316.11	0.468825	0.234413	−	0.972137i	$-0.424683\pi$
$199$	1316.11	0.468825	0.234413	+	0.972137i	$0.424683\pi$
$200$	200.000	0.0707107
$201$	−429.192	−0.150611
$202$	1285.35	0.447708
$203$	−178.607	−0.0617524
$204$	398.100	0.136630
$205$	1138.40	0.387851
$206$	3243.98	1.09718
$207$	36.5544	0.0122739
$208$	1003.64	0.334568
$209$	−885.028	−0.292912
$210$	−253.593	−0.0833314
$211$	−3399.19	−1.10905	−0.554525	−	0.832167i	$-0.687100\pi$
$211$	−3399.19	−1.10905	−0.554525	+	0.832167i	$0.687100\pi$
$212$	1320.73	0.427869
$213$	1863.00	0.599300
$214$	2981.72	0.952458
$215$	2184.81	0.693037
$216$	1152.93	0.363180
$217$	1418.86	0.443865
$218$	2408.00	0.748121
$219$	1563.62	0.482466
$220$	−111.644	−0.0342137
$221$	−1238.46	−0.376960
$222$	1411.26	0.426657
$223$	864.660	0.259650	0.129825	−	0.991537i	$-0.458558\pi$
$223$	864.660	0.259650	0.129825	+	0.991537i	$0.458558\pi$
$224$	160.983	0.0480184
$225$	−39.7330	−0.0117727
$226$	553.543	0.162925
$227$	−1979.40	−0.578754	−0.289377	−	0.957215i	$-0.593448\pi$
$227$	−1979.40	−0.578754	−0.289377	+	0.957215i	$0.593448\pi$
$228$	−3196.84	−0.928578
$229$	−3113.53	−0.898462	−0.449231	−	0.893416i	$-0.648302\pi$
$229$	−3113.53	−0.898462	−0.449231	+	0.893416i	$0.648302\pi$
$230$	−230.000	−0.0659380
$231$	141.560	0.0403203
$232$	−284.026	−0.0803761
$233$	6018.65	1.69225	0.846126	−	0.532983i	$-0.178929\pi$
$233$	6018.65	1.69225	0.846126	+	0.532983i	$0.178929\pi$
$234$	−199.389	−0.0557028
$235$	451.350	0.125289
$236$	−3184.81	−0.878447
$237$	6681.49	1.83126
$238$	−198.648	−0.0541026
$239$	−4224.88	−1.14345	−0.571725	−	0.820445i	$-0.693726\pi$
$239$	−4224.88	−1.14345	−0.571725	+	0.820445i	$0.693726\pi$
$240$	−403.272	−0.108463
$241$	1394.24	0.372658	0.186329	−	0.982487i	$-0.440341\pi$
$241$	1394.24	0.372658	0.186329	+	0.982487i	$0.440341\pi$
$242$	−2599.68	−0.690552
$243$	−445.360	−0.117571
$244$	−2274.32	−0.596715
$245$	−1588.46	−0.414216
$246$	−2295.43	−0.594923
$247$	9945.16	2.56192
$248$	2256.32	0.577729
$249$	800.523	0.203739
$250$	250.000	0.0632456
$251$	−5968.83	−1.50099	−0.750497	−	0.660874i	$-0.770186\pi$
$251$	−5968.83	−1.50099	−0.750497	+	0.660874i	$0.770186\pi$
$252$	−31.9816	−0.00799466
$253$	128.390	0.0319045
$254$	3105.57	0.767169
$255$	497.625	0.122206
$256$	256.000	0.0625000
$257$	−1636.06	−0.397100	−0.198550	−	0.980091i	$-0.563623\pi$
$257$	−1636.06	−0.397100	−0.198550	+	0.980091i	$0.563623\pi$
$258$	−4405.37	−1.06305
$259$	−704.206	−0.168947
$260$	1254.55	0.299247
$261$	56.4261	0.0133820
$262$	−627.745	−0.148024
$263$	2995.55	0.702333	0.351166	−	0.936313i	$-0.385785\pi$
$263$	2995.55	0.702333	0.351166	+	0.936313i	$0.385785\pi$
$264$	225.114	0.0524803
$265$	1650.91	0.382697
$266$	1595.19	0.367696
$267$	6219.92	1.42567
$268$	340.568	0.0776250
$269$	−5190.17	−1.17640	−0.588198	−	0.808717i	$-0.700162\pi$
$269$	−5190.17	−1.17640	−0.588198	+	0.808717i	$0.700162\pi$
$270$	1441.16	0.324838
$271$	6720.43	1.50641	0.753205	−	0.657786i	$-0.228507\pi$
$271$	6720.43	1.50641	0.753205	+	0.657786i	$0.228507\pi$
$272$	−315.896	−0.0704192
$273$	−1590.73	−0.352657
$274$	−2132.18	−0.470109
$275$	−139.555	−0.0306017
$276$	463.763	0.101142
$277$	−6114.74	−1.32635	−0.663176	−	0.748464i	$-0.730792\pi$
$277$	−6114.74	−1.32635	−0.663176	+	0.748464i	$0.730792\pi$
$278$	−3189.58	−0.688123
$279$	−448.253	−0.0961871
$280$	201.228	0.0429489
$281$	−3549.07	−0.753450	−0.376725	−	0.926325i	$-0.622950\pi$
$281$	−3549.07	−0.753450	−0.376725	+	0.926325i	$0.622950\pi$
$282$	−910.085	−0.192180
$283$	3103.11	0.651806	0.325903	−	0.945403i	$-0.394332\pi$
$283$	3103.11	0.651806	0.325903	+	0.945403i	$0.394332\pi$
$284$	−1478.31	−0.308879
$285$	−3996.05	−0.830545
$286$	−700.316	−0.144792
$287$	1145.39	0.235576
$288$	−50.8583	−0.0104057
$289$	−4523.19	−0.920658
$290$	−355.033	−0.0718905
$291$	536.297	0.108035
$292$	−1240.75	−0.248662
$293$	1218.51	0.242957	0.121478	−	0.992594i	$-0.461237\pi$
$293$	1218.51	0.242957	0.121478	+	0.992594i	$0.461237\pi$
$294$	3202.91	0.635365
$295$	−3981.01	−0.785707
$296$	−1119.85	−0.219899
$297$	−804.482	−0.157174
$298$	−2193.82	−0.426458
$299$	−1442.74	−0.279049
$300$	−504.090	−0.0970122
$301$	2198.23	0.420943
$302$	5468.82	1.04204
$303$	−3239.67	−0.614238
$304$	2536.72	0.478588
$305$	−2842.90	−0.533718
$306$	62.7575	0.0117242
$307$	2564.45	0.476745	0.238373	−	0.971174i	$-0.423386\pi$
$307$	2564.45	0.476745	0.238373	+	0.971174i	$0.423386\pi$
$308$	−112.329	−0.0207811
$309$	−8176.30	−1.50529
$310$	2820.41	0.516736
$311$	−92.6253	−0.0168884	−0.00844421	−	0.999964i	$-0.502688\pi$
$311$	−92.6253	−0.0168884	−0.00844421	+	0.999964i	$0.502688\pi$
$312$	−2529.63	−0.459014
$313$	−4276.44	−0.772263	−0.386132	−	0.922444i	$-0.626189\pi$
$313$	−4276.44	−0.772263	−0.386132	+	0.922444i	$0.626189\pi$
$314$	−2879.25	−0.517470
$315$	−39.9771	−0.00715064
$316$	−5301.82	−0.943832
$317$	−2964.24	−0.525199	−0.262600	−	0.964905i	$-0.584580\pi$
$317$	−2964.24	−0.525199	−0.262600	+	0.964905i	$0.584580\pi$
$318$	−3328.84	−0.587018
$319$	198.186	0.0347846
$320$	320.000	0.0559017
$321$	−7515.27	−1.30673
$322$	−231.413	−0.0400501
$323$	−3130.23	−0.539229
$324$	−2734.25	−0.468836
$325$	1568.19	0.267654
$326$	−5991.63	−1.01793
$327$	−6069.24	−1.02639
$328$	1821.44	0.306623
$329$	454.123	0.0760991
$330$	281.393	0.0469398
$331$	−1348.81	−0.223979	−0.111989	−	0.993709i	$-0.535722\pi$
$331$	−1348.81	−0.223979	−0.111989	+	0.993709i	$0.535722\pi$
$332$	−635.223	−0.105007
$333$	222.475	0.0366113
$334$	−703.064	−0.115180
$335$	425.710	0.0694299
$336$	−405.749	−0.0658792
$337$	−5764.30	−0.931755	−0.465878	−	0.884849i	$-0.654261\pi$
$337$	−5764.30	−0.931755	−0.465878	+	0.884849i	$0.654261\pi$
$338$	3475.53	0.559301
$339$	−1395.18	−0.223527
$340$	−394.870	−0.0629848
$341$	−1574.40	−0.250026
$342$	−503.958	−0.0796810
$343$	−3323.75	−0.523223
$344$	3495.70	0.547894
$345$	579.704	0.0904643
$346$	−7403.53	−1.15034
$347$	4066.16	0.629057	0.314528	−	0.949248i	$-0.398154\pi$
$347$	4066.16	0.629057	0.314528	+	0.949248i	$0.398154\pi$
$348$	715.875	0.110273
$349$	8407.82	1.28957	0.644786	−	0.764363i	$-0.276947\pi$
$349$	8407.82	1.28957	0.644786	+	0.764363i	$0.276947\pi$
$350$	251.536	0.0384147
$351$	9040.06	1.37471
$352$	−178.630	−0.0270483
$353$	256.068	0.0386095	0.0193047	−	0.999814i	$-0.493855\pi$
$353$	256.068	0.0386095	0.0193047	+	0.999814i	$0.493855\pi$
$354$	8027.16	1.20519
$355$	−1847.89	−0.276270
$356$	−4935.56	−0.734787
$357$	500.682	0.0742266
$358$	7168.19	1.05824
$359$	−12052.5	−1.77189	−0.885943	−	0.463794i	$-0.846488\pi$
$359$	−12052.5	−1.77189	−0.885943	+	0.463794i	$0.846488\pi$
$360$	−63.5728	−0.00930717
$361$	18277.5	2.66475
$362$	1567.34	0.227563
$363$	6552.36	0.947410
$364$	1262.26	0.181759
$365$	−1550.94	−0.222410
$366$	5732.31	0.818669
$367$	−9245.40	−1.31500	−0.657502	−	0.753453i	$-0.728387\pi$
$367$	−9245.40	−1.31500	−0.657502	+	0.753453i	$0.728387\pi$
$368$	−368.000	−0.0521286
$369$	−361.857	−0.0510502
$370$	−1399.81	−0.196683
$371$	1661.05	0.232446
$372$	−5686.96	−0.792621
$373$	−869.265	−0.120667	−0.0603335	−	0.998178i	$-0.519216\pi$
$373$	−869.265	−0.120667	−0.0603335	+	0.998178i	$0.519216\pi$
$374$	220.424	0.0304755
$375$	−630.113	−0.0867703
$376$	722.161	0.0990495
$377$	−2227.04	−0.304240
$378$	1450.01	0.197303
$379$	1278.76	0.173313	0.0866566	−	0.996238i	$-0.472382\pi$
$379$	1278.76	0.173313	0.0866566	+	0.996238i	$0.472382\pi$
$380$	3170.90	0.428062
$381$	−7827.44	−1.05252
$382$	2983.89	0.399658
$383$	−5343.75	−0.712932	−0.356466	−	0.934308i	$-0.616018\pi$
$383$	−5343.75	−0.712932	−0.356466	+	0.934308i	$0.616018\pi$
$384$	−645.235	−0.0857475
$385$	−140.412	−0.0185871
$386$	6182.19	0.815194
$387$	−694.473	−0.0912198
$388$	−425.557	−0.0556814
$389$	−708.346	−0.0923254	−0.0461627	−	0.998934i	$-0.514699\pi$
$389$	−708.346	−0.0923254	−0.0461627	+	0.998934i	$0.514699\pi$
$390$	−3162.04	−0.410554
$391$	454.101	0.0587336
$392$	−2541.54	−0.327467
$393$	1582.20	0.203083
$394$	5640.60	0.721241
$395$	−6627.28	−0.844189
$396$	35.4875	0.00450332
$397$	−5924.01	−0.748911	−0.374455	−	0.927245i	$-0.622170\pi$
$397$	−5924.01	−0.748911	−0.374455	+	0.927245i	$0.622170\pi$
$398$	2632.21	0.331510
$399$	−4020.59	−0.504464
$400$	400.000	0.0500000
$401$	−11393.6	−1.41888	−0.709441	−	0.704765i	$-0.751052\pi$
$401$	−11393.6	−1.41888	−0.709441	+	0.704765i	$0.751052\pi$
$402$	−858.384	−0.106498
$403$	17691.8	2.18682
$404$	2570.71	0.316578
$405$	−3417.81	−0.419339
$406$	−357.214	−0.0436656
$407$	781.402	0.0951663
$408$	796.200	0.0966122
$409$	13804.4	1.66891	0.834457	−	0.551073i	$-0.185782\pi$
$409$	13804.4	1.66891	0.834457	+	0.551073i	$0.185782\pi$
$410$	2276.80	0.274252
$411$	5374.06	0.644971
$412$	6487.96	0.775823
$413$	−4005.47	−0.477230
$414$	73.1087	0.00867898
$415$	−794.028	−0.0939212
$416$	2007.29	0.236575
$417$	8039.17	0.944076
$418$	−1770.06	−0.207120
$419$	−14795.8	−1.72512	−0.862558	−	0.505958i	$-0.831139\pi$
$419$	−14795.8	−1.72512	−0.862558	+	0.505958i	$0.831139\pi$
$420$	−507.186	−0.0589242
$421$	5804.66	0.671976	0.335988	−	0.941866i	$-0.390930\pi$
$421$	5804.66	0.671976	0.335988	+	0.941866i	$0.390930\pi$
$422$	−6798.37	−0.784217
$423$	−143.468	−0.0164909
$424$	2641.46	0.302549
$425$	−493.588	−0.0563353
$426$	3726.01	0.423769
$427$	−2860.36	−0.324175
$428$	5963.44	0.673490
$429$	1765.11	0.198649
$430$	4369.62	0.490051
$431$	15268.2	1.70636	0.853181	−	0.521615i	$-0.174670\pi$
$431$	15268.2	1.70636	0.853181	+	0.521615i	$0.174670\pi$
$432$	2305.85	0.256807
$433$	2250.62	0.249788	0.124894	−	0.992170i	$-0.460141\pi$
$433$	2250.62	0.249788	0.124894	+	0.992170i	$0.460141\pi$
$434$	2837.73	0.313860
$435$	894.843	0.0986309
$436$	4816.00	0.529001
$437$	−3646.53	−0.399170
$438$	3127.25	0.341155
$439$	10366.2	1.12700	0.563499	−	0.826117i	$-0.309455\pi$
$439$	10366.2	1.12700	0.563499	+	0.826117i	$0.309455\pi$
$440$	−223.288	−0.0241928
$441$	504.914	0.0545205
$442$	−2476.93	−0.266551
$443$	−3881.11	−0.416246	−0.208123	−	0.978103i	$-0.566736\pi$
$443$	−3881.11	−0.416246	−0.208123	+	0.978103i	$0.566736\pi$
$444$	2822.53	0.301692
$445$	−6169.45	−0.657214
$446$	1729.32	0.183600
$447$	5529.41	0.585083
$448$	321.965	0.0339541
$449$	−10146.5	−1.06647	−0.533233	−	0.845968i	$-0.679023\pi$
$449$	−10146.5	−1.06647	−0.533233	+	0.845968i	$0.679023\pi$
$450$	−79.4660	−0.00832459
$451$	−1270.95	−0.132698
$452$	1107.09	0.115206
$453$	−13783.9	−1.42963
$454$	−3958.79	−0.409241
$455$	1577.82	0.162570
$456$	−6393.68	−0.656604
$457$	−4728.87	−0.484042	−0.242021	−	0.970271i	$-0.577810\pi$
$457$	−4728.87	−0.484042	−0.242021	+	0.970271i	$0.577810\pi$
$458$	−6227.06	−0.635308
$459$	−2845.35	−0.289346
$460$	−460.000	−0.0466252
$461$	8380.69	0.846698	0.423349	−	0.905967i	$-0.360854\pi$
$461$	8380.69	0.846698	0.423349	+	0.905967i	$0.360854\pi$
$462$	283.121	0.0285108
$463$	6845.17	0.687089	0.343545	−	0.939136i	$-0.388372\pi$
$463$	6845.17	0.687089	0.343545	+	0.939136i	$0.388372\pi$
$464$	−568.053	−0.0568345
$465$	−7108.69	−0.708941
$466$	12037.3	1.19660
$467$	−14884.0	−1.47484	−0.737418	−	0.675436i	$-0.763955\pi$
$467$	−14884.0	−1.47484	−0.737418	+	0.675436i	$0.763955\pi$
$468$	−398.778	−0.0393878
$469$	428.324	0.0421710
$470$	902.701	0.0885925
$471$	7257.01	0.709948
$472$	−6369.62	−0.621156
$473$	−2439.20	−0.237114
$474$	13363.0	1.29490
$475$	3963.62	0.382871
$476$	−397.295	−0.0382563
$477$	−524.766	−0.0503719
$478$	−8449.76	−0.808542
$479$	6048.69	0.576976	0.288488	−	0.957483i	$-0.406847\pi$
$479$	6048.69	0.576976	0.288488	+	0.957483i	$0.406847\pi$
$480$	−806.544	−0.0766949
$481$	−8780.71	−0.832361
$482$	2788.47	0.263509
$483$	583.264	0.0549471
$484$	−5199.36	−0.488294
$485$	−531.946	−0.0498029
$486$	−890.720	−0.0831355
$487$	3199.35	0.297693	0.148846	−	0.988860i	$-0.452444\pi$
$487$	3199.35	0.297693	0.148846	+	0.988860i	$0.452444\pi$
$488$	−4548.64	−0.421941
$489$	15101.6	1.39656
$490$	−3176.92	−0.292895
$491$	−1614.41	−0.148385	−0.0741926	−	0.997244i	$-0.523638\pi$
$491$	−1614.41	−0.148385	−0.0741926	+	0.997244i	$0.523638\pi$
$492$	−4590.85	−0.420674
$493$	700.960	0.0640358
$494$	19890.3	1.81155
$495$	44.3594	0.00402789
$496$	4512.65	0.408516
$497$	−1859.24	−0.167803
$498$	1601.05	0.144066
$499$	−5392.04	−0.483729	−0.241864	−	0.970310i	$-0.577759\pi$
$499$	−5392.04	−0.483729	−0.241864	+	0.970310i	$0.577759\pi$
$500$	500.000	0.0447214
$501$	1772.04	0.158022
$502$	−11937.7	−1.06136
$503$	12625.4	1.11917	0.559583	−	0.828775i	$-0.310961\pi$
$503$	12625.4	1.11917	0.559583	+	0.828775i	$0.310961\pi$
$504$	−63.9633	−0.00565308
$505$	3213.38	0.283156
$506$	256.781	0.0225599
$507$	−8759.89	−0.767338
$508$	6211.15	0.542471
$509$	7065.76	0.615294	0.307647	−	0.951501i	$-0.400459\pi$
$509$	7065.76	0.615294	0.307647	+	0.951501i	$0.400459\pi$
$510$	995.250	0.0864126
$511$	−1560.46	−0.135090
$512$	512.000	0.0441942
$513$	22848.9	1.96647
$514$	−3272.12	−0.280792
$515$	8109.96	0.693917
$516$	−8810.73	−0.751688
$517$	−503.905	−0.0428660
$518$	−1408.41	−0.119463
$519$	18660.2	1.57822
$520$	2509.11	0.211599
$521$	−8399.20	−0.706287	−0.353144	−	0.935569i	$-0.614887\pi$
$521$	−8399.20	−0.706287	−0.353144	+	0.935569i	$0.614887\pi$
$522$	112.852	0.00946247
$523$	−7002.06	−0.585428	−0.292714	−	0.956200i	$-0.594558\pi$
$523$	−7002.06	−0.585428	−0.292714	+	0.956200i	$0.594558\pi$
$524$	−1255.49	−0.104669
$525$	−633.983	−0.0527034
$526$	5991.10	0.496624
$527$	−5568.47	−0.460278
$528$	450.228	0.0371092
$529$	529.000	0.0434783
$530$	3301.83	0.270608
$531$	1265.42	0.103417
$532$	3190.37	0.260001
$533$	14281.9	1.16063
$534$	12439.8	1.00810
$535$	7454.30	0.602388
$536$	681.136	0.0548891
$537$	−18067.1	−1.45186
$538$	−10380.3	−0.831838
$539$	1773.42	0.141719
$540$	2882.32	0.229695
$541$	3338.13	0.265282	0.132641	−	0.991164i	$-0.457654\pi$
$541$	3338.13	0.265282	0.132641	+	0.991164i	$0.457654\pi$
$542$	13440.9	1.06519
$543$	−3950.41	−0.312207
$544$	−631.792	−0.0497939
$545$	6020.00	0.473153
$546$	−3181.46	−0.249366
$547$	9609.09	0.751106	0.375553	−	0.926801i	$-0.377453\pi$
$547$	9609.09	0.751106	0.375553	+	0.926801i	$0.377453\pi$
$548$	−4264.37	−0.332417
$549$	903.656	0.0702497
$550$	−279.109	−0.0216387
$551$	−5628.87	−0.435205
$552$	927.526	0.0715183
$553$	−6667.98	−0.512751
$554$	−12229.5	−0.937872
$555$	3528.16	0.269842
$556$	−6379.15	−0.486576
$557$	−11931.1	−0.907608	−0.453804	−	0.891102i	$-0.649933\pi$
$557$	−11931.1	−0.907608	−0.453804	+	0.891102i	$0.649933\pi$
$558$	−896.506	−0.0680146
$559$	27409.6	2.07389
$560$	402.457	0.0303695
$561$	−555.567	−0.0418112
$562$	−7098.13	−0.532770
$563$	−10082.4	−0.754746	−0.377373	−	0.926061i	$-0.623173\pi$
$563$	−10082.4	−0.754746	−0.377373	+	0.926061i	$0.623173\pi$
$564$	−1820.17	−0.135892
$565$	1383.86	0.103043
$566$	6206.23	0.460896
$567$	−3438.80	−0.254702
$568$	−2956.62	−0.218410
$569$	−18710.5	−1.37853	−0.689267	−	0.724507i	$-0.742067\pi$
$569$	−18710.5	−1.37853	−0.689267	+	0.724507i	$0.742067\pi$
$570$	−7992.09	−0.587284
$571$	13510.1	0.990159	0.495079	−	0.868848i	$-0.335139\pi$
$571$	13510.1	0.990159	0.495079	+	0.868848i	$0.335139\pi$
$572$	−1400.63	−0.102383
$573$	−7520.75	−0.548314
$574$	2290.79	0.166578
$575$	−575.000	−0.0417029
$576$	−101.717	−0.00735797
$577$	11582.3	0.835662	0.417831	−	0.908525i	$-0.362790\pi$
$577$	11582.3	0.835662	0.417831	+	0.908525i	$0.362790\pi$
$578$	−9046.39	−0.651004
$579$	−15581.9	−1.11841
$580$	−710.066	−0.0508343
$581$	−798.905	−0.0570468
$582$	1072.59	0.0763926
$583$	−1843.14	−0.130935
$584$	−2481.50	−0.175831
$585$	−498.472	−0.0352295
$586$	2437.03	0.171796
$587$	−6019.34	−0.423245	−0.211623	−	0.977351i	$-0.567875\pi$
$587$	−6019.34	−0.423245	−0.211623	+	0.977351i	$0.567875\pi$
$588$	6405.81	0.449271
$589$	44716.1	3.12818
$590$	−7962.03	−0.555579
$591$	−14216.8	−0.989514
$592$	−2239.70	−0.155492
$593$	26299.3	1.82122	0.910608	−	0.413270i	$-0.135613\pi$
$593$	26299.3	1.82122	0.910608	+	0.413270i	$0.135613\pi$
$594$	−1608.96	−0.111139
$595$	−496.619	−0.0342175
$596$	−4387.63	−0.301551
$597$	−6634.36	−0.454818
$598$	−2885.47	−0.197317
$599$	−27368.0	−1.86682	−0.933409	−	0.358813i	$-0.883181\pi$
$599$	−27368.0	−1.86682	−0.933409	+	0.358813i	$0.883181\pi$
$600$	−1008.18	−0.0685980
$601$	−3472.33	−0.235673	−0.117836	−	0.993033i	$-0.537596\pi$
$601$	−3472.33	−0.235673	−0.117836	+	0.993033i	$0.537596\pi$
$602$	4396.46	0.297652
$603$	−135.318	−0.00913859
$604$	10937.6	0.736832
$605$	−6499.20	−0.436744
$606$	−6479.33	−0.434332
$607$	5061.10	0.338425	0.169212	−	0.985580i	$-0.445878\pi$
$607$	5061.10	0.338425	0.169212	+	0.985580i	$0.445878\pi$
$608$	5073.44	0.338413
$609$	900.339	0.0599074
$610$	−5685.80	−0.377396
$611$	5662.44	0.374922
$612$	125.515	0.00829027
$613$	−28272.6	−1.86283	−0.931417	−	0.363953i	$-0.881427\pi$
$613$	−28272.6	−1.86283	−0.931417	+	0.363953i	$0.881427\pi$
$614$	5128.90	0.337110
$615$	−5738.57	−0.376262
$616$	−224.659	−0.0146944
$617$	−2222.47	−0.145013	−0.0725066	−	0.997368i	$-0.523100\pi$
$617$	−2222.47	−0.145013	−0.0725066	+	0.997368i	$0.523100\pi$
$618$	−16352.6	−1.06440
$619$	−10498.2	−0.681679	−0.340840	−	0.940121i	$-0.610711\pi$
$619$	−10498.2	−0.681679	−0.340840	+	0.940121i	$0.610711\pi$
$620$	5640.81	0.365388
$621$	−3314.67	−0.214192
$622$	−185.251	−0.0119419
$623$	−6207.34	−0.399185
$624$	−5059.27	−0.324572
$625$	625.000	0.0400000
$626$	−8552.87	−0.546073
$627$	4461.34	0.284160
$628$	−5758.51	−0.365907
$629$	2763.72	0.175194
$630$	−79.9541	−0.00505627
$631$	−11402.2	−0.719355	−0.359678	−	0.933077i	$-0.617113\pi$
$631$	−11402.2	−0.719355	−0.359678	+	0.933077i	$0.617113\pi$
$632$	−10603.6	−0.667390
$633$	17135.0	1.07591
$634$	−5928.47	−0.371372
$635$	7763.93	0.485200
$636$	−6657.67	−0.415085
$637$	−19928.1	−1.23953
$638$	396.372	0.0245964
$639$	587.377	0.0363635
$640$	640.000	0.0395285
$641$	26128.3	1.60999	0.804996	−	0.593280i	$-0.202167\pi$
$641$	26128.3	1.60999	0.804996	+	0.593280i	$0.202167\pi$
$642$	−15030.5	−0.924001
$643$	863.502	0.0529599	0.0264799	−	0.999649i	$-0.491570\pi$
$643$	863.502	0.0529599	0.0264799	+	0.999649i	$0.491570\pi$
$644$	−462.825	−0.0283197
$645$	−11013.4	−0.672330
$646$	−6260.47	−0.381292
$647$	−5477.43	−0.332828	−0.166414	−	0.986056i	$-0.553219\pi$
$647$	−5477.43	−0.332828	−0.166414	+	0.986056i	$0.553219\pi$
$648$	−5468.50	−0.331517
$649$	4444.55	0.268820
$650$	3136.38	0.189260
$651$	−7152.36	−0.430604
$652$	−11983.3	−0.719787
$653$	19233.2	1.15261	0.576305	−	0.817235i	$-0.304494\pi$
$653$	19233.2	1.15261	0.576305	+	0.817235i	$0.304494\pi$
$654$	−12138.5	−0.725768
$655$	−1569.36	−0.0936185
$656$	3642.88	0.216815
$657$	492.987	0.0292744
$658$	908.245	0.0538102
$659$	9952.51	0.588307	0.294154	−	0.955758i	$-0.404962\pi$
$659$	9952.51	0.588307	0.294154	+	0.955758i	$0.404962\pi$
$660$	562.785	0.0331915
$661$	3047.96	0.179352	0.0896762	−	0.995971i	$-0.471417\pi$
$661$	3047.96	0.179352	0.0896762	+	0.995971i	$0.471417\pi$
$662$	−2697.61	−0.158377
$663$	6242.98	0.365697
$664$	−1270.45	−0.0742513
$665$	3987.97	0.232552
$666$	444.950	0.0258881
$667$	816.576	0.0474032
$668$	−1406.13	−0.0814442
$669$	−4358.67	−0.251892
$670$	851.419	0.0490943
$671$	3173.92	0.182605
$672$	−811.498	−0.0465836
$673$	16245.9	0.930508	0.465254	−	0.885177i	$-0.345963\pi$
$673$	16245.9	0.930508	0.465254	+	0.885177i	$0.345963\pi$
$674$	−11528.6	−0.658850
$675$	3602.90	0.205445
$676$	6951.05	0.395486
$677$	−30056.6	−1.70631	−0.853154	−	0.521659i	$-0.825313\pi$
$677$	−30056.6	−1.70631	−0.853154	+	0.521659i	$0.825313\pi$
$678$	−2790.35	−0.158057
$679$	−535.213	−0.0302498
$680$	−789.740	−0.0445370
$681$	9977.94	0.561462
$682$	−3148.81	−0.176795
$683$	10064.8	0.563866	0.281933	−	0.959434i	$-0.409024\pi$
$683$	10064.8	0.563866	0.281933	+	0.959434i	$0.409024\pi$
$684$	−1007.92	−0.0563430
$685$	−5330.46	−0.297323
$686$	−6647.50	−0.369975
$687$	15695.0	0.871617
$688$	6991.39	0.387419
$689$	20711.6	1.14521
$690$	1159.41	0.0639679
$691$	10260.7	0.564886	0.282443	−	0.959284i	$-0.408855\pi$
$691$	10260.7	0.564886	0.282443	+	0.959284i	$0.408855\pi$
$692$	−14807.1	−0.813411
$693$	44.6319	0.00244650
$694$	8132.31	0.444810
$695$	−7973.94	−0.435207
$696$	1431.75	0.0779746
$697$	−4495.21	−0.244287
$698$	16815.6	0.911865
$699$	−30339.4	−1.64169
$700$	503.071	0.0271633
$701$	−19815.6	−1.06766	−0.533828	−	0.845593i	$-0.679247\pi$
$701$	−19815.6	−1.06766	−0.533828	+	0.845593i	$0.679247\pi$
$702$	18080.1	0.972066
$703$	−22193.3	−1.19067
$704$	−357.260	−0.0191261
$705$	−2275.21	−0.121545
$706$	512.136	0.0273010
$707$	3233.12	0.171986
$708$	16054.3	0.852201
$709$	−30533.5	−1.61736	−0.808681	−	0.588247i	$-0.799818\pi$
$709$	−30533.5	−1.61736	−0.808681	+	0.588247i	$0.799818\pi$
$710$	−3695.78	−0.195352
$711$	2106.57	0.111115
$712$	−9871.12	−0.519573
$713$	−6486.93	−0.340726
$714$	1001.36	0.0524861
$715$	−1750.79	−0.0915745
$716$	14336.4	0.748290
$717$	21297.2	1.10929
$718$	−24105.0	−1.25291
$719$	9125.45	0.473327	0.236663	−	0.971592i	$-0.423946\pi$
$719$	9125.45	0.473327	0.236663	+	0.971592i	$0.423946\pi$
$720$	−127.146	−0.00658116
$721$	8159.77	0.421478
$722$	36555.0	1.88426
$723$	−7028.21	−0.361524
$724$	3134.69	0.160911
$725$	−887.583	−0.0454676
$726$	13104.7	0.669920
$727$	2635.53	0.134452	0.0672259	−	0.997738i	$-0.478585\pi$
$727$	2635.53	0.134452	0.0672259	+	0.997738i	$0.478585\pi$
$728$	2524.52	0.128523
$729$	20701.2	1.05173
$730$	−3101.88	−0.157268
$731$	−8627.17	−0.436508
$732$	11464.6	0.578886
$733$	10778.0	0.543102	0.271551	−	0.962424i	$-0.412463\pi$
$733$	10778.0	0.543102	0.271551	+	0.962424i	$0.412463\pi$
$734$	−18490.8	−0.929848
$735$	8007.27	0.401840
$736$	−736.000	−0.0368605
$737$	−475.278	−0.0237545
$738$	−723.714	−0.0360979
$739$	−1758.72	−0.0875449	−0.0437725	−	0.999042i	$-0.513938\pi$
$739$	−1758.72	−0.0875449	−0.0437725	+	0.999042i	$0.513938\pi$
$740$	−2799.63	−0.139076
$741$	−50132.6	−2.48538
$742$	3322.11	0.164364
$743$	9737.97	0.480823	0.240412	−	0.970671i	$-0.422718\pi$
$743$	9737.97	0.480823	0.240412	+	0.970671i	$0.422718\pi$
$744$	−11373.9	−0.560467
$745$	−5484.54	−0.269716
$746$	−1738.53	−0.0853245
$747$	252.393	0.0123622
$748$	440.848	0.0215495
$749$	7500.08	0.365884
$750$	−1260.23	−0.0613559
$751$	−23795.7	−1.15621	−0.578107	−	0.815961i	$-0.696208\pi$
$751$	−23795.7	−1.15621	−0.578107	+	0.815961i	$0.696208\pi$
$752$	1444.32	0.0700385
$753$	30088.3	1.45615
$754$	−4454.08	−0.215130
$755$	13672.1	0.659043
$756$	2900.02	0.139514
$757$	23647.6	1.13538	0.567692	−	0.823241i	$-0.307837\pi$
$757$	23647.6	1.13538	0.567692	+	0.823241i	$0.307837\pi$
$758$	2557.53	0.122551
$759$	−647.203	−0.0309512
$760$	6341.80	0.302686
$761$	−4606.09	−0.219410	−0.109705	−	0.993964i	$-0.534991\pi$
$761$	−4606.09	−0.219410	−0.109705	+	0.993964i	$0.534991\pi$
$762$	−15654.9	−0.744248
$763$	6056.98	0.287388
$764$	5967.79	0.282601
$765$	156.894	0.00741504
$766$	−10687.5	−0.504119
$767$	−49944.0	−2.35120
$768$	−1290.47	−0.0606326
$769$	17760.9	0.832867	0.416433	−	0.909166i	$-0.363280\pi$
$769$	17760.9	0.832867	0.416433	+	0.909166i	$0.363280\pi$
$770$	−280.824	−0.0131431
$771$	8247.22	0.385235
$772$	12364.4	0.576430
$773$	7147.47	0.332570	0.166285	−	0.986078i	$-0.446823\pi$
$773$	7147.47	0.332570	0.166285	+	0.986078i	$0.446823\pi$
$774$	−1388.95	−0.0645021
$775$	7051.02	0.326813
$776$	−851.114	−0.0393727
$777$	3549.83	0.163899
$778$	−1416.69	−0.0652839
$779$	36097.6	1.66024
$780$	−6324.08	−0.290306
$781$	2063.05	0.0945222
$782$	908.201	0.0415310
$783$	−5116.59	−0.233528
$784$	−5083.07	−0.231554
$785$	−7198.13	−0.327277
$786$	3164.40	0.143601
$787$	−31719.1	−1.43668	−0.718338	−	0.695694i	$-0.755097\pi$
$787$	−31719.1	−1.43668	−0.718338	+	0.695694i	$0.755097\pi$
$788$	11281.2	0.509995
$789$	−15100.3	−0.681348
$790$	−13254.6	−0.596932
$791$	1392.36	0.0625872
$792$	70.9751	0.00318433
$793$	−35665.7	−1.59713
$794$	−11848.0	−0.529560
$795$	−8322.09	−0.371263
$796$	5264.42	0.234413
$797$	30828.3	1.37013	0.685066	−	0.728481i	$-0.259773\pi$
$797$	30828.3	1.37013	0.685066	+	0.728481i	$0.259773\pi$
$798$	−8041.18	−0.356710
$799$	−1782.25	−0.0789129
$800$	800.000	0.0353553
$801$	1961.05	0.0865046
$802$	−22787.3	−1.00330
$803$	1731.53	0.0760949
$804$	−1716.77	−0.0753057
$805$	−578.532	−0.0253299
$806$	35383.5	1.54632
$807$	26163.2	1.14125
$808$	5141.41	0.223854
$809$	36679.2	1.59403	0.797015	−	0.603959i	$-0.206411\pi$
$809$	36679.2	1.59403	0.797015	+	0.603959i	$0.206411\pi$
$810$	−6835.62	−0.296518
$811$	−12210.0	−0.528672	−0.264336	−	0.964431i	$-0.585153\pi$
$811$	−12210.0	−0.528672	−0.264336	+	0.964431i	$0.585153\pi$
$812$	−714.427	−0.0308762
$813$	−33877.0	−1.46140
$814$	1562.80	0.0672927
$815$	−14979.1	−0.643797
$816$	1592.40	0.0683152
$817$	69278.2	2.96663
$818$	27608.9	1.18010
$819$	−501.534	−0.0213981
$820$	4553.60	0.193925
$821$	−9996.47	−0.424944	−0.212472	−	0.977167i	$-0.568151\pi$
$821$	−9996.47	−0.424944	−0.212472	+	0.977167i	$0.568151\pi$
$822$	10748.1	0.456063
$823$	−42868.8	−1.81569	−0.907845	−	0.419306i	$-0.862273\pi$
$823$	−42868.8	−1.81569	−0.907845	+	0.419306i	$0.862273\pi$
$824$	12975.9	0.548590
$825$	703.481	0.0296874
$826$	−8010.93	−0.337453
$827$	−15833.4	−0.665759	−0.332880	−	0.942969i	$-0.608020\pi$
$827$	−15833.4	−0.665759	−0.332880	+	0.942969i	$0.608020\pi$
$828$	146.217	0.00613697
$829$	−17722.3	−0.742484	−0.371242	−	0.928536i	$-0.621068\pi$
$829$	−17722.3	−0.742484	−0.371242	+	0.928536i	$0.621068\pi$
$830$	−1588.06	−0.0664123
$831$	30823.8	1.28672
$832$	4014.57	0.167284
$833$	6272.35	0.260893
$834$	16078.3	0.667563
$835$	−1757.66	−0.0728459
$836$	−3540.11	−0.146456
$837$	40646.5	1.67855
$838$	−29591.7	−1.21984
$839$	−40528.4	−1.66769	−0.833847	−	0.551996i	$-0.813866\pi$
$839$	−40528.4	−1.66769	−0.833847	+	0.551996i	$0.813866\pi$
$840$	−1014.37	−0.0416657
$841$	−23128.5	−0.948317
$842$	11609.3	0.475159
$843$	17890.5	0.730938
$844$	−13596.7	−0.554525
$845$	8688.82	0.353733
$846$	−286.936	−0.0116608
$847$	−6539.11	−0.265273
$848$	5282.92	0.213934
$849$	−15642.5	−0.632331
$850$	−987.175	−0.0398351
$851$	3219.57	0.129689
$852$	7452.02	0.299650
$853$	8116.97	0.325814	0.162907	−	0.986641i	$-0.447913\pi$
$853$	8116.97	0.325814	0.162907	+	0.986641i	$0.447913\pi$
$854$	−5720.73	−0.229226
$855$	−1259.89	−0.0503947
$856$	11926.9	0.476229
$857$	16285.5	0.649126	0.324563	−	0.945864i	$-0.394783\pi$
$857$	16285.5	0.649126	0.324563	+	0.945864i	$0.394783\pi$
$858$	3530.22	0.140466
$859$	−26487.5	−1.05209	−0.526043	−	0.850458i	$-0.676325\pi$
$859$	−26487.5	−1.05209	−0.526043	+	0.850458i	$0.676325\pi$
$860$	8739.24	0.346518
$861$	−5773.81	−0.228538
$862$	30536.3	1.20658
$863$	40396.2	1.59340	0.796699	−	0.604376i	$-0.206578\pi$
$863$	40396.2	1.59340	0.796699	+	0.604376i	$0.206578\pi$
$864$	4611.71	0.181590
$865$	−18508.8	−0.727537
$866$	4501.25	0.176627
$867$	22801.0	0.893151
$868$	5675.46	0.221933
$869$	7398.94	0.288828
$870$	1789.69	0.0697426
$871$	5340.76	0.207767
$872$	9632.00	0.374060
$873$	169.087	0.00655523
$874$	−7293.07	−0.282256
$875$	628.839	0.0242956
$876$	6254.50	0.241233
$877$	10962.9	0.422109	0.211054	−	0.977474i	$-0.432310\pi$
$877$	10962.9	0.422109	0.211054	+	0.977474i	$0.432310\pi$
$878$	20732.4	0.796908
$879$	−6142.40	−0.235698
$880$	−446.575	−0.0171069
$881$	23906.5	0.914222	0.457111	−	0.889410i	$-0.348884\pi$
$881$	23906.5	0.914222	0.457111	+	0.889410i	$0.348884\pi$
$882$	1009.83	0.0385518
$883$	−30509.1	−1.16275	−0.581377	−	0.813634i	$-0.697486\pi$
$883$	−30509.1	−1.16275	−0.581377	+	0.813634i	$0.697486\pi$
$884$	−4953.86	−0.188480
$885$	20067.9	0.762232
$886$	−7762.22	−0.294331
$887$	−40034.3	−1.51547	−0.757733	−	0.652565i	$-0.773693\pi$
$887$	−40034.3	−1.51547	−0.757733	+	0.652565i	$0.773693\pi$
$888$	5645.06	0.213328
$889$	7811.62	0.294706
$890$	−12338.9	−0.464720
$891$	3815.77	0.143472
$892$	3458.64	0.129825
$893$	14311.9	0.536314
$894$	11058.8	0.413716
$895$	17920.5	0.669291
$896$	643.931	0.0240092
$897$	7272.69	0.270711
$898$	−20293.0	−0.754106
$899$	−10013.4	−0.371485
$900$	−158.932	−0.00588637
$901$	−6518.96	−0.241041
$902$	−2541.91	−0.0938318
$903$	−11081.1	−0.408366
$904$	2214.17	0.0814626
$905$	3918.36	0.143923
$906$	−27567.8	−1.01090
$907$	−2843.48	−0.104097	−0.0520486	−	0.998645i	$-0.516575\pi$
$907$	−2843.48	−0.104097	−0.0520486	+	0.998645i	$0.516575\pi$
$908$	−7917.58	−0.289377
$909$	−1021.42	−0.0372699
$910$	3155.65	0.114955
$911$	42268.6	1.53723	0.768617	−	0.639710i	$-0.220945\pi$
$911$	42268.6	1.53723	0.768617	+	0.639710i	$0.220945\pi$
$912$	−12787.4	−0.464289
$913$	886.483	0.0321340
$914$	−9457.74	−0.342269
$915$	14330.8	0.517772
$916$	−12454.1	−0.449231
$917$	−1579.00	−0.0568629
$918$	−5690.71	−0.204598
$919$	−12699.6	−0.455844	−0.227922	−	0.973679i	$-0.573193\pi$
$919$	−12699.6	−0.455844	−0.227922	+	0.973679i	$0.573193\pi$
$920$	−920.000	−0.0329690
$921$	−12927.1	−0.462501
$922$	16761.4	0.598706
$923$	−23182.8	−0.826728
$924$	566.242	0.0201602
$925$	−3499.53	−0.124393
$926$	13690.3	0.485845
$927$	−2577.86	−0.0913357
$928$	−1136.11	−0.0401880
$929$	−24889.6	−0.879011	−0.439505	−	0.898240i	$-0.644846\pi$
$929$	−24889.6	−0.879011	−0.439505	+	0.898240i	$0.644846\pi$
$930$	−14217.4	−0.501297
$931$	−50368.5	−1.77310
$932$	24074.6	0.846126
$933$	466.915	0.0163838
$934$	−29768.0	−1.04287
$935$	551.060	0.0192744
$936$	−797.555	−0.0278514
$937$	9585.48	0.334199	0.167099	−	0.985940i	$-0.446560\pi$
$937$	9585.48	0.334199	0.167099	+	0.985940i	$0.446560\pi$
$938$	856.649	0.0298194
$939$	21557.1	0.749189
$940$	1805.40	0.0626444
$941$	−21146.9	−0.732592	−0.366296	−	0.930498i	$-0.619374\pi$
$941$	−21146.9	−0.732592	−0.366296	+	0.930498i	$0.619374\pi$
$942$	14514.0	0.502009
$943$	−5236.65	−0.180836
$944$	−12739.2	−0.439224
$945$	3625.03	0.124785
$946$	−4878.41	−0.167665
$947$	48747.2	1.67272	0.836362	−	0.548177i	$-0.184678\pi$
$947$	48747.2	1.67272	0.836362	+	0.548177i	$0.184678\pi$
$948$	26726.0	0.915632
$949$	−19457.3	−0.665556
$950$	7927.25	0.270730
$951$	14942.4	0.509507
$952$	−794.591	−0.0270513
$953$	24925.9	0.847249	0.423625	−	0.905838i	$-0.360758\pi$
$953$	24925.9	0.847249	0.423625	+	0.905838i	$0.360758\pi$
$954$	−1049.53	−0.0356183
$955$	7459.73	0.252766
$956$	−16899.5	−0.571725
$957$	−999.036	−0.0337453
$958$	12097.4	0.407984
$959$	−5363.20	−0.180591
$960$	−1613.09	−0.0542315
$961$	49755.9	1.67017
$962$	−17561.4	−0.588568
$963$	−2369.45	−0.0792882
$964$	5576.95	0.186329
$965$	15455.5	0.515574
$966$	1166.53	0.0388534
$967$	−1881.92	−0.0625838	−0.0312919	−	0.999510i	$-0.509962\pi$
$967$	−1881.92	−0.0625838	−0.0312919	+	0.999510i	$0.509962\pi$
$968$	−10398.7	−0.345276
$969$	15779.2	0.523117
$970$	−1063.89	−0.0352160
$971$	−14637.3	−0.483763	−0.241881	−	0.970306i	$-0.577764\pi$
$971$	−14637.3	−0.483763	−0.241881	+	0.970306i	$0.577764\pi$
$972$	−1781.44	−0.0587857
$973$	−8022.92	−0.264340
$974$	6398.70	0.210501
$975$	−7905.10	−0.259657
$976$	−9097.28	−0.298358
$977$	42591.4	1.39470	0.697348	−	0.716733i	$-0.254363\pi$
$977$	42591.4	1.39470	0.697348	+	0.716733i	$0.254363\pi$
$978$	30203.2	0.987518
$979$	6887.81	0.224857
$980$	−6353.84	−0.207108
$981$	−1913.54	−0.0622780
$982$	−3228.81	−0.104924
$983$	−48858.3	−1.58529	−0.792644	−	0.609684i	$-0.791296\pi$
$983$	−48858.3	−1.58529	−0.792644	+	0.609684i	$0.791296\pi$
$984$	−9181.71	−0.297462
$985$	14101.5	0.456153
$986$	1401.92	0.0452801
$987$	−2289.19	−0.0738254
$988$	39780.6	1.28096
$989$	−10050.1	−0.323130
$990$	88.7189	0.00284815
$991$	−56522.1	−1.81179	−0.905895	−	0.423502i	$-0.860801\pi$
$991$	−56522.1	−1.81179	−0.905895	+	0.423502i	$0.860801\pi$
$992$	9025.30	0.288864
$993$	6799.19	0.217287
$994$	−3718.48	−0.118655
$995$	6580.53	0.209665
$996$	3202.09	0.101870
$997$	−20767.9	−0.659706	−0.329853	−	0.944032i	$-0.606999\pi$
$997$	−20767.9	−0.659706	−0.329853	+	0.944032i	$0.606999\pi$
$998$	−10784.1	−0.342048
$999$	−20173.5	−0.638902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.j.1.1	✓	4
3.2	odd	2		2070.4.a.bg.1.3		4
4.3	odd	2		1840.4.a.k.1.4		4
5.2	odd	4		1150.4.b.o.599.8		8
5.3	odd	4		1150.4.b.o.599.1		8
5.4	even	2		1150.4.a.n.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.j.1.1	✓	4	1.1	even	1	trivial
1150.4.a.n.1.4		4	5.4	even	2
1150.4.b.o.599.1		8	5.3	odd	4
1150.4.b.o.599.8		8	5.2	odd	4
1840.4.a.k.1.4		4	4.3	odd	2
2070.4.a.bg.1.3		4	3.2	odd	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -5.04090 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.0818 q^{6} +5.03071 q^{7} +8.00000 q^{8} -1.58932 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -5.04090 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.0818 q^{6} +5.03071 q^{7} +8.00000 q^{8} -1.58932 q^{9} +10.0000 q^{10} -5.58219 q^{11} -20.1636 q^{12} +62.7277 q^{13} +10.0614 q^{14} -25.2045 q^{15} +16.0000 q^{16} -19.7435 q^{17} -3.17864 q^{18} +158.545 q^{19} +20.0000 q^{20} -25.3593 q^{21} -11.1644 q^{22} -23.0000 q^{23} -40.3272 q^{24} +25.0000 q^{25} +125.455 q^{26} +144.116 q^{27} +20.1228 q^{28} -35.5033 q^{29} -50.4090 q^{30} +282.041 q^{31} +32.0000 q^{32} +28.1393 q^{33} -39.4870 q^{34} +25.1536 q^{35} -6.35728 q^{36} -139.981 q^{37} +317.090 q^{38} -316.204 q^{39} +40.0000 q^{40} +227.680 q^{41} -50.7186 q^{42} +436.962 q^{43} -22.3288 q^{44} -7.94660 q^{45} -46.0000 q^{46} +90.2701 q^{47} -80.6544 q^{48} -317.692 q^{49} +50.0000 q^{50} +99.5250 q^{51} +250.911 q^{52} +330.183 q^{53} +288.232 q^{54} -27.9109 q^{55} +40.2457 q^{56} -799.209 q^{57} -71.0066 q^{58} -796.203 q^{59} -100.818 q^{60} -568.580 q^{61} +564.081 q^{62} -7.99541 q^{63} +64.0000 q^{64} +313.638 q^{65} +56.2785 q^{66} +85.1419 q^{67} -78.9740 q^{68} +115.941 q^{69} +50.3071 q^{70} -369.578 q^{71} -12.7146 q^{72} -310.188 q^{73} -279.963 q^{74} -126.023 q^{75} +634.180 q^{76} -28.0824 q^{77} -632.408 q^{78} -1325.46 q^{79} +80.0000 q^{80} -683.562 q^{81} +455.360 q^{82} -158.806 q^{83} -101.437 q^{84} -98.7175 q^{85} +873.924 q^{86} +178.969 q^{87} -44.6575 q^{88} -1233.89 q^{89} -15.8932 q^{90} +315.565 q^{91} -92.0000 q^{92} -1421.74 q^{93} +180.540 q^{94} +792.725 q^{95} -161.309 q^{96} -106.389 q^{97} -635.384 q^{98} +8.87189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9} + 40 q^{10} + 21 q^{11} + 56 q^{12} + 70 q^{13} + 16 q^{14} + 70 q^{15} + 64 q^{16} + 56 q^{17} + 128 q^{18} + 173 q^{19} + 80 q^{20} - 120 q^{21} + 42 q^{22} - 92 q^{23} + 112 q^{24} + 100 q^{25} + 140 q^{26} + 389 q^{27} + 32 q^{28} - 118 q^{29} + 140 q^{30} + 17 q^{31} + 128 q^{32} - 89 q^{33} + 112 q^{34} + 40 q^{35} + 256 q^{36} - 343 q^{37} + 346 q^{38} - 221 q^{39} + 160 q^{40} + 139 q^{41} - 240 q^{42} - 50 q^{43} + 84 q^{44} + 320 q^{45} - 184 q^{46} + 367 q^{47} + 224 q^{48} - 124 q^{49} + 200 q^{50} + 439 q^{51} + 280 q^{52} - 353 q^{53} + 778 q^{54} + 105 q^{55} + 64 q^{56} - 238 q^{57} - 236 q^{58} - 453 q^{59} + 280 q^{60} - 327 q^{61} + 34 q^{62} - 1723 q^{63} + 256 q^{64} + 350 q^{65} - 178 q^{66} - 455 q^{67} + 224 q^{68} - 322 q^{69} + 80 q^{70} + 195 q^{71} + 512 q^{72} - 633 q^{73} - 686 q^{74} + 350 q^{75} + 692 q^{76} - 2 q^{77} - 442 q^{78} - 1140 q^{79} + 320 q^{80} + 1456 q^{81} + 278 q^{82} - 1199 q^{83} - 480 q^{84} + 280 q^{85} - 100 q^{86} - 1775 q^{87} + 168 q^{88} - 2170 q^{89} + 640 q^{90} + 557 q^{91} - 368 q^{92} - 3241 q^{93} + 734 q^{94} + 865 q^{95} + 448 q^{96} - 703 q^{97} - 248 q^{98} - 2745 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9 + 40 * q^10 + 21 * q^11 + 56 * q^12 + 70 * q^13 + 16 * q^14 + 70 * q^15 + 64 * q^16 + 56 * q^17 + 128 * q^18 + 173 * q^19 + 80 * q^20 - 120 * q^21 + 42 * q^22 - 92 * q^23 + 112 * q^24 + 100 * q^25 + 140 * q^26 + 389 * q^27 + 32 * q^28 - 118 * q^29 + 140 * q^30 + 17 * q^31 + 128 * q^32 - 89 * q^33 + 112 * q^34 + 40 * q^35 + 256 * q^36 - 343 * q^37 + 346 * q^38 - 221 * q^39 + 160 * q^40 + 139 * q^41 - 240 * q^42 - 50 * q^43 + 84 * q^44 + 320 * q^45 - 184 * q^46 + 367 * q^47 + 224 * q^48 - 124 * q^49 + 200 * q^50 + 439 * q^51 + 280 * q^52 - 353 * q^53 + 778 * q^54 + 105 * q^55 + 64 * q^56 - 238 * q^57 - 236 * q^58 - 453 * q^59 + 280 * q^60 - 327 * q^61 + 34 * q^62 - 1723 * q^63 + 256 * q^64 + 350 * q^65 - 178 * q^66 - 455 * q^67 + 224 * q^68 - 322 * q^69 + 80 * q^70 + 195 * q^71 + 512 * q^72 - 633 * q^73 - 686 * q^74 + 350 * q^75 + 692 * q^76 - 2 * q^77 - 442 * q^78 - 1140 * q^79 + 320 * q^80 + 1456 * q^81 + 278 * q^82 - 1199 * q^83 - 480 * q^84 + 280 * q^85 - 100 * q^86 - 1775 * q^87 + 168 * q^88 - 2170 * q^89 + 640 * q^90 + 557 * q^91 - 368 * q^92 - 3241 * q^93 + 734 * q^94 + 865 * q^95 + 448 * q^96 - 703 * q^97 - 248 * q^98 - 2745 * q^99

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