LMFDB - Embedded newform 25.36.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,36,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 36, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 36 $
Character orbit:	$[\chi]$	$=$	25.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:	$193.987826584$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 12422194x - 2645665785 $ x^3 - 12422194*x - 2645665785
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-213.765$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+165109. q^{2} +3.45913e8 q^{3} -7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14 q^{7} -6.84517e15 q^{8} +6.96245e16 q^{9} +O(q^{10})$	\(q+165109. q^{2} +3.45913e8 q^{3} -7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14 q^{7} -6.84517e15 q^{8} +6.96245e16 q^{9} -1.70842e18 q^{11} -2.45554e18 q^{12} +4.94986e19 q^{13} +2.06651e19 q^{14} -8.86291e20 q^{16} -1.32045e21 q^{17} +1.14956e22 q^{18} +3.94388e21 q^{19} +4.32945e22 q^{21} -2.82076e23 q^{22} +3.48881e23 q^{23} -2.36784e24 q^{24} +8.17268e24 q^{26} +6.77748e24 q^{27} -8.88473e23 q^{28} +3.21628e25 q^{29} +3.41044e25 q^{31} +8.88635e25 q^{32} -5.90965e26 q^{33} -2.18018e26 q^{34} -4.94244e26 q^{36} +4.03624e27 q^{37} +6.51171e26 q^{38} +1.71222e28 q^{39} +8.65857e27 q^{41} +7.14832e27 q^{42} -9.89389e26 q^{43} +1.21276e28 q^{44} +5.76034e28 q^{46} -1.95852e29 q^{47} -3.06580e29 q^{48} -3.63154e29 q^{49} -4.56760e29 q^{51} -3.51376e29 q^{52} +9.96909e29 q^{53} +1.11902e30 q^{54} -8.56741e29 q^{56} +1.36424e30 q^{57} +5.31037e30 q^{58} +3.91953e30 q^{59} +7.64909e29 q^{61} +5.63096e30 q^{62} +8.71420e30 q^{63} +4.51249e31 q^{64} -9.75738e31 q^{66} +1.64301e32 q^{67} +9.37346e30 q^{68} +1.20682e32 q^{69} +7.65930e31 q^{71} -4.76592e32 q^{72} +7.08063e32 q^{73} +6.66421e32 q^{74} -2.79964e31 q^{76} -2.13826e32 q^{77} +2.82704e33 q^{78} +2.34599e33 q^{79} -1.13900e33 q^{81} +1.42961e33 q^{82} -5.18971e33 q^{83} -3.07335e32 q^{84} -1.63357e32 q^{86} +1.11255e34 q^{87} +1.16944e34 q^{88} +1.44578e34 q^{89} +6.19525e33 q^{91} -2.47660e33 q^{92} +1.17972e34 q^{93} -3.23369e34 q^{94} +3.07391e34 q^{96} +2.87399e34 q^{97} -5.99600e34 q^{98} -1.18948e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 139656 q^{2} + 104875308 q^{3} + 34841262144 q^{4} - 4786530564384 q^{6} - 878422149346056 q^{7} - 22\!\cdots\!00 q^{8}+ \cdots + 15\!\cdots\!51 q^{9}+O(q^{10}) $ 3 * q - 139656 * q^2 + 104875308 * q^3 + 34841262144 * q^4 - 4786530564384 * q^6 - 878422149346056 * q^7 - 22336009925337600 * q^8 + 150091978876243551 * q^9	$ 3 q - 139656 q^{2} + 104875308 q^{3} + 34841262144 q^{4} - 4786530564384 q^{6} - 878422149346056 q^{7} - 22\!\cdots\!00 q^{8}+ \cdots + 30\!\cdots\!52 q^{99}+O(q^{100}) $ 3 * q - 139656 * q^2 + 104875308 * q^3 + 34841262144 * q^4 - 4786530564384 * q^6 - 878422149346056 * q^7 - 22336009925337600 * q^8 + 150091978876243551 * q^9 - 1157945428549987044 * q^11 + 22548891526776486144 * q^12 + 62139610550998650558 * q^13 + 135909343255071438528 * q^14 + 2155694017285818421248 * q^16 + 3932636930193139724394 * q^17 + 23007400170989698594008 * q^18 - 32303396242934620550940 * q^19 + 222122458753667398807776 * q^21 - 22658809266113247402912 * q^22 + 514822069421375217224808 * q^23 - 3760729014923614708254720 * q^24 + 4284481859934908169468336 * q^26 - 27373531144823515220747400 * q^27 - 10448754713452503022622208 * q^28 - 38460399143984437598248110 * q^29 + 103731594563724689730029856 * q^31 + 9222369125611166314758144 * q^32 - 1184565114402567148957069584 * q^33 - 554136735348503783026707312 * q^34 - 6052204716130590310531484352 * q^36 - 2464613172948888017021063706 * q^37 + 12543374691225905672793885600 * q^38 + 18611981954062877742706387512 * q^39 + 23522986584532768129037087406 * q^41 + 33931371616975894880367698688 * q^42 + 47516297135443858184325274308 * q^43 - 80954820698705302013923898112 * q^44 + 310121697020384938950505889856 * q^46 - 164346768841318947159729902256 * q^47 - 445342931723856383878644744192 * q^48 - 595089038084925731622037450821 * q^49 - 1803044074850794727352259927704 * q^51 + 511632617456400883939009686144 * q^52 + 1670480551111723484744458809558 * q^53 + 4424231404769003900494105901760 * q^54 + 5670920217413056567252590243840 * q^56 - 4048712721984947152977307522800 * q^57 + 23757672063982901326871265032400 * q^58 + 4370528583092646699845243631180 * q^59 + 23537078276516028947219080488306 * q^61 - 29401231764447267309574710842112 * q^62 - 45614247892704690123948892506792 * q^63 + 93510280736634320631093264384 * q^64 - 75640417841065837797640948042368 * q^66 + 188845033384156918977315211921644 * q^67 - 21990159186015794982823459732608 * q^68 - 325983212396274250308653315934048 * q^69 + 348774602295358210538621162006856 * q^71 - 314101495165322886769992842611200 * q^72 + 285174964854822786615792218987058 * q^73 + 2106337383176566865790045395789808 * q^74 - 2729074287668324197849535448894720 * q^76 - 691501421964810422051915307575712 * q^77 + 2213086042571083132613626950273216 * q^78 - 426212862591061661901736630874160 * q^79 + 1867221150796978455595408934723163 * q^81 + 4061181362173286538873115152234288 * q^82 - 14867187331664065317008883105766692 * q^83 - 13024788508690842242825242575869952 * q^84 + 148490750656470812540405098190496 * q^86 + 7833119385476156993771606256673800 * q^87 + 18777218849949122679898044025804800 * q^88 + 30583590846193751335205992418034270 * q^89 + 1003391702519487362566122156997296 * q^91 - 83662070125024358323030039384121856 * q^92 + 40914650682166972019906140161446016 * q^93 + 19076193270418512575422277142000768 * q^94 - 32392027865954425966997293222723584 * q^96 + 106165667044630951063328618701091994 * q^97 + 13202051562017808504422115585262392 * q^98 + 30288686341597731928441860752034252 * 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 $

$2$	165109.	0.890730	0.445365	−	0.895349i	$-0.353074\pi$
$2$	165109.	0.890730	0.445365	+	0.895349i	$0.353074\pi$
$3$	3.45913e8	1.54648	0.773242	−	0.634111i	$-0.218634\pi$
$3$	3.45913e8	1.54648	0.773242	+	0.634111i	$0.218634\pi$
$4$	−7.09870e9	−0.206599
$5$	0	0
$5$	0	0
$6$	5.71135e13	1.37750
$7$	1.25160e14	0.203353	0.101676	−	0.994818i	$-0.467579\pi$
$7$	1.25160e14	0.203353	0.101676	+	0.994818i	$0.467579\pi$
$8$	−6.84517e15	−1.07475
$9$	6.96245e16	1.39161
$10$	0	0
$11$	−1.70842e18	−1.01911	−0.509557	−	0.860437i	$-0.670191\pi$
$11$	−1.70842e18	−1.01911	−0.509557	+	0.860437i	$0.670191\pi$
$12$	−2.45554e18	−0.319503
$13$	4.94986e19	1.58703	0.793514	−	0.608552i	$-0.208249\pi$
$13$	4.94986e19	1.58703	0.793514	+	0.608552i	$0.208249\pi$
$14$	2.06651e19	0.181132
$15$	0	0
$16$	−8.86291e20	−0.750717
$17$	−1.32045e21	−0.387137	−0.193569	−	0.981087i	$-0.562006\pi$
$17$	−1.32045e21	−0.387137	−0.193569	+	0.981087i	$0.562006\pi$
$18$	1.14956e22	1.23955
$19$	3.94388e21	0.165096	0.0825479	−	0.996587i	$-0.473694\pi$
$19$	3.94388e21	0.165096	0.0825479	+	0.996587i	$0.473694\pi$
$20$	0	0
$21$	4.32945e22	0.314482
$22$	−2.82076e23	−0.907756
$23$	3.48881e23	0.515750	0.257875	−	0.966178i	$-0.416978\pi$
$23$	3.48881e23	0.515750	0.257875	+	0.966178i	$0.416978\pi$
$24$	−2.36784e24	−1.66209
$25$	0	0
$26$	8.17268e24	1.41361
$27$	6.77748e24	0.605623
$28$	−8.88473e23	−0.0420125
$29$	3.21628e25	0.822979	0.411489	−	0.911415i	$-0.365009\pi$
$29$	3.21628e25	0.822979	0.411489	+	0.911415i	$0.365009\pi$
$30$	0	0
$31$	3.41044e25	0.271632	0.135816	−	0.990734i	$-0.456634\pi$
$31$	3.41044e25	0.271632	0.135816	+	0.990734i	$0.456634\pi$
$32$	8.88635e25	0.406068
$33$	−5.90965e26	−1.57604
$34$	−2.18018e26	−0.344835
$35$	0	0
$36$	−4.94244e26	−0.287506
$37$	4.03624e27	1.45361	0.726804	−	0.686845i	$-0.241005\pi$
$37$	4.03624e27	1.45361	0.726804	+	0.686845i	$0.241005\pi$
$38$	6.51171e26	0.147056
$39$	1.71222e28	2.45431
$40$	0	0
$41$	8.65857e27	0.517283	0.258642	−	0.965973i	$-0.416725\pi$
$41$	8.65857e27	0.517283	0.258642	+	0.965973i	$0.416725\pi$
$42$	7.14832e27	0.280118
$43$	−9.89389e26	−0.0256844	−0.0128422	−	0.999918i	$-0.504088\pi$
$43$	−9.89389e26	−0.0256844	−0.0128422	+	0.999918i	$0.504088\pi$
$44$	1.21276e28	0.210548
$45$	0	0
$46$	5.76034e28	0.459395
$47$	−1.95852e29	−1.07205	−0.536025	−	0.844202i	$-0.680075\pi$
$47$	−1.95852e29	−1.07205	−0.536025	+	0.844202i	$0.680075\pi$
$48$	−3.06580e29	−1.16097
$49$	−3.63154e29	−0.958648
$50$	0	0
$51$	−4.56760e29	−0.598702
$52$	−3.51376e29	−0.327879
$53$	9.96909e29	0.666543	0.333271	−	0.942831i	$-0.391847\pi$
$53$	9.96909e29	0.666543	0.333271	+	0.942831i	$0.391847\pi$
$54$	1.11902e30	0.539447
$55$	0	0
$56$	−8.56741e29	−0.218554
$57$	1.36424e30	0.255318
$58$	5.31037e30	0.733052
$59$	3.91953e30	0.401166	0.200583	−	0.979677i	$-0.435716\pi$
$59$	3.91953e30	0.401166	0.200583	+	0.979677i	$0.435716\pi$
$60$	0	0
$61$	7.64909e29	0.0436855	0.0218428	−	0.999761i	$-0.493047\pi$
$61$	7.64909e29	0.0436855	0.0218428	+	0.999761i	$0.493047\pi$
$62$	5.63096e30	0.241951
$63$	8.71420e30	0.282988
$64$	4.51249e31	1.11241
$65$	0	0
$66$	−9.75738e31	−1.40383
$67$	1.64301e32	1.81690	0.908451	−	0.417992i	$-0.137266\pi$
$67$	1.64301e32	1.81690	0.908451	+	0.417992i	$0.137266\pi$
$68$	9.37346e30	0.0799823
$69$	1.20682e32	0.797600
$70$	0	0
$71$	7.65930e31	0.307021	0.153510	−	0.988147i	$-0.450942\pi$
$71$	7.65930e31	0.307021	0.153510	+	0.988147i	$0.450942\pi$
$72$	−4.76592e32	−1.49564
$73$	7.08063e32	1.74551	0.872754	−	0.488160i	$-0.162332\pi$
$73$	7.08063e32	1.74551	0.872754	+	0.488160i	$0.162332\pi$
$74$	6.66421e32	1.29477
$75$	0	0
$76$	−2.79964e31	−0.0341087
$77$	−2.13826e32	−0.207239
$78$	2.82704e33	2.18613
$79$	2.34599e33	1.45162	0.725809	−	0.687896i	$-0.241466\pi$
$79$	2.34599e33	1.45162	0.725809	+	0.687896i	$0.241466\pi$
$80$	0	0
$81$	−1.13900e33	−0.455027
$82$	1.42961e33	0.460760
$83$	−5.18971e33	−1.35293	−0.676467	−	0.736473i	$-0.736490\pi$
$83$	−5.18971e33	−1.35293	−0.676467	+	0.736473i	$0.736490\pi$
$84$	−3.07335e32	−0.0649717
$85$	0	0
$86$	−1.63357e32	−0.0228779
$87$	1.11255e34	1.27272
$88$	1.16944e34	1.09530
$89$	1.44578e34	1.11116	0.555582	−	0.831461i	$-0.312495\pi$
$89$	1.44578e34	1.11116	0.555582	+	0.831461i	$0.312495\pi$
$90$	0	0
$91$	6.19525e33	0.322726
$92$	−2.47660e33	−0.106554
$93$	1.17972e34	0.420075
$94$	−3.23369e34	−0.954907
$95$	0	0
$96$	3.07391e34	0.627978
$97$	2.87399e34	0.489756	0.244878	−	0.969554i	$-0.421252\pi$
$97$	2.87399e34	0.489756	0.244878	+	0.969554i	$0.421252\pi$
$98$	−5.99600e34	−0.853897
$99$	−1.18948e35	−1.41821
$100$	0	0
$101$	1.13198e35	0.951079	0.475539	−	0.879694i	$-0.342253\pi$
$101$	1.13198e35	0.951079	0.475539	+	0.879694i	$0.342253\pi$
$102$	−7.54153e34	−0.533282
$103$	−2.53635e35	−1.51202	−0.756011	−	0.654559i	$-0.772855\pi$
$103$	−2.53635e35	−1.51202	−0.756011	+	0.654559i	$0.772855\pi$
$104$	−3.38826e35	−1.70567
$105$	0	0
$106$	1.64599e35	0.593710
$107$	3.63939e35	1.11381	0.556907	−	0.830575i	$-0.311988\pi$
$107$	3.63939e35	1.11381	0.556907	+	0.830575i	$0.311988\pi$
$108$	−4.81113e34	−0.125121
$109$	−4.65371e34	−0.103000	−0.0514998	−	0.998673i	$-0.516400\pi$
$109$	−4.65371e34	−0.103000	−0.0514998	+	0.998673i	$0.516400\pi$
$110$	0	0
$111$	1.39619e36	2.24798
$112$	−1.10928e35	−0.152660
$113$	2.18346e35	0.257201	0.128601	−	0.991696i	$-0.458951\pi$
$113$	2.18346e35	0.257201	0.128601	+	0.991696i	$0.458951\pi$
$114$	2.25249e35	0.227419
$115$	0	0
$116$	−2.28314e35	−0.170027
$117$	3.44632e36	2.20853
$118$	6.47150e35	0.357330
$119$	−1.65267e35	−0.0787254
$120$	0	0
$121$	1.08456e35	0.0385932
$122$	1.26293e35	0.0389120
$123$	2.99511e36	0.799970
$124$	−2.42097e35	−0.0561191
$125$	0	0
$126$	1.43880e36	0.252066
$127$	−4.19558e36	−0.640070	−0.320035	−	0.947406i	$-0.603695\pi$
$127$	−4.19558e36	−0.640070	−0.320035	+	0.947406i	$0.603695\pi$
$128$	4.39721e36	0.584793
$129$	−3.42243e35	−0.0397205
$130$	0	0
$131$	2.40631e36	0.213355	0.106678	−	0.994294i	$-0.465979\pi$
$131$	2.40631e36	0.213355	0.106678	+	0.994294i	$0.465979\pi$
$132$	4.19509e36	0.325610
$133$	4.93616e35	0.0335727
$134$	2.71276e37	1.61837
$135$	0	0
$136$	9.03869e36	0.416078
$137$	2.14718e37	0.869477	0.434739	−	0.900557i	$-0.356841\pi$
$137$	2.14718e37	0.869477	0.434739	+	0.900557i	$0.356841\pi$
$138$	1.99258e37	0.710446
$139$	2.63209e37	0.827068	0.413534	−	0.910489i	$-0.364294\pi$
$139$	2.63209e37	0.827068	0.413534	+	0.910489i	$0.364294\pi$
$140$	0	0
$141$	−6.77477e37	−1.65791
$142$	1.26462e37	0.273473
$143$	−8.45645e37	−1.61736
$144$	−6.17076e37	−1.04471
$145$	0	0
$146$	1.16908e38	1.55478
$147$	−1.25620e38	−1.48253
$148$	−2.86521e37	−0.300314
$149$	−1.74389e38	−1.62465	−0.812324	−	0.583206i	$-0.801798\pi$
$149$	−1.74389e38	−1.62465	−0.812324	+	0.583206i	$0.801798\pi$
$150$	0	0
$151$	−1.40947e38	−1.03982	−0.519912	−	0.854220i	$-0.674035\pi$
$151$	−1.40947e38	−1.03982	−0.519912	+	0.854220i	$0.674035\pi$
$152$	−2.69965e37	−0.177437
$153$	−9.19355e37	−0.538745
$154$	−3.53046e37	−0.184595
$155$	0	0
$156$	−1.21546e38	−0.507059
$157$	−1.49924e38	−0.559277	−0.279639	−	0.960105i	$-0.590215\pi$
$157$	−1.49924e38	−0.559277	−0.279639	+	0.960105i	$0.590215\pi$
$158$	3.87345e38	1.29300
$159$	3.44844e38	1.03080
$160$	0	0
$161$	4.36659e37	0.104879
$162$	−1.88060e38	−0.405306
$163$	−8.60787e38	−1.66576	−0.832880	−	0.553453i	$-0.813310\pi$
$163$	−8.60787e38	−1.66576	−0.832880	+	0.553453i	$0.813310\pi$
$164$	−6.14646e37	−0.106870
$165$	0	0
$166$	−8.56869e38	−1.20510
$167$	9.23344e38	1.16903	0.584515	−	0.811383i	$-0.301285\pi$
$167$	9.23344e38	1.16903	0.584515	+	0.811383i	$0.301285\pi$
$168$	−2.96358e38	−0.337991
$169$	1.47733e39	1.51866
$170$	0	0
$171$	2.74591e38	0.229749
$172$	7.02337e36	0.00530638
$173$	1.33161e39	0.909012	0.454506	−	0.890744i	$-0.349816\pi$
$173$	1.33161e39	0.909012	0.454506	+	0.890744i	$0.349816\pi$
$174$	1.83693e39	1.13365
$175$	0	0
$176$	1.51416e39	0.765066
$177$	1.35582e39	0.620396
$178$	2.38712e39	0.989748
$179$	6.27202e38	0.235765	0.117883	−	0.993028i	$-0.462389\pi$
$179$	6.27202e38	0.235765	0.117883	+	0.993028i	$0.462389\pi$
$180$	0	0
$181$	−2.39965e39	−0.742629	−0.371315	−	0.928507i	$-0.621093\pi$
$181$	−2.39965e39	−0.742629	−0.371315	+	0.928507i	$0.621093\pi$
$182$	1.02289e39	0.287462
$183$	2.64592e38	0.0675590
$184$	−2.38815e39	−0.554305
$185$	0	0
$186$	1.94782e39	0.374174
$187$	2.25588e39	0.394537
$188$	1.39029e39	0.221485
$189$	8.48269e38	0.123155
$190$	0	0
$191$	8.14518e39	0.983596	0.491798	−	0.870709i	$-0.336340\pi$
$191$	8.14518e39	0.983596	0.491798	+	0.870709i	$0.336340\pi$
$192$	1.56093e40	1.72033
$193$	−1.38549e40	−1.39428	−0.697139	−	0.716936i	$-0.745544\pi$
$193$	−1.38549e40	−1.39428	−0.697139	+	0.716936i	$0.745544\pi$
$194$	4.74522e39	0.436240
$195$	0	0
$196$	2.57792e39	0.198056
$197$	1.15539e40	0.812026	0.406013	−	0.913867i	$-0.366919\pi$
$197$	1.15539e40	0.812026	0.406013	+	0.913867i	$0.366919\pi$
$198$	−1.96394e40	−1.26324
$199$	−4.76691e39	−0.280742	−0.140371	−	0.990099i	$-0.544830\pi$
$199$	−4.76691e39	−0.280742	−0.140371	+	0.990099i	$0.544830\pi$
$200$	0	0
$201$	5.68340e40	2.80981
$202$	1.86901e40	0.847155
$203$	4.02549e39	0.167355
$204$	3.24241e39	0.123691
$205$	0	0
$206$	−4.18775e40	−1.34680
$207$	2.42906e40	0.717725
$208$	−4.38702e40	−1.19141
$209$	−6.73781e39	−0.168251
$210$	0	0
$211$	−1.87354e40	−0.396022	−0.198011	−	0.980200i	$-0.563448\pi$
$211$	−1.87354e40	−0.396022	−0.198011	+	0.980200i	$0.563448\pi$
$212$	−7.07676e39	−0.137707
$213$	2.64945e40	0.474803
$214$	6.00896e40	0.992107
$215$	0	0
$216$	−4.63930e40	−0.650896
$217$	4.26851e39	0.0552371
$218$	−7.68370e39	−0.0917448
$219$	2.44929e41	2.69940
$220$	0	0
$221$	−6.53603e40	−0.614398
$222$	2.30524e41	2.00234
$223$	7.12100e40	0.571750	0.285875	−	0.958267i	$-0.407716\pi$
$223$	7.12100e40	0.571750	0.285875	+	0.958267i	$0.407716\pi$
$224$	1.11222e40	0.0825750
$225$	0	0
$226$	3.60510e40	0.229097
$227$	1.04005e41	0.611787	0.305893	−	0.952066i	$-0.401045\pi$
$227$	1.04005e41	0.611787	0.305893	+	0.952066i	$0.401045\pi$
$228$	−9.68434e39	−0.0527485
$229$	1.82859e41	0.922564	0.461282	−	0.887254i	$-0.347390\pi$
$229$	1.82859e41	0.922564	0.461282	+	0.887254i	$0.347390\pi$
$230$	0	0
$231$	−7.39652e40	−0.320493
$232$	−2.20160e41	−0.884501
$233$	−1.57847e41	−0.588177	−0.294088	−	0.955778i	$-0.595016\pi$
$233$	−1.57847e41	−0.588177	−0.294088	+	0.955778i	$0.595016\pi$
$234$	5.69019e41	1.96720
$235$	0	0
$236$	−2.78236e40	−0.0828806
$237$	8.11510e41	2.24490
$238$	−2.72871e40	−0.0701231
$239$	5.00984e41	1.19636	0.598178	−	0.801363i	$-0.295892\pi$
$239$	5.00984e41	1.19636	0.598178	+	0.801363i	$0.295892\pi$
$240$	0	0
$241$	−3.33164e41	−0.687638	−0.343819	−	0.939036i	$-0.611721\pi$
$241$	−3.33164e41	−0.687638	−0.343819	+	0.939036i	$0.611721\pi$
$242$	1.79072e40	0.0343762
$243$	−7.33084e41	−1.30931
$244$	−5.42986e39	−0.00902540
$245$	0	0
$246$	4.94521e41	0.712558
$247$	1.95217e41	0.262011
$248$	−2.33451e41	−0.291938
$249$	−1.79519e42	−2.09229
$250$	0	0
$251$	1.52760e42	1.54782	0.773909	−	0.633297i	$-0.218299\pi$
$251$	1.52760e42	1.54782	0.773909	+	0.633297i	$0.218299\pi$
$252$	−6.18595e40	−0.0584652
$253$	−5.96035e41	−0.525608
$254$	−6.92730e41	−0.570130
$255$	0	0
$256$	−8.24460e41	−0.591521
$257$	2.72482e42	1.82603	0.913016	−	0.407925i	$-0.133747\pi$
$257$	2.72482e42	1.82603	0.913016	+	0.407925i	$0.133747\pi$
$258$	−5.65074e40	−0.0353802
$259$	5.05176e41	0.295595
$260$	0	0
$261$	2.23932e42	1.14527
$262$	3.97303e41	0.190042
$263$	−4.22055e40	−0.0188861	−0.00944307	−	0.999955i	$-0.503006\pi$
$263$	−4.22055e40	−0.0188861	−0.00944307	+	0.999955i	$0.503006\pi$
$264$	4.04526e42	1.69386
$265$	0	0
$266$	8.15005e40	0.0299042
$267$	5.00116e42	1.71840
$268$	−1.16632e42	−0.375371
$269$	−1.30618e42	−0.393858	−0.196929	−	0.980418i	$-0.563097\pi$
$269$	−1.30618e42	−0.393858	−0.196929	+	0.980418i	$0.563097\pi$
$270$	0	0
$271$	−4.11918e41	−0.109106	−0.0545529	−	0.998511i	$-0.517373\pi$
$271$	−4.11918e41	−0.109106	−0.0545529	+	0.998511i	$0.517373\pi$
$272$	1.17030e42	0.290631
$273$	2.14302e42	0.499091
$274$	3.54519e42	0.774470
$275$	0	0
$276$	−8.56689e41	−0.164784
$277$	−7.38232e42	−1.33290	−0.666449	−	0.745551i	$-0.732187\pi$
$277$	−7.38232e42	−1.33290	−0.666449	+	0.745551i	$0.732187\pi$
$278$	4.34582e42	0.736694
$279$	2.37451e42	0.378007
$280$	0	0
$281$	4.08223e42	0.573505	0.286752	−	0.958005i	$-0.407424\pi$
$281$	4.08223e42	0.573505	0.286752	+	0.958005i	$0.407424\pi$
$282$	−1.11858e43	−1.47675
$283$	1.06503e43	1.32159	0.660796	−	0.750565i	$-0.270219\pi$
$283$	1.06503e43	1.32159	0.660796	+	0.750565i	$0.270219\pi$
$284$	−5.43711e41	−0.0634303
$285$	0	0
$286$	−1.39624e43	−1.44063
$287$	1.08371e42	0.105191
$288$	6.18708e42	0.565089
$289$	−9.88997e42	−0.850125
$290$	0	0
$291$	9.94151e42	0.757399
$292$	−5.02633e42	−0.360621
$293$	−1.90474e43	−1.28722	−0.643610	−	0.765353i	$-0.722564\pi$
$293$	−1.90474e43	−1.28722	−0.643610	+	0.765353i	$0.722564\pi$
$294$	−2.07410e43	−1.32054
$295$	0	0
$296$	−2.76288e43	−1.56227
$297$	−1.15788e43	−0.617199
$298$	−2.87932e43	−1.44712
$299$	1.72691e43	0.818510
$300$	0	0
$301$	−1.23832e41	−0.00522298
$302$	−2.32717e43	−0.926203
$303$	3.91569e43	1.47083
$304$	−3.49543e42	−0.123940
$305$	0	0
$306$	−1.51794e43	−0.479877
$307$	1.39752e43	0.417288	0.208644	−	0.977992i	$-0.433095\pi$
$307$	1.39752e43	0.417288	0.208644	+	0.977992i	$0.433095\pi$
$308$	1.51789e42	0.0428156
$309$	−8.77359e43	−2.33832
$310$	0	0
$311$	2.22377e43	0.529399	0.264700	−	0.964331i	$-0.414727\pi$
$311$	2.22377e43	0.529399	0.264700	+	0.964331i	$0.414727\pi$
$312$	−1.17205e44	−2.63778
$313$	−3.63171e43	−0.772833	−0.386417	−	0.922324i	$-0.626287\pi$
$313$	−3.63171e43	−0.772833	−0.386417	+	0.922324i	$0.626287\pi$
$314$	−2.47538e43	−0.498165
$315$	0	0
$316$	−1.66535e43	−0.299903
$317$	−5.29385e43	−0.902058	−0.451029	−	0.892509i	$-0.648943\pi$
$317$	−5.29385e43	−0.902058	−0.451029	+	0.892509i	$0.648943\pi$
$318$	5.69370e43	0.918163
$319$	−5.49476e43	−0.838709
$320$	0	0
$321$	1.25891e44	1.72249
$322$	7.20964e42	0.0934191
$323$	−5.20769e42	−0.0639147
$324$	8.08544e42	0.0940083
$325$	0	0
$326$	−1.42124e44	−1.48374
$327$	−1.60978e43	−0.159287
$328$	−5.92693e43	−0.555953
$329$	−2.45128e43	−0.218004
$330$	0	0
$331$	6.25551e43	0.500349	0.250174	−	0.968201i	$-0.419512\pi$
$331$	6.25551e43	0.500349	0.250174	+	0.968201i	$0.419512\pi$
$332$	3.68402e43	0.279515
$333$	2.81022e44	2.02286
$334$	1.52453e44	1.04129
$335$	0	0
$336$	−3.83715e43	−0.236087
$337$	1.04185e44	0.608529	0.304264	−	0.952588i	$-0.401589\pi$
$337$	1.04185e44	0.608529	0.304264	+	0.952588i	$0.401589\pi$
$338$	2.43920e44	1.35271
$339$	7.55289e43	0.397757
$340$	0	0
$341$	−5.82647e43	−0.276824
$342$	4.53375e43	0.204645
$343$	−9.28652e43	−0.398296
$344$	6.77253e42	0.0276044
$345$	0	0
$346$	2.19861e44	0.809685
$347$	3.07657e44	1.07721	0.538606	−	0.842557i	$-0.318951\pi$
$347$	3.07657e44	1.07721	0.538606	+	0.842557i	$0.318951\pi$
$348$	−7.89769e43	−0.262944
$349$	−2.62767e44	−0.832005	−0.416003	−	0.909363i	$-0.636569\pi$
$349$	−2.62767e44	−0.832005	−0.416003	+	0.909363i	$0.636569\pi$
$350$	0	0
$351$	3.35476e44	0.961140
$352$	−1.51816e44	−0.413830
$353$	−7.06671e44	−1.83299	−0.916494	−	0.400048i	$-0.868994\pi$
$353$	−7.06671e44	−1.83299	−0.916494	+	0.400048i	$0.868994\pi$
$354$	2.23858e44	0.552606
$355$	0	0
$356$	−1.02632e44	−0.229566
$357$	−5.71681e43	−0.121748
$358$	1.03557e44	0.210003
$359$	−5.35788e44	−1.03476	−0.517380	−	0.855756i	$-0.673093\pi$
$359$	−5.35788e44	−1.03476	−0.517380	+	0.855756i	$0.673093\pi$
$360$	0	0
$361$	−5.55104e44	−0.972743
$362$	−3.96204e44	−0.661483
$363$	3.75165e43	0.0596838
$364$	−4.39782e43	−0.0666750
$365$	0	0
$366$	4.36866e43	0.0601768
$367$	3.00056e44	0.394045	0.197022	−	0.980399i	$-0.436873\pi$
$367$	3.00056e44	0.394045	0.197022	+	0.980399i	$0.436873\pi$
$368$	−3.09210e44	−0.387183
$369$	6.02849e44	0.719858
$370$	0	0
$371$	1.24773e44	0.135543
$372$	−8.37447e43	−0.0867872
$373$	−1.08201e45	−1.06986	−0.534932	−	0.844895i	$-0.679663\pi$
$373$	−1.08201e45	−1.06986	−0.534932	+	0.844895i	$0.679663\pi$
$374$	3.72466e44	0.351426
$375$	0	0
$376$	1.34064e45	1.15219
$377$	1.59201e45	1.30609
$378$	1.40057e44	0.109698
$379$	1.21847e45	0.911229	0.455614	−	0.890177i	$-0.349420\pi$
$379$	1.21847e45	0.911229	0.455614	+	0.890177i	$0.349420\pi$
$380$	0	0
$381$	−1.45131e45	−0.989858
$382$	1.34484e45	0.876119
$383$	9.53201e43	0.0593207	0.0296603	−	0.999560i	$-0.490557\pi$
$383$	9.53201e43	0.0593207	0.0296603	+	0.999560i	$0.490557\pi$
$384$	1.52105e45	0.904373
$385$	0	0
$386$	−2.28757e45	−1.24193
$387$	−6.88857e43	−0.0357427
$388$	−2.04016e44	−0.101183
$389$	1.90493e45	0.903152	0.451576	−	0.892233i	$-0.350862\pi$
$389$	1.90493e45	0.903152	0.451576	+	0.892233i	$0.350862\pi$
$390$	0	0
$391$	−4.60678e44	−0.199666
$392$	2.48585e45	1.03031
$393$	8.32373e44	0.329950
$394$	1.90766e45	0.723296
$395$	0	0
$396$	8.44376e44	0.293002
$397$	−3.96399e45	−1.31613	−0.658065	−	0.752961i	$-0.728625\pi$
$397$	−3.96399e45	−1.31613	−0.658065	+	0.752961i	$0.728625\pi$
$398$	−7.87060e44	−0.250066
$399$	1.70748e44	0.0519196
$400$	0	0
$401$	−5.53039e44	−0.154074	−0.0770369	−	0.997028i	$-0.524546\pi$
$401$	−5.53039e44	−0.154074	−0.0770369	+	0.997028i	$0.524546\pi$
$402$	9.38381e45	2.50278
$403$	1.68812e45	0.431088
$404$	−8.03562e44	−0.196492
$405$	0	0
$406$	6.64646e44	0.149068
$407$	−6.89560e45	−1.48139
$408$	3.12660e45	0.643457
$409$	3.35495e45	0.661498	0.330749	−	0.943719i	$-0.392699\pi$
$409$	3.35495e45	0.661498	0.330749	+	0.943719i	$0.392699\pi$
$410$	0	0
$411$	7.42738e45	1.34463
$412$	1.80048e45	0.312383
$413$	4.90568e44	0.0815781
$414$	4.01061e45	0.639299
$415$	0	0
$416$	4.39862e45	0.644441
$417$	9.10474e45	1.27905
$418$	−1.11247e45	−0.149867
$419$	−7.69138e45	−0.993708	−0.496854	−	0.867834i	$-0.665512\pi$
$419$	−7.69138e45	−0.993708	−0.496854	+	0.867834i	$0.665512\pi$
$420$	0	0
$421$	−2.77229e45	−0.329535	−0.164767	−	0.986332i	$-0.552687\pi$
$421$	−2.77229e45	−0.329535	−0.164767	+	0.986332i	$0.552687\pi$
$422$	−3.09338e45	−0.352749
$423$	−1.36361e46	−1.49188
$424$	−6.82401e45	−0.716370
$425$	0	0
$426$	4.37449e45	0.422921
$427$	9.57360e43	0.00888357
$428$	−2.58349e45	−0.230113
$429$	−2.92520e46	−2.50122
$430$	0	0
$431$	6.18484e45	0.487502	0.243751	−	0.969838i	$-0.421622\pi$
$431$	6.18484e45	0.487502	0.243751	+	0.969838i	$0.421622\pi$
$432$	−6.00681e45	−0.454651
$433$	−2.21783e46	−1.61209	−0.806047	−	0.591852i	$-0.798397\pi$
$433$	−2.21783e46	−1.61209	−0.806047	+	0.591852i	$0.798397\pi$
$434$	7.04770e44	0.0492014
$435$	0	0
$436$	3.30353e44	0.0212796
$437$	1.37594e45	0.0851482
$438$	4.04399e46	2.40444
$439$	1.91766e45	0.109557	0.0547787	−	0.998499i	$-0.482555\pi$
$439$	1.91766e45	0.109557	0.0547787	+	0.998499i	$0.482555\pi$
$440$	0	0
$441$	−2.52844e46	−1.33407
$442$	−1.07916e46	−0.547263
$443$	3.00864e46	1.46658	0.733290	−	0.679916i	$-0.237984\pi$
$443$	3.00864e46	1.46658	0.733290	+	0.679916i	$0.237984\pi$
$444$	−9.91114e45	−0.464431
$445$	0	0
$446$	1.17574e46	0.509275
$447$	−6.03235e46	−2.51249
$448$	5.64783e45	0.226212
$449$	5.68788e45	0.219099	0.109549	−	0.993981i	$-0.465059\pi$
$449$	5.68788e45	0.219099	0.109549	+	0.993981i	$0.465059\pi$
$450$	0	0
$451$	−1.47925e46	−0.527171
$452$	−1.54997e45	−0.0531376
$453$	−4.87555e46	−1.60807
$454$	1.71721e46	0.544937
$455$	0	0
$456$	−9.33846e45	−0.274404
$457$	−4.67626e46	−1.32241	−0.661204	−	0.750206i	$-0.729954\pi$
$457$	−4.67626e46	−1.32241	−0.661204	+	0.750206i	$0.729954\pi$
$458$	3.01918e46	0.821755
$459$	−8.94930e45	−0.234459
$460$	0	0
$461$	−3.72978e46	−0.905560	−0.452780	−	0.891622i	$-0.649568\pi$
$461$	−3.72978e46	−0.905560	−0.452780	+	0.891622i	$0.649568\pi$
$462$	−1.22123e46	−0.285472
$463$	3.67649e46	0.827497	0.413748	−	0.910391i	$-0.364219\pi$
$463$	3.67649e46	0.827497	0.413748	+	0.910391i	$0.364219\pi$
$464$	−2.85056e46	−0.617825
$465$	0	0
$466$	−2.60620e46	−0.523907
$467$	2.37743e46	0.460323	0.230161	−	0.973152i	$-0.426075\pi$
$467$	2.37743e46	0.460323	0.230161	+	0.973152i	$0.426075\pi$
$468$	−2.44644e46	−0.456280
$469$	2.05639e46	0.369472
$470$	0	0
$471$	−5.18607e46	−0.864914
$472$	−2.68298e46	−0.431155
$473$	1.69029e45	0.0261753
$474$	1.33988e47	1.99960
$475$	0	0
$476$	1.17318e45	0.0162646
$477$	6.94094e46	0.927569
$478$	8.27170e46	1.06563
$479$	−8.80315e46	−1.09337	−0.546684	−	0.837339i	$-0.684110\pi$
$479$	−8.80315e46	−1.09337	−0.546684	+	0.837339i	$0.684110\pi$
$480$	0	0
$481$	1.99788e47	2.30691
$482$	−5.50084e46	−0.612500
$483$	1.51046e46	0.162194
$484$	−7.69900e44	−0.00797334
$485$	0	0
$486$	−1.21039e47	−1.16625
$487$	−7.13443e46	−0.663136	−0.331568	−	0.943431i	$-0.607578\pi$
$487$	−7.13443e46	−0.663136	−0.331568	+	0.943431i	$0.607578\pi$
$488$	−5.23593e45	−0.0469512
$489$	−2.97758e47	−2.57607
$490$	0	0
$491$	8.49115e46	0.683975	0.341988	−	0.939704i	$-0.388900\pi$
$491$	8.49115e46	0.683975	0.341988	+	0.939704i	$0.388900\pi$
$492$	−2.12614e46	−0.165273
$493$	−4.24693e46	−0.318606
$494$	3.22321e46	0.233382
$495$	0	0
$496$	−3.02265e46	−0.203919
$497$	9.58638e45	0.0624335
$498$	−2.96402e47	−1.86367
$499$	−1.75876e47	−1.06770	−0.533848	−	0.845581i	$-0.679255\pi$
$499$	−1.75876e47	−1.06770	−0.533848	+	0.845581i	$0.679255\pi$
$500$	0	0
$501$	3.19397e47	1.80789
$502$	2.52221e47	1.37869
$503$	−1.24051e47	−0.654880	−0.327440	−	0.944872i	$-0.606186\pi$
$503$	−1.24051e47	−0.654880	−0.327440	+	0.944872i	$0.606186\pi$
$504$	−5.96502e46	−0.304143
$505$	0	0
$506$	−9.84108e46	−0.468175
$507$	5.11027e47	2.34858
$508$	2.97832e46	0.132238
$509$	3.71512e47	1.59372	0.796859	−	0.604166i	$-0.206493\pi$
$509$	3.71512e47	1.59372	0.796859	+	0.604166i	$0.206493\pi$
$510$	0	0
$511$	8.86212e46	0.354954
$512$	−2.87213e47	−1.11168
$513$	2.67296e46	0.0999857
$514$	4.49893e47	1.62650
$515$	0	0
$516$	2.42948e45	0.00820623
$517$	3.34597e47	1.09254
$518$	8.34092e46	0.263295
$519$	4.60621e47	1.40577
$520$	0	0
$521$	7.89659e45	0.0225309	0.0112655	−	0.999937i	$-0.496414\pi$
$521$	7.89659e45	0.0225309	0.0112655	+	0.999937i	$0.496414\pi$
$522$	3.69732e47	1.02012
$523$	−1.18122e47	−0.315175	−0.157588	−	0.987505i	$-0.550372\pi$
$523$	−1.18122e47	−0.315175	−0.157588	+	0.987505i	$0.550372\pi$
$524$	−1.70816e46	−0.0440790
$525$	0	0
$526$	−6.96851e45	−0.0168225
$527$	−4.50331e46	−0.105159
$528$	5.23767e47	1.18316
$529$	−3.35870e47	−0.734001
$530$	0	0
$531$	2.72895e47	0.558267
$532$	−3.50403e45	−0.00693609
$533$	4.28587e47	0.820943
$534$	8.25738e47	1.53063
$535$	0	0
$536$	−1.12467e48	−1.95272
$537$	2.16958e47	0.364607
$538$	−2.15663e47	−0.350821
$539$	6.20419e47	0.976971
$540$	0	0
$541$	−6.62658e47	−0.977997	−0.488998	−	0.872285i	$-0.662638\pi$
$541$	−6.62658e47	−0.977997	−0.488998	+	0.872285i	$0.662638\pi$
$542$	−6.80114e46	−0.0971839
$543$	−8.30070e47	−1.14846
$544$	−1.17340e47	−0.157204
$545$	0	0
$546$	3.53832e47	0.444555
$547$	1.12424e47	0.136798	0.0683990	−	0.997658i	$-0.478211\pi$
$547$	1.12424e47	0.136798	0.0683990	+	0.997658i	$0.478211\pi$
$548$	−1.52422e47	−0.179633
$549$	5.32564e46	0.0607933
$550$	0	0
$551$	1.26846e47	0.135870
$552$	−8.26092e47	−0.857224
$553$	2.93624e47	0.295190
$554$	−1.21889e48	−1.18725
$555$	0	0
$556$	−1.86844e47	−0.170872
$557$	−6.68090e47	−0.592064	−0.296032	−	0.955178i	$-0.595664\pi$
$557$	−6.68090e47	−0.592064	−0.296032	+	0.955178i	$0.595664\pi$
$558$	3.92053e47	0.336702
$559$	−4.89734e46	−0.0407618
$560$	0	0
$561$	7.80339e47	0.610145
$562$	6.74014e47	0.510838
$563$	−2.47733e48	−1.82007	−0.910033	−	0.414536i	$-0.863944\pi$
$563$	−2.47733e48	−1.82007	−0.910033	+	0.414536i	$0.863944\pi$
$564$	4.80921e47	0.342523
$565$	0	0
$566$	1.75846e48	1.17718
$567$	−1.42558e47	−0.0925309
$568$	−5.24292e47	−0.329972
$569$	8.59661e47	0.524641	0.262321	−	0.964981i	$-0.415512\pi$
$569$	8.59661e47	0.524641	0.262321	+	0.964981i	$0.415512\pi$
$570$	0	0
$571$	−3.39185e48	−1.94673	−0.973364	−	0.229266i	$-0.926367\pi$
$571$	−3.39185e48	−1.94673	−0.973364	+	0.229266i	$0.926367\pi$
$572$	6.00298e47	0.334146
$573$	2.81753e48	1.52112
$574$	1.78930e47	0.0936968
$575$	0	0
$576$	3.14180e48	1.54805
$577$	−2.12534e48	−1.01590	−0.507951	−	0.861386i	$-0.669597\pi$
$577$	−2.12534e48	−1.01590	−0.507951	+	0.861386i	$0.669597\pi$
$578$	−1.63292e48	−0.757232
$579$	−4.79258e48	−2.15623
$580$	0	0
$581$	−6.49544e47	−0.275123
$582$	1.64143e48	0.674639
$583$	−1.70314e48	−0.679283
$584$	−4.84681e48	−1.87599
$585$	0	0
$586$	−3.14491e48	−1.14657
$587$	−1.06269e48	−0.376044	−0.188022	−	0.982165i	$-0.560208\pi$
$587$	−1.06269e48	−0.376044	−0.188022	+	0.982165i	$0.560208\pi$
$588$	8.91737e47	0.306290
$589$	1.34504e47	0.0448453
$590$	0	0
$591$	3.99665e48	1.25578
$592$	−3.57728e48	−1.09125
$593$	3.98260e48	1.17953	0.589766	−	0.807574i	$-0.299220\pi$
$593$	3.98260e48	1.17953	0.589766	+	0.807574i	$0.299220\pi$
$594$	−1.91176e48	−0.549758
$595$	0	0
$596$	1.23794e48	0.335651
$597$	−1.64894e48	−0.434163
$598$	2.85129e48	0.729072
$599$	5.14535e48	1.27775	0.638874	−	0.769311i	$-0.279401\pi$
$599$	5.14535e48	1.27775	0.638874	+	0.769311i	$0.279401\pi$
$600$	0	0
$601$	−1.83878e48	−0.430751	−0.215375	−	0.976531i	$-0.569098\pi$
$601$	−1.83878e48	−0.430751	−0.215375	+	0.976531i	$0.569098\pi$
$602$	−2.04458e46	−0.00465227
$603$	1.14394e49	2.52842
$604$	1.00054e48	0.214827
$605$	0	0
$606$	6.46516e48	1.31011
$607$	−2.06846e48	−0.407236	−0.203618	−	0.979050i	$-0.565270\pi$
$607$	−2.06846e48	−0.407236	−0.203618	+	0.979050i	$0.565270\pi$
$608$	3.50467e47	0.0670401
$609$	1.39247e48	0.258812
$610$	0	0
$611$	−9.69439e48	−1.70137
$612$	6.52623e47	0.111304
$613$	−1.02050e48	−0.169143	−0.0845717	−	0.996417i	$-0.526952\pi$
$613$	−1.02050e48	−0.169143	−0.0845717	+	0.996417i	$0.526952\pi$
$614$	2.30743e48	0.371691
$615$	0	0
$616$	1.46367e48	0.222732
$617$	3.46313e48	0.512246	0.256123	−	0.966644i	$-0.417555\pi$
$617$	3.46313e48	0.512246	0.256123	+	0.966644i	$0.417555\pi$
$618$	−1.44860e49	−2.08281
$619$	6.56428e48	0.917488	0.458744	−	0.888568i	$-0.348299\pi$
$619$	6.56428e48	0.917488	0.458744	+	0.888568i	$0.348299\pi$
$620$	0	0
$621$	2.36453e48	0.312350
$622$	3.67165e48	0.471552
$623$	1.80954e48	0.225958
$624$	−1.51753e49	−1.84249
$625$	0	0
$626$	−5.99629e48	−0.688386
$627$	−2.33070e48	−0.260198
$628$	1.06427e48	0.115546
$629$	−5.32965e48	−0.562746
$630$	0	0
$631$	5.18692e48	0.518079	0.259039	−	0.965867i	$-0.416594\pi$
$631$	5.18692e48	0.518079	0.259039	+	0.965867i	$0.416594\pi$
$632$	−1.60587e49	−1.56013
$633$	−6.48082e48	−0.612442
$634$	−8.74063e48	−0.803490
$635$	0	0
$636$	−2.44795e48	−0.212962
$637$	−1.79756e49	−1.52140
$638$	−9.07235e48	−0.747064
$639$	5.33275e48	0.427254
$640$	0	0
$641$	−6.15569e48	−0.466940	−0.233470	−	0.972364i	$-0.575008\pi$
$641$	−6.15569e48	−0.466940	−0.233470	+	0.972364i	$0.575008\pi$
$642$	2.07858e49	1.53428
$643$	6.50853e48	0.467510	0.233755	−	0.972296i	$-0.424899\pi$
$643$	6.50853e48	0.467510	0.233755	+	0.972296i	$0.424899\pi$
$644$	−3.09971e47	−0.0216680
$645$	0	0
$646$	−8.59837e47	−0.0569308
$647$	−2.43533e49	−1.56940	−0.784698	−	0.619878i	$-0.787182\pi$
$647$	−2.43533e49	−1.56940	−0.784698	+	0.619878i	$0.787182\pi$
$648$	7.79667e48	0.489042
$649$	−6.69620e48	−0.408833
$650$	0	0
$651$	1.47654e48	0.0854233
$652$	6.11047e48	0.344145
$653$	−4.33343e48	−0.237602	−0.118801	−	0.992918i	$-0.537905\pi$
$653$	−4.33343e48	−0.237602	−0.118801	+	0.992918i	$0.537905\pi$
$654$	−2.65789e48	−0.141882
$655$	0	0
$656$	−7.67401e48	−0.388334
$657$	4.92986e49	2.42907
$658$	−4.04729e48	−0.194183
$659$	2.26798e49	1.05960	0.529802	−	0.848121i	$-0.322266\pi$
$659$	2.26798e49	1.05960	0.529802	+	0.848121i	$0.322266\pi$
$660$	0	0
$661$	−2.84364e49	−1.25994	−0.629969	−	0.776620i	$-0.716932\pi$
$661$	−2.84364e49	−1.25994	−0.629969	+	0.776620i	$0.716932\pi$
$662$	1.03284e49	0.445676
$663$	−2.26090e49	−0.950156
$664$	3.55245e49	1.45407
$665$	0	0
$666$	4.63992e49	1.80182
$667$	1.12210e49	0.424452
$668$	−6.55455e48	−0.241521
$669$	2.46325e49	0.884202
$670$	0	0
$671$	−1.30679e48	−0.0445205
$672$	3.84730e48	0.127701
$673$	−1.14434e49	−0.370077	−0.185039	−	0.982731i	$-0.559241\pi$
$673$	−1.14434e49	−0.370077	−0.185039	+	0.982731i	$0.559241\pi$
$674$	1.72019e49	0.542035
$675$	0	0
$676$	−1.04871e49	−0.313753
$677$	3.00594e49	0.876351	0.438175	−	0.898890i	$-0.355625\pi$
$677$	3.00594e49	0.876351	0.438175	+	0.898890i	$0.355625\pi$
$678$	1.24705e49	0.354295
$679$	3.59708e48	0.0995931
$680$	0	0
$681$	3.59766e49	0.946119
$682$	−9.62004e48	−0.246576
$683$	7.78736e49	1.94549	0.972743	−	0.231885i	$-0.0744894\pi$
$683$	7.78736e49	1.94549	0.972743	+	0.231885i	$0.0744894\pi$
$684$	−1.94924e48	−0.0474661
$685$	0	0
$686$	−1.53329e49	−0.354774
$687$	6.32535e49	1.42673
$688$	8.76886e47	0.0192817
$689$	4.93456e49	1.05782
$690$	0	0
$691$	9.61614e49	1.95945	0.979726	−	0.200340i	$-0.0642046\pi$
$691$	9.61614e49	1.95945	0.979726	+	0.200340i	$0.0642046\pi$
$692$	−9.45269e48	−0.187801
$693$	−1.48875e49	−0.288397
$694$	5.07971e49	0.959506
$695$	0	0
$696$	−7.61562e49	−1.36787
$697$	−1.14332e49	−0.200260
$698$	−4.33853e49	−0.741093
$699$	−5.46014e49	−0.909606
$700$	0	0
$701$	1.19741e49	0.189748	0.0948742	−	0.995489i	$-0.469755\pi$
$701$	1.19741e49	0.189748	0.0948742	+	0.995489i	$0.469755\pi$
$702$	5.53901e49	0.856116
$703$	1.59185e49	0.239984
$704$	−7.70923e49	−1.13368
$705$	0	0
$706$	−1.16678e50	−1.63270
$707$	1.41679e49	0.193404
$708$	−9.62454e48	−0.128173
$709$	−4.80032e49	−0.623680	−0.311840	−	0.950135i	$-0.600945\pi$
$709$	−4.80032e49	−0.623680	−0.311840	+	0.950135i	$0.600945\pi$
$710$	0	0
$711$	1.63339e50	2.02009
$712$	−9.89664e49	−1.19423
$713$	1.18984e49	0.140094
$714$	−9.43898e48	−0.108444
$715$	0	0
$716$	−4.45232e48	−0.0487089
$717$	1.73297e50	1.85015
$718$	−8.84635e49	−0.921693
$719$	−1.45387e49	−0.147832	−0.0739162	−	0.997264i	$-0.523550\pi$
$719$	−1.45387e49	−0.147832	−0.0739162	+	0.997264i	$0.523550\pi$
$720$	0	0
$721$	−3.17450e49	−0.307474
$722$	−9.16528e49	−0.866452
$723$	−1.15246e50	−1.06342
$724$	1.70344e49	0.153427
$725$	0	0
$726$	6.19432e48	0.0531622
$727$	−1.25503e50	−1.05148	−0.525742	−	0.850644i	$-0.676212\pi$
$727$	−1.25503e50	−1.05148	−0.525742	+	0.850644i	$0.676212\pi$
$728$	−4.24075e49	−0.346851
$729$	−1.96598e50	−1.56981
$730$	0	0
$731$	1.30644e48	0.00994338
$732$	−1.87826e48	−0.0139576
$733$	1.40440e50	1.01899	0.509495	−	0.860473i	$-0.329832\pi$
$733$	1.40440e50	1.01899	0.509495	+	0.860473i	$0.329832\pi$
$734$	4.95419e49	0.350988
$735$	0	0
$736$	3.10027e49	0.209430
$737$	−2.80695e50	−1.85163
$738$	9.95358e49	0.641199
$739$	2.93572e49	0.184687	0.0923435	−	0.995727i	$-0.470564\pi$
$739$	2.93572e49	0.184687	0.0923435	+	0.995727i	$0.470564\pi$
$740$	0	0
$741$	6.75281e49	0.405197
$742$	2.06012e49	0.120732
$743$	−1.10795e50	−0.634185	−0.317093	−	0.948395i	$-0.602707\pi$
$743$	−1.10795e50	−0.634185	−0.317093	+	0.948395i	$0.602707\pi$
$744$	−8.07537e49	−0.451478
$745$	0	0
$746$	−1.78650e50	−0.952960
$747$	−3.61331e50	−1.88276
$748$	−1.60138e49	−0.0815111
$749$	4.55506e49	0.226497
$750$	0	0
$751$	−4.13601e50	−1.96283	−0.981416	−	0.191892i	$-0.938538\pi$
$751$	−4.13601e50	−1.96283	−0.981416	+	0.191892i	$0.938538\pi$
$752$	1.73582e50	0.804806
$753$	5.28418e50	2.39368
$754$	2.62856e50	1.16337
$755$	0	0
$756$	−6.02161e48	−0.0254437
$757$	−3.15399e50	−1.30221	−0.651106	−	0.758987i	$-0.725695\pi$
$757$	−3.15399e50	−1.30221	−0.651106	+	0.758987i	$0.725695\pi$
$758$	2.01180e50	0.811659
$759$	−2.06176e50	−0.812845
$760$	0	0
$761$	−3.65841e50	−1.37740	−0.688702	−	0.725045i	$-0.741819\pi$
$761$	−3.65841e50	−1.37740	−0.688702	+	0.725045i	$0.741819\pi$
$762$	−2.39624e50	−0.881696
$763$	−5.82458e48	−0.0209452
$764$	−5.78202e49	−0.203210
$765$	0	0
$766$	1.57382e49	0.0528387
$767$	1.94011e50	0.636661
$768$	−2.85192e50	−0.914778
$769$	−2.07264e50	−0.649849	−0.324925	−	0.945740i	$-0.605339\pi$
$769$	−2.07264e50	−0.649849	−0.324925	+	0.945740i	$0.605339\pi$
$770$	0	0
$771$	9.42552e50	2.82393
$772$	9.83516e49	0.288057
$773$	−2.04692e50	−0.586084	−0.293042	−	0.956100i	$-0.594668\pi$
$773$	−2.04692e50	−0.586084	−0.293042	+	0.956100i	$0.594668\pi$
$774$	−1.13737e49	−0.0318371
$775$	0	0
$776$	−1.96729e50	−0.526367
$777$	1.74747e50	0.457133
$778$	3.14521e50	0.804465
$779$	3.41484e49	0.0854013
$780$	0	0
$781$	−1.30853e50	−0.312889
$782$	−7.60622e49	−0.177849
$783$	2.17983e50	0.498415
$784$	3.21860e50	0.719673
$785$	0	0
$786$	1.37432e50	0.293897
$787$	2.74398e50	0.573882	0.286941	−	0.957948i	$-0.407362\pi$
$787$	2.74398e50	0.573882	0.286941	+	0.957948i	$0.407362\pi$
$788$	−8.20177e49	−0.167764
$789$	−1.45994e49	−0.0292071
$790$	0	0
$791$	2.73282e49	0.0523025
$792$	8.14219e50	1.52423
$793$	3.78619e49	0.0693301
$794$	−6.54491e50	−1.17232
$795$	0	0
$796$	3.38388e49	0.0580012
$797$	−3.73868e50	−0.626899	−0.313450	−	0.949605i	$-0.601485\pi$
$797$	−3.73868e50	−0.626899	−0.313450	+	0.949605i	$0.601485\pi$
$798$	2.81921e49	0.0462463
$799$	2.58612e50	0.415030
$800$	0	0
$801$	1.00662e51	1.54631
$802$	−9.13117e49	−0.137238
$803$	−1.20967e51	−1.77887
$804$	−4.03447e50	−0.580505
$805$	0	0
$806$	2.78725e50	0.383983
$807$	−4.51827e50	−0.609095
$808$	−7.74862e50	−1.02218
$809$	−3.87407e50	−0.500114	−0.250057	−	0.968231i	$-0.580449\pi$
$809$	−3.87407e50	−0.500114	−0.250057	+	0.968231i	$0.580449\pi$
$810$	0	0
$811$	−9.21816e50	−1.13967	−0.569835	−	0.821759i	$-0.692993\pi$
$811$	−9.21816e50	−1.13967	−0.569835	+	0.821759i	$0.692993\pi$
$812$	−2.85758e49	−0.0345754
$813$	−1.42488e50	−0.168730
$814$	−1.13853e51	−1.31952
$815$	0	0
$816$	4.04823e50	0.449456
$817$	−3.90203e48	−0.00424038
$818$	5.53933e50	0.589216
$819$	4.31341e50	0.449110
$820$	0	0
$821$	1.64737e51	1.64357	0.821783	−	0.569801i	$-0.192980\pi$
$821$	1.64737e51	1.64357	0.821783	+	0.569801i	$0.192980\pi$
$822$	1.22633e51	1.19771
$823$	6.02163e50	0.575727	0.287864	−	0.957671i	$-0.407055\pi$
$823$	6.02163e50	0.575727	0.287864	+	0.957671i	$0.407055\pi$
$824$	1.73618e51	1.62505
$825$	0	0
$826$	8.09973e49	0.0726641
$827$	4.30476e50	0.378097	0.189048	−	0.981968i	$-0.439460\pi$
$827$	4.30476e50	0.378097	0.189048	+	0.981968i	$0.439460\pi$
$828$	−1.72432e50	−0.148282
$829$	8.88751e50	0.748300	0.374150	−	0.927368i	$-0.377935\pi$
$829$	8.88751e50	0.748300	0.374150	+	0.927368i	$0.377935\pi$
$830$	0	0
$831$	−2.55364e51	−2.06131
$832$	2.23362e51	1.76543
$833$	4.79525e50	0.371128
$834$	1.50328e51	1.13929
$835$	0	0
$836$	4.78297e49	0.0347606
$837$	2.31142e50	0.164507
$838$	−1.26992e51	−0.885126
$839$	3.76912e50	0.257280	0.128640	−	0.991691i	$-0.458939\pi$
$839$	3.76912e50	0.257280	0.128640	+	0.991691i	$0.458939\pi$
$840$	0	0
$841$	−4.92875e50	−0.322706
$842$	−4.57730e50	−0.293527
$843$	1.41210e51	0.886916
$844$	1.32997e50	0.0818179
$845$	0	0
$846$	−2.25144e51	−1.32886
$847$	1.35744e49	0.00784804
$848$	−8.83551e50	−0.500385
$849$	3.68407e51	2.04382
$850$	0	0
$851$	1.40817e51	0.749699
$852$	−1.88077e50	−0.0980940
$853$	3.00248e51	1.53417	0.767083	−	0.641547i	$-0.221707\pi$
$853$	3.00248e51	1.53417	0.767083	+	0.641547i	$0.221707\pi$
$854$	1.58069e49	0.00791286
$855$	0	0
$856$	−2.49122e51	−1.19708
$857$	2.46088e50	0.115858	0.0579291	−	0.998321i	$-0.481550\pi$
$857$	2.46088e50	0.115858	0.0579291	+	0.998321i	$0.481550\pi$
$858$	−4.82977e51	−2.22792
$859$	2.64506e51	1.19551	0.597757	−	0.801677i	$-0.296059\pi$
$859$	2.64506e51	1.19551	0.597757	+	0.801677i	$0.296059\pi$
$860$	0	0
$861$	3.74868e50	0.162676
$862$	1.02117e51	0.434233
$863$	9.93861e50	0.414130	0.207065	−	0.978327i	$-0.433609\pi$
$863$	9.93861e50	0.414130	0.207065	+	0.978327i	$0.433609\pi$
$864$	6.02270e50	0.245924
$865$	0	0
$866$	−3.66184e51	−1.43594
$867$	−3.42107e51	−1.31470
$868$	−3.03009e49	−0.0114120
$869$	−4.00794e51	−1.47936
$870$	0	0
$871$	8.13268e51	2.88347
$872$	3.18554e50	0.110699
$873$	2.00100e51	0.681550
$874$	2.27181e50	0.0758441
$875$	0	0
$876$	−1.73867e51	−0.557695
$877$	2.79832e50	0.0879842	0.0439921	−	0.999032i	$-0.485992\pi$
$877$	2.79832e50	0.0879842	0.0439921	+	0.999032i	$0.485992\pi$
$878$	3.16623e50	0.0975861
$879$	−6.58876e51	−1.99067
$880$	0	0
$881$	−5.95050e50	−0.172773	−0.0863863	−	0.996262i	$-0.527532\pi$
$881$	−5.95050e50	−0.172773	−0.0863863	+	0.996262i	$0.527532\pi$
$882$	−4.17469e51	−1.18829
$883$	3.85350e51	1.07533	0.537667	−	0.843157i	$-0.319306\pi$
$883$	3.85350e51	1.07533	0.537667	+	0.843157i	$0.319306\pi$
$884$	4.63973e50	0.126934
$885$	0	0
$886$	4.96755e51	1.30633
$887$	4.56338e50	0.117658	0.0588292	−	0.998268i	$-0.481263\pi$
$887$	4.56338e50	0.117658	0.0588292	+	0.998268i	$0.481263\pi$
$888$	−9.55716e51	−2.41603
$889$	−5.25119e50	−0.130160
$890$	0	0
$891$	1.94590e51	0.463724
$892$	−5.05498e50	−0.118123
$893$	−7.72416e50	−0.176991
$894$	−9.95996e51	−2.23795
$895$	0	0
$896$	5.50354e50	0.118919
$897$	5.97362e51	1.26581
$898$	9.39122e50	0.195158
$899$	1.09689e51	0.223548
$900$	0	0
$901$	−1.31637e51	−0.258044
$902$	−2.44237e51	−0.469567
$903$	−4.28351e49	−0.00807726
$904$	−1.49462e51	−0.276428
$905$	0	0
$906$	−8.04998e51	−1.43236
$907$	4.12286e51	0.719566	0.359783	−	0.933036i	$-0.382851\pi$
$907$	4.12286e51	0.719566	0.359783	+	0.933036i	$0.382851\pi$
$908$	−7.38298e50	−0.126395
$909$	7.88139e51	1.32353
$910$	0	0
$911$	6.95561e51	1.12399	0.561996	−	0.827140i	$-0.310034\pi$
$911$	6.95561e51	1.12399	0.561996	+	0.827140i	$0.310034\pi$
$912$	−1.20911e51	−0.191672
$913$	8.86621e51	1.37879
$914$	−7.72094e51	−1.17791
$915$	0	0
$916$	−1.29806e51	−0.190601
$917$	3.01173e50	0.0433863
$918$	−1.47761e51	−0.208840
$919$	1.23335e51	0.171027	0.0855136	−	0.996337i	$-0.472747\pi$
$919$	1.23335e51	0.171027	0.0855136	+	0.996337i	$0.472747\pi$
$920$	0	0
$921$	4.83420e51	0.645329
$922$	−6.15821e51	−0.806610
$923$	3.79125e51	0.487251
$924$	5.25057e50	0.0662136
$925$	0	0
$926$	6.07023e51	0.737076
$927$	−1.76592e52	−2.10415
$928$	2.85810e51	0.334185
$929$	−9.97208e51	−1.14422	−0.572112	−	0.820176i	$-0.693876\pi$
$929$	−9.97208e51	−1.14422	−0.572112	+	0.820176i	$0.693876\pi$
$930$	0	0
$931$	−1.43224e51	−0.158269
$932$	1.12051e51	0.121517
$933$	7.69232e51	0.818707
$934$	3.92536e51	0.410024
$935$	0	0
$936$	−2.35906e52	−2.37363
$937$	−6.01334e51	−0.593844	−0.296922	−	0.954902i	$-0.595960\pi$
$937$	−6.01334e51	−0.593844	−0.296922	+	0.954902i	$0.595960\pi$
$938$	3.39529e51	0.329100
$939$	−1.25626e52	−1.19517
$940$	0	0
$941$	1.38035e52	1.26523	0.632617	−	0.774465i	$-0.281981\pi$
$941$	1.38035e52	1.26523	0.632617	+	0.774465i	$0.281981\pi$
$942$	−8.56268e51	−0.770405
$943$	3.02081e51	0.266789
$944$	−3.47384e51	−0.301162
$945$	0	0
$946$	2.79083e50	0.0233151
$947$	9.01648e51	0.739456	0.369728	−	0.929140i	$-0.379451\pi$
$947$	9.01648e51	0.739456	0.369728	+	0.929140i	$0.379451\pi$
$948$	−5.76067e51	−0.463796
$949$	3.50482e52	2.77017
$950$	0	0
$951$	−1.83121e52	−1.39502
$952$	1.13128e51	0.0846105
$953$	−4.32450e51	−0.317549	−0.158774	−	0.987315i	$-0.550754\pi$
$953$	−4.32450e51	−0.317549	−0.158774	+	0.987315i	$0.550754\pi$
$954$	1.14601e52	0.826214
$955$	0	0
$956$	−3.55633e51	−0.247166
$957$	−1.90071e52	−1.29705
$958$	−1.45348e52	−0.973897
$959$	2.68741e51	0.176810
$960$	0	0
$961$	−1.46006e52	−0.926216
$962$	3.29869e52	2.05484
$963$	2.53391e52	1.55000
$964$	2.36503e51	0.142066
$965$	0	0
$966$	2.49391e51	0.144471
$967$	1.91085e51	0.108709	0.0543543	−	0.998522i	$-0.482690\pi$
$967$	1.91085e51	0.108709	0.0543543	+	0.998522i	$0.482690\pi$
$968$	−7.42403e50	−0.0414783
$969$	−1.80141e51	−0.0988431
$970$	0	0
$971$	2.54698e52	1.34800	0.674000	−	0.738732i	$-0.264575\pi$
$971$	2.54698e52	1.34800	0.674000	+	0.738732i	$0.264575\pi$
$972$	5.20394e51	0.270504
$973$	3.29432e51	0.168186
$974$	−1.17796e52	−0.590675
$975$	0	0
$976$	−6.77932e50	−0.0327955
$977$	−2.34465e52	−1.11410	−0.557048	−	0.830480i	$-0.688066\pi$
$977$	−2.34465e52	−1.11410	−0.557048	+	0.830480i	$0.688066\pi$
$978$	−4.91625e52	−2.29459
$979$	−2.47001e52	−1.13240
$980$	0	0
$981$	−3.24012e51	−0.143335
$982$	1.40197e52	0.609238
$983$	−1.06892e52	−0.456308	−0.228154	−	0.973625i	$-0.573269\pi$
$983$	−1.06892e52	−0.456308	−0.228154	+	0.973625i	$0.573269\pi$
$984$	−2.05021e52	−0.859772
$985$	0	0
$986$	−7.01207e51	−0.283792
$987$	−8.47931e51	−0.337140
$988$	−1.38579e51	−0.0541314
$989$	−3.45178e50	−0.0132467
$990$	0	0
$991$	1.97227e52	0.730597	0.365298	−	0.930891i	$-0.380967\pi$
$991$	1.97227e52	0.730597	0.365298	+	0.930891i	$0.380967\pi$
$992$	3.03064e51	0.110301
$993$	2.16387e52	0.773782
$994$	1.58280e51	0.0556114
$995$	0	0
$996$	1.27435e52	0.432266
$997$	1.44359e52	0.481149	0.240575	−	0.970631i	$-0.422664\pi$
$997$	1.44359e52	0.481149	0.240575	+	0.970631i	$0.422664\pi$
$998$	−2.90388e52	−0.951029
$999$	2.73555e52	0.880338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.36.a.a.1.3		3
5.2	odd	4		25.36.b.a.24.5		6
5.3	odd	4		25.36.b.a.24.2		6
5.4	even	2		1.36.a.a.1.1	✓	3
15.14	odd	2		9.36.a.b.1.3		3
20.19	odd	2		16.36.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.36.a.a.1.1	✓	3	5.4	even	2
9.36.a.b.1.3		3	15.14	odd	2
16.36.a.d.1.3		3	20.19	odd	2
25.36.a.a.1.3		3	1.1	even	1	trivial
25.36.b.a.24.2		6	5.3	odd	4
25.36.b.a.24.5		6	5.2	odd	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+165109. q^{2} +3.45913e8 q^{3} -7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14 q^{7} -6.84517e15 q^{8} +6.96245e16 q^{9} +O(q^{10})\)	\(q+165109. q^{2} +3.45913e8 q^{3} -7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14 q^{7} -6.84517e15 q^{8} +6.96245e16 q^{9} -1.70842e18 q^{11} -2.45554e18 q^{12} +4.94986e19 q^{13} +2.06651e19 q^{14} -8.86291e20 q^{16} -1.32045e21 q^{17} +1.14956e22 q^{18} +3.94388e21 q^{19} +4.32945e22 q^{21} -2.82076e23 q^{22} +3.48881e23 q^{23} -2.36784e24 q^{24} +8.17268e24 q^{26} +6.77748e24 q^{27} -8.88473e23 q^{28} +3.21628e25 q^{29} +3.41044e25 q^{31} +8.88635e25 q^{32} -5.90965e26 q^{33} -2.18018e26 q^{34} -4.94244e26 q^{36} +4.03624e27 q^{37} +6.51171e26 q^{38} +1.71222e28 q^{39} +8.65857e27 q^{41} +7.14832e27 q^{42} -9.89389e26 q^{43} +1.21276e28 q^{44} +5.76034e28 q^{46} -1.95852e29 q^{47} -3.06580e29 q^{48} -3.63154e29 q^{49} -4.56760e29 q^{51} -3.51376e29 q^{52} +9.96909e29 q^{53} +1.11902e30 q^{54} -8.56741e29 q^{56} +1.36424e30 q^{57} +5.31037e30 q^{58} +3.91953e30 q^{59} +7.64909e29 q^{61} +5.63096e30 q^{62} +8.71420e30 q^{63} +4.51249e31 q^{64} -9.75738e31 q^{66} +1.64301e32 q^{67} +9.37346e30 q^{68} +1.20682e32 q^{69} +7.65930e31 q^{71} -4.76592e32 q^{72} +7.08063e32 q^{73} +6.66421e32 q^{74} -2.79964e31 q^{76} -2.13826e32 q^{77} +2.82704e33 q^{78} +2.34599e33 q^{79} -1.13900e33 q^{81} +1.42961e33 q^{82} -5.18971e33 q^{83} -3.07335e32 q^{84} -1.63357e32 q^{86} +1.11255e34 q^{87} +1.16944e34 q^{88} +1.44578e34 q^{89} +6.19525e33 q^{91} -2.47660e33 q^{92} +1.17972e34 q^{93} -3.23369e34 q^{94} +3.07391e34 q^{96} +2.87399e34 q^{97} -5.99600e34 q^{98} -1.18948e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 139656 q^{2} + 104875308 q^{3} + 34841262144 q^{4} - 4786530564384 q^{6} - 878422149346056 q^{7} - 22\!\cdots\!00 q^{8}+ \cdots + 15\!\cdots\!51 q^{9}+O(q^{10}) \) 3 * q - 139656 * q^2 + 104875308 * q^3 + 34841262144 * q^4 - 4786530564384 * q^6 - 878422149346056 * q^7 - 22336009925337600 * q^8 + 150091978876243551 * q^9	\( 3 q - 139656 q^{2} + 104875308 q^{3} + 34841262144 q^{4} - 4786530564384 q^{6} - 878422149346056 q^{7} - 22\!\cdots\!00 q^{8}+ \cdots + 30\!\cdots\!52 q^{99}+O(q^{100}) \) 3 * q - 139656 * q^2 + 104875308 * q^3 + 34841262144 * q^4 - 4786530564384 * q^6 - 878422149346056 * q^7 - 22336009925337600 * q^8 + 150091978876243551 * q^9 - 1157945428549987044 * q^11 + 22548891526776486144 * q^12 + 62139610550998650558 * q^13 + 135909343255071438528 * q^14 + 2155694017285818421248 * q^16 + 3932636930193139724394 * q^17 + 23007400170989698594008 * q^18 - 32303396242934620550940 * q^19 + 222122458753667398807776 * q^21 - 22658809266113247402912 * q^22 + 514822069421375217224808 * q^23 - 3760729014923614708254720 * q^24 + 4284481859934908169468336 * q^26 - 27373531144823515220747400 * q^27 - 10448754713452503022622208 * q^28 - 38460399143984437598248110 * q^29 + 103731594563724689730029856 * q^31 + 9222369125611166314758144 * q^32 - 1184565114402567148957069584 * q^33 - 554136735348503783026707312 * q^34 - 6052204716130590310531484352 * q^36 - 2464613172948888017021063706 * q^37 + 12543374691225905672793885600 * q^38 + 18611981954062877742706387512 * q^39 + 23522986584532768129037087406 * q^41 + 33931371616975894880367698688 * q^42 + 47516297135443858184325274308 * q^43 - 80954820698705302013923898112 * q^44 + 310121697020384938950505889856 * q^46 - 164346768841318947159729902256 * q^47 - 445342931723856383878644744192 * q^48 - 595089038084925731622037450821 * q^49 - 1803044074850794727352259927704 * q^51 + 511632617456400883939009686144 * q^52 + 1670480551111723484744458809558 * q^53 + 4424231404769003900494105901760 * q^54 + 5670920217413056567252590243840 * q^56 - 4048712721984947152977307522800 * q^57 + 23757672063982901326871265032400 * q^58 + 4370528583092646699845243631180 * q^59 + 23537078276516028947219080488306 * q^61 - 29401231764447267309574710842112 * q^62 - 45614247892704690123948892506792 * q^63 + 93510280736634320631093264384 * q^64 - 75640417841065837797640948042368 * q^66 + 188845033384156918977315211921644 * q^67 - 21990159186015794982823459732608 * q^68 - 325983212396274250308653315934048 * q^69 + 348774602295358210538621162006856 * q^71 - 314101495165322886769992842611200 * q^72 + 285174964854822786615792218987058 * q^73 + 2106337383176566865790045395789808 * q^74 - 2729074287668324197849535448894720 * q^76 - 691501421964810422051915307575712 * q^77 + 2213086042571083132613626950273216 * q^78 - 426212862591061661901736630874160 * q^79 + 1867221150796978455595408934723163 * q^81 + 4061181362173286538873115152234288 * q^82 - 14867187331664065317008883105766692 * q^83 - 13024788508690842242825242575869952 * q^84 + 148490750656470812540405098190496 * q^86 + 7833119385476156993771606256673800 * q^87 + 18777218849949122679898044025804800 * q^88 + 30583590846193751335205992418034270 * q^89 + 1003391702519487362566122156997296 * q^91 - 83662070125024358323030039384121856 * q^92 + 40914650682166972019906140161446016 * q^93 + 19076193270418512575422277142000768 * q^94 - 32392027865954425966997293222723584 * q^96 + 106165667044630951063328618701091994 * q^97 + 13202051562017808504422115585262392 * q^98 + 30288686341597731928441860752034252 * q^99

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