LMFDB - Embedded newform 25.36.a.a.1.1

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			1.1
Root			$3626.53$ 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)

$f(q)$	$=$	$q-331573. q^{2} +1.54691e8 q^{3} +7.55810e10 q^{4} -5.12913e13 q^{6} -3.96640e14 q^{7} -1.36679e16 q^{8} -2.61023e16 q^{9} +O(q^{10})$	\(q-331573. q^{2} +1.54691e8 q^{3} +7.55810e10 q^{4} -5.12913e13 q^{6} -3.96640e14 q^{7} -1.36679e16 q^{8} -2.61023e16 q^{9} -6.82681e17 q^{11} +1.16917e19 q^{12} +1.17949e19 q^{13} +1.31515e20 q^{14} +1.93496e21 q^{16} +1.33083e21 q^{17} +8.65483e21 q^{18} -3.58945e22 q^{19} -6.13565e22 q^{21} +2.26359e23 q^{22} -6.92195e23 q^{23} -2.11429e24 q^{24} -3.91088e24 q^{26} -1.17772e25 q^{27} -2.99785e25 q^{28} -5.67568e25 q^{29} +1.02960e26 q^{31} -1.71955e26 q^{32} -1.05604e26 q^{33} -4.41267e26 q^{34} -1.97284e27 q^{36} -4.50412e27 q^{37} +1.19017e28 q^{38} +1.82456e27 q^{39} -6.23104e27 q^{41} +2.03442e28 q^{42} +2.75822e27 q^{43} -5.15977e28 q^{44} +2.29513e29 q^{46} -1.41103e29 q^{47} +2.99320e29 q^{48} -2.21495e29 q^{49} +2.05867e29 q^{51} +8.91472e29 q^{52} +2.48503e30 q^{53} +3.90500e30 q^{54} +5.42123e30 q^{56} -5.55255e30 q^{57} +1.88190e31 q^{58} +5.47495e30 q^{59} +2.30979e31 q^{61} -3.41386e31 q^{62} +1.03532e31 q^{63} -9.46893e30 q^{64} +3.50156e31 q^{66} -1.55814e31 q^{67} +1.00585e32 q^{68} -1.07076e32 q^{69} -1.13262e32 q^{71} +3.56763e32 q^{72} -3.23524e32 q^{73} +1.49345e33 q^{74} -2.71294e33 q^{76} +2.70778e32 q^{77} -6.04976e32 q^{78} -1.44166e32 q^{79} -5.15885e32 q^{81} +2.06605e33 q^{82} -3.50421e33 q^{83} -4.63739e33 q^{84} -9.14551e32 q^{86} -8.77975e33 q^{87} +9.33079e33 q^{88} +9.37543e33 q^{89} -4.67833e33 q^{91} -5.23168e34 q^{92} +1.59269e34 q^{93} +4.67858e34 q^{94} -2.65998e34 q^{96} -3.59603e33 q^{97} +7.34419e34 q^{98} +1.78195e34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−331573.	−1.78877	−0.894385	−	0.447298i	$-0.852386\pi$
$2$	−331573.	−1.78877	−0.894385	+	0.447298i	$0.852386\pi$
$3$	1.54691e8	0.691580	0.345790	−	0.938312i	$-0.387611\pi$
$3$	1.54691e8	0.691580	0.345790	+	0.938312i	$0.387611\pi$
$4$	7.55810e10	2.19970
$5$	0	0
$5$	0	0
$6$	−5.12913e13	−1.23708
$7$	−3.96640e14	−0.644438	−0.322219	−	0.946665i	$-0.604429\pi$
$7$	−3.96640e14	−0.644438	−0.322219	+	0.946665i	$0.604429\pi$
$8$	−1.36679e16	−2.14598
$9$	−2.61023e16	−0.521717
$10$	0	0
$11$	−6.82681e17	−0.407236	−0.203618	−	0.979050i	$-0.565270\pi$
$11$	−6.82681e17	−0.407236	−0.203618	+	0.979050i	$0.565270\pi$
$12$	1.16917e19	1.52127
$13$	1.17949e19	0.378169	0.189085	−	0.981961i	$-0.439448\pi$
$13$	1.17949e19	0.378169	0.189085	+	0.981961i	$0.439448\pi$
$14$	1.31515e20	1.15275
$15$	0	0
$16$	1.93496e21	1.63897
$17$	1.33083e21	0.390181	0.195090	−	0.980785i	$-0.437500\pi$
$17$	1.33083e21	0.390181	0.195090	+	0.980785i	$0.437500\pi$
$18$	8.65483e21	0.933232
$19$	−3.58945e22	−1.50259	−0.751294	−	0.659967i	$-0.770570\pi$
$19$	−3.58945e22	−1.50259	−0.751294	+	0.659967i	$0.770570\pi$
$20$	0	0
$21$	−6.13565e22	−0.445680
$22$	2.26359e23	0.728451
$23$	−6.92195e23	−1.02327	−0.511636	−	0.859202i	$-0.670961\pi$
$23$	−6.92195e23	−1.02327	−0.511636	+	0.859202i	$0.670961\pi$
$24$	−2.11429e24	−1.48412
$25$	0	0
$26$	−3.91088e24	−0.676457
$27$	−1.17772e25	−1.05239
$28$	−2.99785e25	−1.41757
$29$	−5.67568e25	−1.45229	−0.726144	−	0.687542i	$-0.758690\pi$
$29$	−5.67568e25	−1.45229	−0.726144	+	0.687542i	$0.758690\pi$
$30$	0	0
$31$	1.02960e26	0.820043	0.410022	−	0.912076i	$-0.365521\pi$
$31$	1.02960e26	0.820043	0.410022	+	0.912076i	$0.365521\pi$
$32$	−1.71955e26	−0.785760
$33$	−1.05604e26	−0.281636
$34$	−4.41267e26	−0.697943
$35$	0	0
$36$	−1.97284e27	−1.14762
$37$	−4.50412e27	−1.62211	−0.811054	−	0.584971i	$-0.801106\pi$
$37$	−4.50412e27	−1.62211	−0.811054	+	0.584971i	$0.801106\pi$
$38$	1.19017e28	2.68779
$39$	1.82456e27	0.261534
$40$	0	0
$41$	−6.23104e27	−0.372257	−0.186129	−	0.982525i	$-0.559594\pi$
$41$	−6.23104e27	−0.372257	−0.186129	+	0.982525i	$0.559594\pi$
$42$	2.03442e28	0.797219
$43$	2.75822e27	0.0716029	0.0358014	−	0.999359i	$-0.488602\pi$
$43$	2.75822e27	0.0716029	0.0358014	+	0.999359i	$0.488602\pi$
$44$	−5.15977e28	−0.895795
$45$	0	0
$46$	2.29513e29	1.83040
$47$	−1.41103e29	−0.772365	−0.386182	−	0.922422i	$-0.626207\pi$
$47$	−1.41103e29	−0.772365	−0.386182	+	0.922422i	$0.626207\pi$
$48$	2.99320e29	1.13348
$49$	−2.21495e29	−0.584700
$50$	0	0
$51$	2.05867e29	0.269841
$52$	8.91472e29	0.831858
$53$	2.48503e30	1.66151	0.830755	−	0.556638i	$-0.187909\pi$
$53$	2.48503e30	1.66151	0.830755	+	0.556638i	$0.187909\pi$
$54$	3.90500e30	1.88248
$55$	0	0
$56$	5.42123e30	1.38295
$57$	−5.55255e30	−1.03916
$58$	1.88190e31	2.59781
$59$	5.47495e30	0.560364	0.280182	−	0.959947i	$-0.409605\pi$
$59$	5.47495e30	0.560364	0.280182	+	0.959947i	$0.409605\pi$
$60$	0	0
$61$	2.30979e31	1.31917	0.659585	−	0.751630i	$-0.270732\pi$
$61$	2.30979e31	1.31917	0.659585	+	0.751630i	$0.270732\pi$
$62$	−3.41386e31	−1.46687
$63$	1.03532e31	0.336214
$64$	−9.46893e30	−0.233427
$65$	0	0
$66$	3.50156e31	0.503782
$67$	−1.55814e31	−0.172304	−0.0861522	−	0.996282i	$-0.527457\pi$
$67$	−1.55814e31	−0.172304	−0.0861522	+	0.996282i	$0.527457\pi$
$68$	1.00585e32	0.858279
$69$	−1.07076e32	−0.707675
$70$	0	0
$71$	−1.13262e32	−0.454008	−0.227004	−	0.973894i	$-0.572893\pi$
$71$	−1.13262e32	−0.454008	−0.227004	+	0.973894i	$0.572893\pi$
$72$	3.56763e32	1.11960
$73$	−3.23524e32	−0.797548	−0.398774	−	0.917049i	$-0.630564\pi$
$73$	−3.23524e32	−0.797548	−0.398774	+	0.917049i	$0.630564\pi$
$74$	1.49345e33	2.90158
$75$	0	0
$76$	−2.71294e33	−3.30524
$77$	2.70778e32	0.262438
$78$	−6.04976e32	−0.467824
$79$	−1.44166e32	−0.0892050	−0.0446025	−	0.999005i	$-0.514202\pi$
$79$	−1.44166e32	−0.0892050	−0.0446025	+	0.999005i	$0.514202\pi$
$80$	0	0
$81$	−5.15885e32	−0.206094
$82$	2.06605e33	0.665882
$83$	−3.50421e33	−0.913532	−0.456766	−	0.889587i	$-0.650992\pi$
$83$	−3.50421e33	−0.913532	−0.456766	+	0.889587i	$0.650992\pi$
$84$	−4.63739e33	−0.980361
$85$	0	0
$86$	−9.14551e32	−0.128081
$87$	−8.77975e33	−1.00437
$88$	9.33079e33	0.873920
$89$	9.37543e33	0.720553	0.360277	−	0.932846i	$-0.382682\pi$
$89$	9.37543e33	0.720553	0.360277	+	0.932846i	$0.382682\pi$
$90$	0	0
$91$	−4.67833e33	−0.243706
$92$	−5.23168e34	−2.25089
$93$	1.59269e34	0.567126
$94$	4.67858e34	1.38158
$95$	0	0
$96$	−2.65998e34	−0.543416
$97$	−3.59603e33	−0.0612799	−0.0306399	−	0.999530i	$-0.509755\pi$
$97$	−3.59603e33	−0.0612799	−0.0306399	+	0.999530i	$0.509755\pi$
$98$	7.34419e34	1.04589
$99$	1.78195e34	0.212462
$100$	0	0
$101$	7.27571e34	0.611296	0.305648	−	0.952145i	$-0.401127\pi$
$101$	7.27571e34	0.611296	0.305648	+	0.952145i	$0.401127\pi$
$102$	−6.82599e34	−0.482683
$103$	−9.48038e34	−0.565164	−0.282582	−	0.959243i	$-0.591191\pi$
$103$	−9.48038e34	−0.565164	−0.282582	+	0.959243i	$0.591191\pi$
$104$	−1.61211e35	−0.811544
$105$	0	0
$106$	−8.23968e35	−2.97206
$107$	−5.43957e35	−1.66475	−0.832374	−	0.554214i	$-0.813019\pi$
$107$	−5.43957e35	−1.66475	−0.832374	+	0.554214i	$0.813019\pi$
$108$	−8.90133e35	−2.31494
$109$	−2.19201e35	−0.485153	−0.242577	−	0.970132i	$-0.577993\pi$
$109$	−2.19201e35	−0.485153	−0.242577	+	0.970132i	$0.577993\pi$
$110$	0	0
$111$	−6.96746e35	−1.12182
$112$	−7.67481e35	−1.05621
$113$	3.57083e35	0.420627	0.210313	−	0.977634i	$-0.432552\pi$
$113$	3.57083e35	0.420627	0.210313	+	0.977634i	$0.432552\pi$
$114$	1.84108e36	1.85882
$115$	0	0
$116$	−4.28974e36	−3.19460
$117$	−3.07875e35	−0.197297
$118$	−1.81535e36	−1.00236
$119$	−5.27859e35	−0.251447
$120$	0	0
$121$	−2.34419e36	−0.834159
$122$	−7.65865e36	−2.35969
$123$	−9.63884e35	−0.257446
$124$	7.78179e36	1.80385
$125$	0	0
$126$	−3.43285e36	−0.601410
$127$	2.98205e36	0.454935	0.227467	−	0.973786i	$-0.426955\pi$
$127$	2.98205e36	0.454935	0.227467	+	0.973786i	$0.426955\pi$
$128$	9.04797e36	1.20331
$129$	4.26671e35	0.0495191
$130$	0	0
$131$	1.67513e37	1.48525	0.742627	−	0.669705i	$-0.233579\pi$
$131$	1.67513e37	1.48525	0.742627	+	0.669705i	$0.233579\pi$
$132$	−7.98169e36	−0.619514
$133$	1.42372e37	0.968325
$134$	5.16636e36	0.308213
$135$	0	0
$136$	−1.81896e37	−0.837321
$137$	−7.05739e36	−0.285782	−0.142891	−	0.989738i	$-0.545640\pi$
$137$	−7.05739e36	−0.285782	−0.142891	+	0.989738i	$0.545640\pi$
$138$	3.55036e37	1.26587
$139$	5.54070e36	0.174103	0.0870514	−	0.996204i	$-0.472256\pi$
$139$	5.54070e36	0.174103	0.0870514	+	0.996204i	$0.472256\pi$
$140$	0	0
$141$	−2.18273e37	−0.534152
$142$	3.75546e37	0.812115
$143$	−8.05216e36	−0.154004
$144$	−5.05068e37	−0.855080
$145$	0	0
$146$	1.07272e38	1.42663
$147$	−3.42633e37	−0.404367
$148$	−3.40426e38	−3.56815
$149$	−1.26594e38	−1.17938	−0.589689	−	0.807631i	$-0.700750\pi$
$149$	−1.26594e38	−1.17938	−0.589689	+	0.807631i	$0.700750\pi$
$150$	0	0
$151$	1.46030e38	1.07732	0.538661	−	0.842523i	$-0.318930\pi$
$151$	1.46030e38	1.07732	0.538661	+	0.842523i	$0.318930\pi$
$152$	4.90602e38	3.22453
$153$	−3.47377e37	−0.203564
$154$	−8.97829e37	−0.469441
$155$	0	0
$156$	1.37902e38	0.575296
$157$	2.57702e38	0.961332	0.480666	−	0.876904i	$-0.340395\pi$
$157$	2.57702e38	0.961332	0.480666	+	0.876904i	$0.340395\pi$
$158$	4.78016e37	0.159567
$159$	3.84410e38	1.14907
$160$	0	0
$161$	2.74552e38	0.659436
$162$	1.71054e38	0.368655
$163$	1.00523e39	1.94529	0.972643	−	0.232306i	$-0.0746270\pi$
$163$	1.00523e39	1.94529	0.972643	+	0.232306i	$0.0746270\pi$
$164$	−4.70948e38	−0.818853
$165$	0	0
$166$	1.16190e39	1.63410
$167$	−4.87583e38	−0.617320	−0.308660	−	0.951172i	$-0.599881\pi$
$167$	−4.87583e38	−0.617320	−0.308660	+	0.951172i	$0.599881\pi$
$168$	8.38614e38	0.956422
$169$	−8.33666e38	−0.856988
$170$	0	0
$171$	9.36930e38	0.783926
$172$	2.08469e38	0.157505
$173$	3.15688e37	0.0215502	0.0107751	−	0.999942i	$-0.496570\pi$
$173$	3.15688e37	0.0215502	0.0107751	+	0.999942i	$0.496570\pi$
$174$	2.91113e39	1.79659
$175$	0	0
$176$	−1.32096e39	−0.667447
$177$	8.46924e38	0.387536
$178$	−3.10864e39	−1.28890
$179$	−4.86041e38	−0.182702	−0.0913512	−	0.995819i	$-0.529119\pi$
$179$	−4.86041e38	−0.182702	−0.0913512	+	0.995819i	$0.529119\pi$
$180$	0	0
$181$	−4.89892e39	−1.51609	−0.758045	−	0.652202i	$-0.773845\pi$
$181$	−4.89892e39	−1.51609	−0.758045	+	0.652202i	$0.773845\pi$
$182$	1.55121e39	0.435935
$183$	3.57303e39	0.912311
$184$	9.46084e39	2.19593
$185$	0	0
$186$	−5.28093e39	−1.01446
$187$	−9.08530e38	−0.158895
$188$	−1.06647e40	−1.69897
$189$	4.67131e39	0.678199
$190$	0	0
$191$	−8.79853e39	−1.06249	−0.531246	−	0.847217i	$-0.678276\pi$
$191$	−8.79853e39	−1.06249	−0.531246	+	0.847217i	$0.678276\pi$
$192$	−1.46476e39	−0.161434
$193$	−1.65403e40	−1.66452	−0.832262	−	0.554383i	$-0.812954\pi$
$193$	−1.65403e40	−1.66452	−0.832262	+	0.554383i	$0.812954\pi$
$194$	1.19235e39	0.109616
$195$	0	0
$196$	−1.67408e40	−1.28616
$197$	−3.96581e36	−0.000278723 0	−0.000139362	−	1.00000i	$-0.500044\pi$
$197$	−3.96581e36	−0.000278723 0	−0.000139362		1.00000i	$0.500044\pi$
$198$	−5.90848e39	−0.380045
$199$	−1.61546e40	−0.951409	−0.475705	−	0.879605i	$-0.657807\pi$
$199$	−1.61546e40	−0.951409	−0.475705	+	0.879605i	$0.657807\pi$
$200$	0	0
$201$	−2.41029e39	−0.119162
$202$	−2.41243e40	−1.09347
$203$	2.25120e40	0.935909
$204$	1.55596e40	0.593569
$205$	0	0
$206$	3.14344e40	1.01095
$207$	1.80679e40	0.533859
$208$	2.28226e40	0.619808
$209$	2.45045e40	0.611908
$210$	0	0
$211$	2.70344e40	0.571444	0.285722	−	0.958313i	$-0.407767\pi$
$211$	2.70344e40	0.571444	0.285722	+	0.958313i	$0.407767\pi$
$212$	1.87821e41	3.65482
$213$	−1.75206e40	−0.313983
$214$	1.80362e41	2.97785
$215$	0	0
$216$	1.60969e41	2.25841
$217$	−4.08379e40	−0.528467
$218$	7.26812e40	0.867827
$219$	−5.00462e40	−0.551569
$220$	0	0
$221$	1.56970e40	0.147554
$222$	2.31022e41	2.00667
$223$	−1.60448e41	−1.28825	−0.644124	−	0.764921i	$-0.722778\pi$
$223$	−1.60448e41	−1.28825	−0.644124	+	0.764921i	$0.722778\pi$
$224$	6.82042e40	0.506374
$225$	0	0
$226$	−1.18399e41	−0.752405
$227$	1.32023e41	0.776597	0.388299	−	0.921534i	$-0.373063\pi$
$227$	1.32023e41	0.776597	0.388299	+	0.921534i	$0.373063\pi$
$228$	−4.19667e41	−2.28584
$229$	−1.27675e41	−0.644147	−0.322073	−	0.946715i	$-0.604380\pi$
$229$	−1.27675e41	−0.644147	−0.322073	+	0.946715i	$0.604380\pi$
$230$	0	0
$231$	4.18869e40	0.181497
$232$	7.75745e41	3.11659
$233$	1.15249e41	0.429445	0.214722	−	0.976675i	$-0.431115\pi$
$233$	1.15249e41	0.429445	0.214722	+	0.976675i	$0.431115\pi$
$234$	1.02083e41	0.352919
$235$	0	0
$236$	4.13802e41	1.23263
$237$	−2.23012e40	−0.0616924
$238$	1.75024e41	0.449781
$239$	1.42881e41	0.341201	0.170601	−	0.985340i	$-0.445429\pi$
$239$	1.42881e41	0.341201	0.170601	+	0.985340i	$0.445429\pi$
$240$	0	0
$241$	−1.47367e41	−0.304160	−0.152080	−	0.988368i	$-0.548597\pi$
$241$	−1.47367e41	−0.304160	−0.152080	+	0.988368i	$0.548597\pi$
$242$	7.77271e41	1.49212
$243$	5.09429e41	0.909859
$244$	1.74576e42	2.90177
$245$	0	0
$246$	3.19598e41	0.460511
$247$	−4.23373e41	−0.568233
$248$	−1.40724e42	−1.75980
$249$	−5.42069e41	−0.631781
$250$	0	0
$251$	1.16925e42	1.18473	0.592363	−	0.805671i	$-0.298195\pi$
$251$	1.16925e42	1.18473	0.592363	+	0.805671i	$0.298195\pi$
$252$	7.82507e41	0.739569
$253$	4.72548e41	0.416713
$254$	−9.88766e41	−0.813773
$255$	0	0
$256$	−2.67471e42	−1.91901
$257$	−6.14627e41	−0.411890	−0.205945	−	0.978564i	$-0.566027\pi$
$257$	−6.14627e41	−0.411890	−0.205945	+	0.978564i	$0.566027\pi$
$258$	−1.41473e41	−0.0885783
$259$	1.78651e42	1.04535
$260$	0	0
$261$	1.48148e42	0.757684
$262$	−5.55428e42	−2.65678
$263$	−5.29428e41	−0.236909	−0.118454	−	0.992959i	$-0.537794\pi$
$263$	−5.29428e41	−0.236909	−0.118454	+	0.992959i	$0.537794\pi$
$264$	1.44339e42	0.604386
$265$	0	0
$266$	−4.72067e42	−1.73211
$267$	1.45029e42	0.498320
$268$	−1.17766e42	−0.379018
$269$	2.61222e42	0.787670	0.393835	−	0.919181i	$-0.371148\pi$
$269$	2.61222e42	0.787670	0.393835	+	0.919181i	$0.371148\pi$
$270$	0	0
$271$	−6.35646e42	−1.68365	−0.841827	−	0.539748i	$-0.818520\pi$
$271$	−6.35646e42	−1.68365	−0.841827	+	0.539748i	$0.818520\pi$
$272$	2.57509e42	0.639495
$273$	−7.23695e41	−0.168542
$274$	2.34004e42	0.511197
$275$	0	0
$276$	−8.09293e42	−1.55667
$277$	−1.32088e41	−0.0238488	−0.0119244	−	0.999929i	$-0.503796\pi$
$277$	−1.32088e41	−0.0238488	−0.0119244	+	0.999929i	$0.503796\pi$
$278$	−1.83715e42	−0.311430
$279$	−2.68748e42	−0.427831
$280$	0	0
$281$	1.21053e43	1.70065	0.850324	−	0.526260i	$-0.176406\pi$
$281$	1.21053e43	1.70065	0.850324	+	0.526260i	$0.176406\pi$
$282$	7.23734e42	0.955475
$283$	−1.08291e41	−0.0134378	−0.00671891	−	0.999977i	$-0.502139\pi$
$283$	−1.08291e41	−0.0134378	−0.00671891	+	0.999977i	$0.502139\pi$
$284$	−8.56046e42	−0.998680
$285$	0	0
$286$	2.66988e42	0.275477
$287$	2.47148e42	0.239896
$288$	4.48842e42	0.409945
$289$	−9.86245e42	−0.847759
$290$	0	0
$291$	−5.56273e41	−0.0423799
$292$	−2.44523e43	−1.75437
$293$	2.38381e42	0.161097	0.0805486	−	0.996751i	$-0.474333\pi$
$293$	2.38381e42	0.161097	0.0805486	+	0.996751i	$0.474333\pi$
$294$	1.13608e43	0.723319
$295$	0	0
$296$	6.15617e43	3.48102
$297$	8.04007e42	0.428570
$298$	4.19751e43	2.10963
$299$	−8.16438e42	−0.386970
$300$	0	0
$301$	−1.09402e42	−0.0461436
$302$	−4.84196e43	−1.92708
$303$	1.12548e43	0.422760
$304$	−6.94543e43	−2.46270
$305$	0	0
$306$	1.15181e43	0.364129
$307$	4.84424e43	1.44645	0.723226	−	0.690611i	$-0.242658\pi$
$307$	4.84424e43	1.44645	0.723226	+	0.690611i	$0.242658\pi$
$308$	2.04657e43	0.577284
$309$	−1.46653e43	−0.390856
$310$	0	0
$311$	1.85715e43	0.442119	0.221060	−	0.975260i	$-0.429048\pi$
$311$	1.85715e43	0.442119	0.221060	+	0.975260i	$0.429048\pi$
$312$	−2.49379e43	−0.561248
$313$	−2.67734e43	−0.569740	−0.284870	−	0.958566i	$-0.591951\pi$
$313$	−2.67734e43	−0.569740	−0.284870	+	0.958566i	$0.591951\pi$
$314$	−8.54470e43	−1.71960
$315$	0	0
$316$	−1.08962e43	−0.196224
$317$	2.42612e43	0.413405	0.206703	−	0.978404i	$-0.433727\pi$
$317$	2.42612e43	0.413405	0.206703	+	0.978404i	$0.433727\pi$
$318$	−1.27460e44	−2.05542
$319$	3.87468e43	0.591423
$320$	0	0
$321$	−8.41452e43	−1.15131
$322$	−9.10342e43	−1.17958
$323$	−4.77694e43	−0.586281
$324$	−3.89911e43	−0.453344
$325$	0	0
$326$	−3.33308e44	−3.47967
$327$	−3.39084e43	−0.335522
$328$	8.51651e43	0.798857
$329$	5.59669e43	0.497741
$330$	0	0
$331$	1.83689e44	1.46924	0.734620	−	0.678479i	$-0.237361\pi$
$331$	1.83689e44	1.46924	0.734620	+	0.678479i	$0.237361\pi$
$332$	−2.64852e44	−2.00950
$333$	1.17568e44	0.846282
$334$	1.61669e44	1.10424
$335$	0	0
$336$	−1.18722e44	−0.730457
$337$	−9.63203e42	−0.0562593	−0.0281297	−	0.999604i	$-0.508955\pi$
$337$	−9.63203e42	−0.0562593	−0.0281297	+	0.999604i	$0.508955\pi$
$338$	2.76421e44	1.53295
$339$	5.52375e43	0.290897
$340$	0	0
$341$	−7.02885e43	−0.333951
$342$	−3.10661e44	−1.40226
$343$	2.38109e44	1.02124
$344$	−3.76990e43	−0.153659
$345$	0	0
$346$	−1.04674e43	−0.0385483
$347$	−2.05198e44	−0.718468	−0.359234	−	0.933247i	$-0.616962\pi$
$347$	−2.05198e44	−0.718468	−0.359234	+	0.933247i	$0.616962\pi$
$348$	−6.63583e44	−2.20932
$349$	−1.00117e44	−0.317003	−0.158501	−	0.987359i	$-0.550666\pi$
$349$	−1.00117e44	−0.317003	−0.158501	+	0.987359i	$0.550666\pi$
$350$	0	0
$351$	−1.38911e44	−0.397981
$352$	1.17390e44	0.319990
$353$	2.71539e44	0.704328	0.352164	−	0.935938i	$-0.385446\pi$
$353$	2.71539e44	0.704328	0.352164	+	0.935938i	$0.385446\pi$
$354$	−2.80817e44	−0.693213
$355$	0	0
$356$	7.08605e44	1.58500
$357$	−8.16550e43	−0.173896
$358$	1.61158e44	0.326813
$359$	8.81356e44	1.70215	0.851076	−	0.525043i	$-0.175951\pi$
$359$	8.81356e44	1.70215	0.851076	+	0.525043i	$0.175951\pi$
$360$	0	0
$361$	7.17758e44	1.25777
$362$	1.62435e45	2.71194
$363$	−3.62625e44	−0.576888
$364$	−3.53593e44	−0.536080
$365$	0	0
$366$	−1.18472e45	−1.63191
$367$	1.11298e45	1.46161	0.730806	−	0.682585i	$-0.239144\pi$
$367$	1.11298e45	1.46161	0.730806	+	0.682585i	$0.239144\pi$
$368$	−1.33937e45	−1.67712
$369$	1.62645e44	0.194213
$370$	0	0
$371$	−9.85661e44	−1.07074
$372$	1.20377e45	1.24750
$373$	5.50495e44	0.544313	0.272157	−	0.962253i	$-0.412263\pi$
$373$	5.50495e44	0.544313	0.272157	+	0.962253i	$0.412263\pi$
$374$	3.01244e44	0.284227
$375$	0	0
$376$	1.92857e45	1.65748
$377$	−6.69441e44	−0.549211
$378$	−1.54888e45	−1.21314
$379$	−1.81534e45	−1.35760	−0.678799	−	0.734325i	$-0.737499\pi$
$379$	−1.81534e45	−1.35760	−0.678799	+	0.734325i	$0.737499\pi$
$380$	0	0
$381$	4.61295e44	0.314624
$382$	2.91736e45	1.90056
$383$	−5.42819e44	−0.337813	−0.168907	−	0.985632i	$-0.554024\pi$
$383$	−5.42819e44	−0.337813	−0.168907	+	0.985632i	$0.554024\pi$
$384$	1.39964e45	0.832184
$385$	0	0
$386$	5.48431e45	2.97745
$387$	−7.19958e43	−0.0373564
$388$	−2.71792e44	−0.134797
$389$	2.27596e45	1.07906	0.539532	−	0.841965i	$-0.318601\pi$
$389$	2.27596e45	1.07906	0.539532	+	0.841965i	$0.318601\pi$
$390$	0	0
$391$	−9.21192e44	−0.399261
$392$	3.02737e45	1.25476
$393$	2.59127e45	1.02717
$394$	1.31496e42	0.000498572 0
$395$	0	0
$396$	1.34682e45	0.467352
$397$	−2.97575e45	−0.988013	−0.494006	−	0.869458i	$-0.664468\pi$
$397$	−2.97575e45	−0.988013	−0.494006	+	0.869458i	$0.664468\pi$
$398$	5.35643e45	1.70185
$399$	2.20236e45	0.669674
$400$	0	0
$401$	−3.35408e45	−0.934429	−0.467215	−	0.884144i	$-0.654742\pi$
$401$	−3.35408e45	−0.934429	−0.467215	+	0.884144i	$0.654742\pi$
$402$	7.99189e44	0.213154
$403$	1.21440e45	0.310115
$404$	5.49906e45	1.34467
$405$	0	0
$406$	−7.46438e45	−1.67413
$407$	3.07488e45	0.660580
$408$	−2.81376e45	−0.579074
$409$	8.75180e45	1.72560	0.862799	−	0.505547i	$-0.168709\pi$
$409$	8.75180e45	1.72560	0.862799	+	0.505547i	$0.168709\pi$
$410$	0	0
$411$	−1.09171e45	−0.197641
$412$	−7.16537e45	−1.24319
$413$	−2.17158e45	−0.361119
$414$	−5.99083e45	−0.954951
$415$	0	0
$416$	−2.02819e45	−0.297150
$417$	8.57095e44	0.120406
$418$	−8.12503e45	−1.09456
$419$	1.99625e45	0.257911	0.128955	−	0.991650i	$-0.458838\pi$
$419$	1.99625e45	0.257911	0.128955	+	0.991650i	$0.458838\pi$
$420$	0	0
$421$	−1.23389e46	−1.46670	−0.733348	−	0.679854i	$-0.762043\pi$
$421$	−1.23389e46	−1.46670	−0.733348	+	0.679854i	$0.762043\pi$
$422$	−8.96388e45	−1.02218
$423$	3.68311e45	0.402956
$424$	−3.39650e46	−3.56557
$425$	0	0
$426$	5.80936e45	0.561643
$427$	−9.16156e45	−0.850122
$428$	−4.11129e46	−3.66194
$429$	−1.24559e45	−0.106506
$430$	0	0
$431$	−1.20357e46	−0.948677	−0.474339	−	0.880343i	$-0.657313\pi$
$431$	−1.20357e46	−0.948677	−0.474339	+	0.880343i	$0.657313\pi$
$432$	−2.27884e46	−1.72484
$433$	2.06332e46	1.49979	0.749893	−	0.661559i	$-0.230105\pi$
$433$	2.06332e46	1.49979	0.749893	+	0.661559i	$0.230105\pi$
$434$	1.35407e46	0.945305
$435$	0	0
$436$	−1.65674e46	−1.06719
$437$	2.48460e46	1.53756
$438$	1.65940e46	0.986629
$439$	3.14998e46	1.79961	0.899805	−	0.436293i	$-0.143709\pi$
$439$	3.14998e46	1.79961	0.899805	+	0.436293i	$0.143709\pi$
$440$	0	0
$441$	5.78154e45	0.305048
$442$	−5.20470e45	−0.263941
$443$	2.49595e46	1.21667	0.608333	−	0.793682i	$-0.291839\pi$
$443$	2.49595e46	1.21667	0.608333	+	0.793682i	$0.291839\pi$
$444$	−5.26608e46	−2.46766
$445$	0	0
$446$	5.32003e46	2.30438
$447$	−1.95829e46	−0.815634
$448$	3.75576e45	0.150429
$449$	3.14792e46	1.21259	0.606294	−	0.795241i	$-0.292656\pi$
$449$	3.14792e46	1.21259	0.606294	+	0.795241i	$0.292656\pi$
$450$	0	0
$451$	4.25381e45	0.151596
$452$	2.69887e46	0.925252
$453$	2.25895e46	0.745054
$454$	−4.37752e46	−1.38915
$455$	0	0
$456$	7.58916e46	2.23002
$457$	−3.21994e46	−0.910572	−0.455286	−	0.890345i	$-0.650463\pi$
$457$	−3.21994e46	−0.910572	−0.455286	+	0.890345i	$0.650463\pi$
$458$	4.23336e46	1.15223
$459$	−1.56734e46	−0.410622
$460$	0	0
$461$	8.96567e45	0.217679	0.108840	−	0.994059i	$-0.465287\pi$
$461$	8.96567e45	0.217679	0.108840	+	0.994059i	$0.465287\pi$
$462$	−1.38886e46	−0.324656
$463$	2.74379e46	0.617566	0.308783	−	0.951133i	$-0.400078\pi$
$463$	2.74379e46	0.617566	0.308783	+	0.951133i	$0.400078\pi$
$464$	−1.09822e47	−2.38026
$465$	0	0
$466$	−3.82134e46	−0.768178
$467$	8.40024e46	1.62647	0.813235	−	0.581935i	$-0.197704\pi$
$467$	8.40024e46	1.62647	0.813235	+	0.581935i	$0.197704\pi$
$468$	−2.32695e46	−0.433994
$469$	6.18019e45	0.111039
$470$	0	0
$471$	3.98641e46	0.664838
$472$	−7.48309e46	−1.20253
$473$	−1.88298e45	−0.0291592
$474$	7.39447e45	0.110353
$475$	0	0
$476$	−3.98962e46	−0.553107
$477$	−6.48649e46	−0.866839
$478$	−4.73755e46	−0.610331
$479$	1.51913e47	1.88679	0.943395	−	0.331671i	$-0.107612\pi$
$479$	1.51913e47	1.88679	0.943395	+	0.331671i	$0.107612\pi$
$480$	0	0
$481$	−5.31257e46	−0.613431
$482$	4.88629e46	0.544072
$483$	4.24707e46	0.456052
$484$	−1.77176e47	−1.83490
$485$	0	0
$486$	−1.68913e47	−1.62753
$487$	9.57009e46	0.889527	0.444764	−	0.895648i	$-0.353288\pi$
$487$	9.57009e46	0.889527	0.444764	+	0.895648i	$0.353288\pi$
$488$	−3.15699e47	−2.83091
$489$	1.55500e47	1.34532
$490$	0	0
$491$	−9.00218e46	−0.725139	−0.362570	−	0.931957i	$-0.618100\pi$
$491$	−9.00218e46	−0.725139	−0.362570	+	0.931957i	$0.618100\pi$
$492$	−7.28514e46	−0.566302
$493$	−7.55335e46	−0.566655
$494$	1.40379e47	1.01644
$495$	0	0
$496$	1.99222e47	1.34403
$497$	4.49242e46	0.292580
$498$	1.79736e47	1.13011
$499$	−1.31845e47	−0.800394	−0.400197	−	0.916429i	$-0.631058\pi$
$499$	−1.31845e47	−0.800394	−0.400197	+	0.916429i	$0.631058\pi$
$500$	0	0
$501$	−7.54246e46	−0.426926
$502$	−3.87693e47	−2.11920
$503$	−3.29261e46	−0.173820	−0.0869101	−	0.996216i	$-0.527699\pi$
$503$	−3.29261e46	−0.173820	−0.0869101	+	0.996216i	$0.527699\pi$
$504$	−1.41507e47	−0.721510
$505$	0	0
$506$	−1.56684e47	−0.745404
$507$	−1.28960e47	−0.592676
$508$	2.25386e47	1.00072
$509$	1.43449e47	0.615370	0.307685	−	0.951488i	$-0.400446\pi$
$509$	1.43449e47	0.615370	0.307685	+	0.951488i	$0.400446\pi$
$510$	0	0
$511$	1.28323e47	0.513970
$512$	5.75978e47	2.22937
$513$	4.22737e47	1.58131
$514$	2.03794e47	0.736777
$515$	0	0
$516$	3.22482e46	0.108927
$517$	9.63280e46	0.314534
$518$	−5.92360e47	−1.86989
$519$	4.88340e45	0.0149037
$520$	0	0
$521$	−2.33055e47	−0.664966	−0.332483	−	0.943109i	$-0.607886\pi$
$521$	−2.33055e47	−0.664966	−0.332483	+	0.943109i	$0.607886\pi$
$522$	−4.91220e47	−1.35532
$523$	4.26380e47	1.13767	0.568836	−	0.822451i	$-0.307394\pi$
$523$	4.26380e47	1.13767	0.568836	+	0.822451i	$0.307394\pi$
$524$	1.26608e48	3.26711
$525$	0	0
$526$	1.75544e47	0.423776
$527$	1.37021e47	0.319965
$528$	−2.04340e47	−0.461593
$529$	2.15467e46	0.0470875
$530$	0	0
$531$	−1.42909e47	−0.292351
$532$	1.07606e48	2.13002
$533$	−7.34945e46	−0.140776
$534$	−4.80878e47	−0.891380
$535$	0	0
$536$	2.12964e47	0.369762
$537$	−7.51860e46	−0.126353
$538$	−8.66140e47	−1.40896
$539$	1.51211e47	0.238111
$540$	0	0
$541$	−5.43835e45	−0.00802629	−0.00401314	−	0.999992i	$-0.501277\pi$
$541$	−5.43835e45	−0.00802629	−0.00401314	+	0.999992i	$0.501277\pi$
$542$	2.10763e48	3.01167
$543$	−7.57817e47	−1.04850
$544$	−2.28842e47	−0.306588
$545$	0	0
$546$	2.39958e47	0.301484
$547$	4.15694e47	0.505820	0.252910	−	0.967490i	$-0.418612\pi$
$547$	4.15694e47	0.505820	0.252910	+	0.967490i	$0.418612\pi$
$548$	−5.33405e47	−0.628633
$549$	−6.02909e47	−0.688233
$550$	0	0
$551$	2.03726e48	2.18219
$552$	1.46350e48	1.51866
$553$	5.71821e46	0.0574871
$554$	4.37967e46	0.0426600
$555$	0	0
$556$	4.18772e47	0.382973
$557$	−1.81613e45	−0.00160947	−0.000804733	−	1.00000i	$-0.500256\pi$
$557$	−1.81613e45	−0.00160947	−0.000804733		1.00000i	$0.500256\pi$
$558$	8.91097e47	0.765291
$559$	3.25329e46	0.0270780
$560$	0	0
$561$	−1.40541e47	−0.109889
$562$	−4.01379e48	−3.04207
$563$	2.19502e48	1.61266	0.806329	−	0.591468i	$-0.201451\pi$
$563$	2.19502e48	1.61266	0.806329	+	0.591468i	$0.201451\pi$
$564$	−1.64973e48	−1.17497
$565$	0	0
$566$	3.59063e46	0.0240372
$567$	2.04621e47	0.132815
$568$	1.54805e48	0.974293
$569$	1.19614e48	0.729993	0.364996	−	0.931009i	$-0.381070\pi$
$569$	1.19614e48	0.729993	0.364996	+	0.931009i	$0.381070\pi$
$570$	0	0
$571$	−1.26426e48	−0.725610	−0.362805	−	0.931865i	$-0.618181\pi$
$571$	−1.26426e48	−0.725610	−0.362805	+	0.931865i	$0.618181\pi$
$572$	−6.08590e47	−0.338762
$573$	−1.36105e48	−0.734799
$574$	−8.19476e47	−0.429120
$575$	0	0
$576$	2.47161e47	0.121783
$577$	−2.42022e48	−1.15686	−0.578428	−	0.815734i	$-0.696333\pi$
$577$	−2.42022e48	−1.15686	−0.578428	+	0.815734i	$0.696333\pi$
$578$	3.27012e48	1.51645
$579$	−2.55863e48	−1.15115
$580$	0	0
$581$	1.38991e48	0.588715
$582$	1.84445e47	0.0758080
$583$	−1.69648e48	−0.676626
$584$	4.42189e48	1.71153
$585$	0	0
$586$	−7.90407e47	−0.288166
$587$	1.04500e48	0.369787	0.184893	−	0.982759i	$-0.440806\pi$
$587$	1.04500e48	0.369787	0.184893	+	0.982759i	$0.440806\pi$
$588$	−2.58965e48	−0.889485
$589$	−3.69568e48	−1.23219
$590$	0	0
$591$	−6.13475e44	−0.000192760 0
$592$	−8.71527e48	−2.65859
$593$	−4.87793e48	−1.44470	−0.722351	−	0.691526i	$-0.756939\pi$
$593$	−4.87793e48	−1.44470	−0.722351	+	0.691526i	$0.756939\pi$
$594$	−2.66587e48	−0.766613
$595$	0	0
$596$	−9.56809e48	−2.59427
$597$	−2.49897e48	−0.657976
$598$	2.70709e48	0.692201
$599$	8.48111e47	0.210612	0.105306	−	0.994440i	$-0.466418\pi$
$599$	8.48111e47	0.210612	0.105306	+	0.994440i	$0.466418\pi$
$600$	0	0
$601$	−6.23099e48	−1.45967	−0.729834	−	0.683624i	$-0.760403\pi$
$601$	−6.23099e48	−1.45967	−0.729834	+	0.683624i	$0.760403\pi$
$602$	3.62747e47	0.0825402
$603$	4.06710e47	0.0898942
$604$	1.10371e49	2.36978
$605$	0	0
$606$	−3.73181e48	−0.756220
$607$	−2.65746e48	−0.523197	−0.261598	−	0.965177i	$-0.584250\pi$
$607$	−2.65746e48	−0.523197	−0.261598	+	0.965177i	$0.584250\pi$
$608$	6.17224e48	1.18067
$609$	3.48240e48	0.647256
$610$	0	0
$611$	−1.66429e48	−0.292085
$612$	−2.62551e48	−0.447779
$613$	−5.89105e48	−0.976415	−0.488208	−	0.872727i	$-0.662349\pi$
$613$	−5.89105e48	−0.976415	−0.488208	+	0.872727i	$0.662349\pi$
$614$	−1.60622e49	−2.58737
$615$	0	0
$616$	−3.70097e48	−0.563187
$617$	2.86204e48	0.423337	0.211668	−	0.977342i	$-0.432110\pi$
$617$	2.86204e48	0.423337	0.211668	+	0.977342i	$0.432110\pi$
$618$	4.86261e48	0.699151
$619$	−9.42149e48	−1.31684	−0.658420	−	0.752651i	$-0.728775\pi$
$619$	−9.42149e48	−1.31684	−0.658420	+	0.752651i	$0.728775\pi$
$620$	0	0
$621$	8.15212e48	1.07688
$622$	−6.15780e48	−0.790850
$623$	−3.71867e48	−0.464352
$624$	3.53045e48	0.428647
$625$	0	0
$626$	8.87733e48	1.01913
$627$	3.79062e48	0.423183
$628$	1.94774e49	2.11464
$629$	−5.99421e48	−0.632915
$630$	0	0
$631$	8.74950e48	0.873915	0.436958	−	0.899482i	$-0.356056\pi$
$631$	8.74950e48	0.873915	0.436958	+	0.899482i	$0.356056\pi$
$632$	1.97045e48	0.191432
$633$	4.18197e48	0.395199
$634$	−8.04438e48	−0.739487
$635$	0	0
$636$	2.90541e49	2.52760
$637$	−2.61252e48	−0.221116
$638$	−1.28474e49	−1.05792
$639$	2.95640e48	0.236864
$640$	0	0
$641$	5.35983e48	0.406571	0.203285	−	0.979120i	$-0.434838\pi$
$641$	5.35983e48	0.406571	0.203285	+	0.979120i	$0.434838\pi$
$642$	2.79003e49	2.05942
$643$	−2.04799e49	−1.47108	−0.735538	−	0.677483i	$-0.763071\pi$
$643$	−2.04799e49	−1.47108	−0.735538	+	0.677483i	$0.763071\pi$
$644$	2.07509e49	1.45056
$645$	0	0
$646$	1.58391e49	1.04872
$647$	−2.13324e49	−1.37472	−0.687360	−	0.726317i	$-0.741231\pi$
$647$	−2.13324e49	−1.37472	−0.687360	+	0.726317i	$0.741231\pi$
$648$	7.05105e48	0.442274
$649$	−3.73764e48	−0.228200
$650$	0	0
$651$	−6.31724e48	−0.365477
$652$	7.59765e49	4.27904
$653$	2.78018e49	1.52438	0.762189	−	0.647354i	$-0.224124\pi$
$653$	2.78018e49	1.52438	0.762189	+	0.647354i	$0.224124\pi$
$654$	1.12431e49	0.600172
$655$	0	0
$656$	−1.20568e49	−0.610119
$657$	8.44474e48	0.416095
$658$	−1.85571e49	−0.890344
$659$	−2.64746e49	−1.23690	−0.618450	−	0.785824i	$-0.712239\pi$
$659$	−2.64746e49	−1.23690	−0.618450	+	0.785824i	$0.712239\pi$
$660$	0	0
$661$	2.31405e49	1.02529	0.512646	−	0.858600i	$-0.328665\pi$
$661$	2.31405e49	1.02529	0.512646	+	0.858600i	$0.328665\pi$
$662$	−6.09062e49	−2.62813
$663$	2.42818e48	0.102046
$664$	4.78952e49	1.96042
$665$	0	0
$666$	−3.89824e49	−1.51380
$667$	3.92868e49	1.48609
$668$	−3.68520e49	−1.35792
$669$	−2.48198e49	−0.890927
$670$	0	0
$671$	−1.57685e49	−0.537213
$672$	1.05506e49	0.350198
$673$	−3.41502e49	−1.10441	−0.552204	−	0.833709i	$-0.686213\pi$
$673$	−3.41502e49	−1.10441	−0.552204	+	0.833709i	$0.686213\pi$
$674$	3.19372e48	0.100635
$675$	0	0
$676$	−6.30093e49	−1.88511
$677$	−1.81760e49	−0.529903	−0.264951	−	0.964262i	$-0.585356\pi$
$677$	−1.81760e49	−0.529903	−0.264951	+	0.964262i	$0.585356\pi$
$678$	−1.83153e49	−0.520348
$679$	1.42633e48	0.0394911
$680$	0	0
$681$	2.04227e49	0.537079
$682$	2.33058e49	0.597361
$683$	1.52341e49	0.380587	0.190294	−	0.981727i	$-0.439056\pi$
$683$	1.52341e49	0.380587	0.190294	+	0.981727i	$0.439056\pi$
$684$	7.08142e49	1.72440
$685$	0	0
$686$	−7.89504e49	−1.82676
$687$	−1.97501e49	−0.445479
$688$	5.33703e48	0.117355
$689$	2.93107e49	0.628332
$690$	0	0
$691$	−1.25243e49	−0.255203	−0.127602	−	0.991825i	$-0.540728\pi$
$691$	−1.25243e49	−0.255203	−0.127602	+	0.991825i	$0.540728\pi$
$692$	2.38600e48	0.0474039
$693$	−7.06795e48	−0.136918
$694$	6.80382e49	1.28517
$695$	0	0
$696$	1.20001e50	2.15537
$697$	−8.29244e48	−0.145247
$698$	3.31961e49	0.567045
$699$	1.78279e49	0.296995
$700$	0	0
$701$	4.20207e49	0.665883	0.332942	−	0.942947i	$-0.391959\pi$
$701$	4.20207e49	0.665883	0.332942	+	0.942947i	$0.391959\pi$
$702$	4.60592e49	0.711896
$703$	1.61673e50	2.43736
$704$	6.46426e48	0.0950598
$705$	0	0
$706$	−9.00351e49	−1.25988
$707$	−2.88584e49	−0.393942
$708$	6.40114e49	0.852463
$709$	9.39998e48	0.122129	0.0610644	−	0.998134i	$-0.480551\pi$
$709$	9.39998e48	0.122129	0.0610644	+	0.998134i	$0.480551\pi$
$710$	0	0
$711$	3.76307e48	0.0465398
$712$	−1.28142e50	−1.54629
$713$	−7.12681e49	−0.839128
$714$	2.70746e49	0.311059
$715$	0	0
$716$	−3.67354e49	−0.401890
$717$	2.21023e49	0.235968
$718$	−2.92234e50	−3.04476
$719$	−7.29315e49	−0.741583	−0.370792	−	0.928716i	$-0.620914\pi$
$719$	−7.29315e49	−0.741583	−0.370792	+	0.928716i	$0.620914\pi$
$720$	0	0
$721$	3.76030e49	0.364213
$722$	−2.37989e50	−2.24987
$723$	−2.27963e49	−0.210351
$724$	−3.70265e50	−3.33494
$725$	0	0
$726$	1.20237e50	1.03192
$727$	4.92620e49	0.412724	0.206362	−	0.978476i	$-0.433838\pi$
$727$	4.92620e49	0.412724	0.206362	+	0.978476i	$0.433838\pi$
$728$	6.39429e49	0.522990
$729$	1.04614e50	0.835334
$730$	0	0
$731$	3.67071e48	0.0279380
$732$	2.70054e50	2.00681
$733$	1.28080e50	0.929310	0.464655	−	0.885492i	$-0.346178\pi$
$733$	1.28080e50	0.929310	0.464655	+	0.885492i	$0.346178\pi$
$734$	−3.69035e50	−2.61449
$735$	0	0
$736$	1.19026e50	0.804047
$737$	1.06371e49	0.0701685
$738$	−5.39286e49	−0.347402
$739$	1.99479e50	1.25493	0.627466	−	0.778644i	$-0.284092\pi$
$739$	1.99479e50	1.25493	0.627466	+	0.778644i	$0.284092\pi$
$740$	0	0
$741$	−6.54918e49	−0.392978
$742$	3.26819e50	1.91531
$743$	−1.05855e50	−0.605907	−0.302954	−	0.953005i	$-0.597973\pi$
$743$	−1.05855e50	−0.605907	−0.302954	+	0.953005i	$0.597973\pi$
$744$	−2.17687e50	−1.21704
$745$	0	0
$746$	−1.82529e50	−0.973651
$747$	9.14681e49	0.476606
$748$	−6.86676e49	−0.349522
$749$	2.15755e50	1.07283
$750$	0	0
$751$	−1.20549e50	−0.572090	−0.286045	−	0.958216i	$-0.592341\pi$
$751$	−1.20549e50	−0.572090	−0.286045	+	0.958216i	$0.592341\pi$
$752$	−2.73027e50	−1.26588
$753$	1.80872e50	0.819333
$754$	2.21969e50	0.982411
$755$	0	0
$756$	3.53062e50	1.49183
$757$	−1.18495e50	−0.489240	−0.244620	−	0.969619i	$-0.578663\pi$
$757$	−1.18495e50	−0.489240	−0.244620	+	0.969619i	$0.578663\pi$
$758$	6.01917e50	2.42843
$759$	7.30989e49	0.288190
$760$	0	0
$761$	2.89900e50	1.09148	0.545741	−	0.837954i	$-0.316248\pi$
$761$	2.89900e50	1.09148	0.545741	+	0.837954i	$0.316248\pi$
$762$	−1.52953e50	−0.562789
$763$	8.69439e49	0.312651
$764$	−6.65002e50	−2.33716
$765$	0	0
$766$	1.79984e50	0.604270
$767$	6.45766e49	0.211912
$768$	−4.13754e50	−1.32715
$769$	6.18664e49	0.193974	0.0969870	−	0.995286i	$-0.469079\pi$
$769$	6.18664e49	0.193974	0.0969870	+	0.995286i	$0.469079\pi$
$770$	0	0
$771$	−9.50771e49	−0.284855
$772$	−1.25013e51	−3.66145
$773$	6.37753e50	1.82604	0.913022	−	0.407911i	$-0.133743\pi$
$773$	6.37753e50	1.82604	0.913022	+	0.407911i	$0.133743\pi$
$774$	2.38719e49	0.0668221
$775$	0	0
$776$	4.91501e49	0.131506
$777$	2.76357e50	0.722941
$778$	−7.54649e50	−1.93020
$779$	2.23660e50	0.559349
$780$	0	0
$781$	7.73218e49	0.184888
$782$	3.05443e50	0.714186
$783$	6.68436e50	1.52837
$784$	−4.28584e50	−0.958307
$785$	0	0
$786$	−8.59196e50	−1.83737
$787$	−6.23653e50	−1.30432	−0.652161	−	0.758080i	$-0.726138\pi$
$787$	−6.23653e50	−1.30432	−0.652161	+	0.758080i	$0.726138\pi$
$788$	−2.99740e47	−0.000613107 0
$789$	−8.18976e49	−0.163841
$790$	0	0
$791$	−1.41634e50	−0.271068
$792$	−2.43555e50	−0.455939
$793$	2.72438e50	0.498869
$794$	9.86679e50	1.76733
$795$	0	0
$796$	−1.22098e51	−2.09281
$797$	−9.07097e50	−1.52101	−0.760507	−	0.649329i	$-0.775050\pi$
$797$	−9.07097e50	−1.52101	−0.760507	+	0.649329i	$0.775050\pi$
$798$	−7.30245e50	−1.19789
$799$	−1.87783e50	−0.301362
$800$	0	0
$801$	−2.44720e50	−0.375925
$802$	1.11212e51	1.67148
$803$	2.20864e50	0.324790
$804$	−1.82172e50	−0.262121
$805$	0	0
$806$	−4.02662e50	−0.554724
$807$	4.04086e50	0.544736
$808$	−9.94435e50	−1.31183
$809$	1.43609e51	1.85389	0.926943	−	0.375202i	$-0.122427\pi$
$809$	1.43609e51	1.85389	0.926943	+	0.375202i	$0.122427\pi$
$810$	0	0
$811$	6.18627e50	0.764828	0.382414	−	0.923991i	$-0.375093\pi$
$811$	6.18627e50	0.764828	0.382414	+	0.923991i	$0.375093\pi$
$812$	1.70148e51	2.05872
$813$	−9.83286e50	−1.16438
$814$	−1.01955e51	−1.18163
$815$	0	0
$816$	3.98343e50	0.442262
$817$	−9.90049e49	−0.107590
$818$	−2.90186e51	−3.08670
$819$	1.22115e50	0.127146
$820$	0	0
$821$	−9.87204e50	−0.984922	−0.492461	−	0.870335i	$-0.663903\pi$
$821$	−9.87204e50	−0.984922	−0.492461	+	0.870335i	$0.663903\pi$
$822$	3.61983e50	0.353534
$823$	1.56871e51	1.49985	0.749923	−	0.661525i	$-0.230091\pi$
$823$	1.56871e51	1.49985	0.749923	+	0.661525i	$0.230091\pi$
$824$	1.29577e51	1.21283
$825$	0	0
$826$	7.20039e50	0.645960
$827$	3.34712e49	0.0293985	0.0146992	−	0.999892i	$-0.495321\pi$
$827$	3.34712e49	0.0293985	0.0146992	+	0.999892i	$0.495321\pi$
$828$	1.36559e51	1.17433
$829$	−1.24277e51	−1.04638	−0.523188	−	0.852217i	$-0.675257\pi$
$829$	−1.24277e51	−1.04638	−0.523188	+	0.852217i	$0.675257\pi$
$830$	0	0
$831$	−2.04327e49	−0.0164933
$832$	−1.11685e50	−0.0882749
$833$	−2.94772e50	−0.228139
$834$	−2.84190e50	−0.215379
$835$	0	0
$836$	1.85208e51	1.34601
$837$	−1.21258e51	−0.863005
$838$	−6.61903e50	−0.461343
$839$	7.06560e50	0.482297	0.241149	−	0.970488i	$-0.422476\pi$
$839$	7.06560e50	0.482297	0.241149	+	0.970488i	$0.422476\pi$
$840$	0	0
$841$	1.69401e51	1.10914
$842$	4.09125e51	2.62358
$843$	1.87258e51	1.17613
$844$	2.04329e51	1.25700
$845$	0	0
$846$	−1.22122e51	−0.720796
$847$	9.29800e50	0.537564
$848$	4.80842e51	2.72317
$849$	−1.67516e49	−0.00929333
$850$	0	0
$851$	3.11773e51	1.65986
$852$	−1.32422e51	−0.690667
$853$	4.40952e50	0.225311	0.112656	−	0.993634i	$-0.464064\pi$
$853$	4.40952e50	0.225311	0.112656	+	0.993634i	$0.464064\pi$
$854$	3.03773e51	1.52067
$855$	0	0
$856$	7.43474e51	3.57252
$857$	2.01998e51	0.951004	0.475502	−	0.879715i	$-0.342267\pi$
$857$	2.01998e51	0.951004	0.475502	+	0.879715i	$0.342267\pi$
$858$	4.13006e50	0.190515
$859$	−2.47558e51	−1.11891	−0.559456	−	0.828860i	$-0.688990\pi$
$859$	−2.47558e51	−1.11891	−0.559456	+	0.828860i	$0.688990\pi$
$860$	0	0
$861$	3.82315e50	0.165908
$862$	3.99071e51	1.69696
$863$	−1.15182e51	−0.479948	−0.239974	−	0.970779i	$-0.577139\pi$
$863$	−1.15182e51	−0.479948	−0.239974	+	0.970779i	$0.577139\pi$
$864$	2.02515e51	0.826926
$865$	0	0
$866$	−6.84143e51	−2.68277
$867$	−1.52563e51	−0.586293
$868$	−3.08657e51	−1.16247
$869$	9.84195e49	0.0363274
$870$	0	0
$871$	−1.83781e50	−0.0651602
$872$	2.99601e51	1.04113
$873$	9.38647e49	0.0319708
$874$	−8.23827e51	−2.75034
$875$	0	0
$876$	−3.78255e51	−1.21328
$877$	−1.21793e50	−0.0382938	−0.0191469	−	0.999817i	$-0.506095\pi$
$877$	−1.21793e50	−0.0382938	−0.0191469	+	0.999817i	$0.506095\pi$
$878$	−1.04445e52	−3.21909
$879$	3.68753e50	0.111412
$880$	0	0
$881$	1.43159e51	0.415663	0.207832	−	0.978165i	$-0.433359\pi$
$881$	1.43159e51	0.415663	0.207832	+	0.978165i	$0.433359\pi$
$882$	−1.91700e51	−0.545661
$883$	−4.21625e51	−1.17656	−0.588280	−	0.808658i	$-0.700195\pi$
$883$	−4.21625e51	−1.17656	−0.588280	+	0.808658i	$0.700195\pi$
$884$	1.18639e51	0.324575
$885$	0	0
$886$	−8.27591e51	−2.17634
$887$	−1.06484e51	−0.274549	−0.137274	−	0.990533i	$-0.543834\pi$
$887$	−1.06484e51	−0.274549	−0.137274	+	0.990533i	$0.543834\pi$
$888$	9.52303e51	2.40740
$889$	−1.18280e51	−0.293177
$890$	0	0
$891$	3.52185e50	0.0839288
$892$	−1.21268e52	−2.83376
$893$	5.06481e51	1.16055
$894$	6.49316e51	1.45898
$895$	0	0
$896$	−3.58879e51	−0.775457
$897$	−1.26295e51	−0.267621
$898$	−1.04377e52	−2.16904
$899$	−5.84365e51	−1.19094
$900$	0	0
$901$	3.30714e51	0.648289
$902$	−1.41045e51	−0.271171
$903$	−1.69235e50	−0.0319120
$904$	−4.88057e51	−0.902658
$905$	0	0
$906$	−7.49007e51	−1.33273
$907$	−5.18332e51	−0.904649	−0.452325	−	0.891853i	$-0.649405\pi$
$907$	−5.18332e51	−0.904649	−0.452325	+	0.891853i	$0.649405\pi$
$908$	9.97841e51	1.70828
$909$	−1.89913e51	−0.318923
$910$	0	0
$911$	9.24676e51	1.49423	0.747116	−	0.664694i	$-0.231438\pi$
$911$	9.24676e51	1.49423	0.747116	+	0.664694i	$0.231438\pi$
$912$	−1.07439e52	−1.70315
$913$	2.39226e51	0.372023
$914$	1.06765e52	1.62880
$915$	0	0
$916$	−9.64981e51	−1.41693
$917$	−6.64424e51	−0.957154
$918$	5.19689e51	0.734508
$919$	−4.29279e51	−0.595275	−0.297638	−	0.954679i	$-0.596199\pi$
$919$	−4.29279e51	−0.595275	−0.297638	+	0.954679i	$0.596199\pi$
$920$	0	0
$921$	7.49359e51	1.00034
$922$	−2.97278e51	−0.389378
$923$	−1.33592e51	−0.171692
$924$	3.16586e51	0.399238
$925$	0	0
$926$	−9.09766e51	−1.10468
$927$	2.47460e51	0.294856
$928$	9.75961e51	1.14115
$929$	4.47733e51	0.513740	0.256870	−	0.966446i	$-0.417309\pi$
$929$	4.47733e51	0.513740	0.256870	+	0.966446i	$0.417309\pi$
$930$	0	0
$931$	7.95047e51	0.878564
$932$	8.71061e51	0.944649
$933$	2.87284e51	0.305761
$934$	−2.78529e52	−2.90938
$935$	0	0
$936$	4.20799e51	0.423397
$937$	1.28073e50	0.0126478	0.00632388	−	0.999980i	$-0.497987\pi$
$937$	1.28073e50	0.0126478	0.00632388	+	0.999980i	$0.497987\pi$
$938$	−2.04919e51	−0.198624
$939$	−4.14159e51	−0.394021
$940$	0	0
$941$	3.26378e50	0.0299160	0.0149580	−	0.999888i	$-0.495239\pi$
$941$	3.26378e50	0.0299160	0.0149580	+	0.999888i	$0.495239\pi$
$942$	−1.32179e52	−1.18924
$943$	4.31310e51	0.380921
$944$	1.05938e52	0.918420
$945$	0	0
$946$	6.24346e50	0.0521591
$947$	1.57573e52	1.29228	0.646140	−	0.763219i	$-0.276382\pi$
$947$	1.57573e52	1.29228	0.646140	+	0.763219i	$0.276382\pi$
$948$	−1.68555e51	−0.135705
$949$	−3.81594e51	−0.301608
$950$	0	0
$951$	3.75299e51	0.285903
$952$	7.21472e51	0.539601
$953$	9.47096e51	0.695454	0.347727	−	0.937596i	$-0.386954\pi$
$953$	9.47096e51	0.695454	0.347727	+	0.937596i	$0.386954\pi$
$954$	2.15075e52	1.55057
$955$	0	0
$956$	1.07991e52	0.750540
$957$	5.99377e51	0.409017
$958$	−5.03703e52	−3.37503
$959$	2.79924e51	0.184168
$960$	0	0
$961$	−5.16308e51	−0.327529
$962$	1.76151e52	1.09729
$963$	1.41985e52	0.868528
$964$	−1.11381e52	−0.669059
$965$	0	0
$966$	−1.40821e52	−0.815773
$967$	−1.42806e52	−0.812424	−0.406212	−	0.913779i	$-0.633151\pi$
$967$	−1.42806e52	−0.812424	−0.406212	+	0.913779i	$0.633151\pi$
$968$	3.20401e52	1.79009
$969$	−7.38949e51	−0.405460
$970$	0	0
$971$	−4.08920e51	−0.216422	−0.108211	−	0.994128i	$-0.534512\pi$
$971$	−4.08920e51	−0.216422	−0.108211	+	0.994128i	$0.534512\pi$
$972$	3.85032e52	2.00141
$973$	−2.19766e51	−0.112198
$974$	−3.17319e52	−1.59116
$975$	0	0
$976$	4.46934e52	2.16208
$977$	−2.55940e52	−1.21614	−0.608071	−	0.793883i	$-0.708056\pi$
$977$	−2.55940e52	−1.21614	−0.608071	+	0.793883i	$0.708056\pi$
$978$	−5.15597e52	−2.40647
$979$	−6.40042e51	−0.293435
$980$	0	0
$981$	5.72166e51	0.253113
$982$	2.98488e52	1.29711
$983$	−1.82270e52	−0.778087	−0.389044	−	0.921219i	$-0.627194\pi$
$983$	−1.82270e52	−0.778087	−0.389044	+	0.921219i	$0.627194\pi$
$984$	1.31742e52	0.552474
$985$	0	0
$986$	2.50449e52	1.01361
$987$	8.65757e51	0.344228
$988$	−3.19989e52	−1.24994
$989$	−1.90922e51	−0.0732693
$990$	0	0
$991$	8.47738e51	0.314031	0.157015	−	0.987596i	$-0.449813\pi$
$991$	8.47738e51	0.314031	0.157015	+	0.987596i	$0.449813\pi$
$992$	−1.77044e52	−0.644358
$993$	2.84149e52	1.01610
$994$	−1.48957e52	−0.523358
$995$	0	0
$996$	−4.09702e52	−1.38973
$997$	4.09490e52	1.36483	0.682414	−	0.730966i	$-0.260930\pi$
$997$	4.09490e52	1.36483	0.682414	+	0.730966i	$0.260930\pi$
$998$	4.37162e52	1.43172
$999$	5.30459e52	1.70709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.36.a.a.1.1		3
5.2	odd	4		25.36.b.a.24.1		6
5.3	odd	4		25.36.b.a.24.6		6
5.4	even	2		1.36.a.a.1.3	✓	3
15.14	odd	2		9.36.a.b.1.1		3
20.19	odd	2		16.36.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.36.a.a.1.3	✓	3	5.4	even	2
9.36.a.b.1.1		3	15.14	odd	2
16.36.a.d.1.2		3	20.19	odd	2
25.36.a.a.1.1		3	1.1	even	1	trivial
25.36.b.a.24.1		6	5.2	odd	4
25.36.b.a.24.6		6	5.3	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)

\(f(q)\)	\(=\)	\(q-331573. q^{2} +1.54691e8 q^{3} +7.55810e10 q^{4} -5.12913e13 q^{6} -3.96640e14 q^{7} -1.36679e16 q^{8} -2.61023e16 q^{9} +O(q^{10})\)	\(q-331573. q^{2} +1.54691e8 q^{3} +7.55810e10 q^{4} -5.12913e13 q^{6} -3.96640e14 q^{7} -1.36679e16 q^{8} -2.61023e16 q^{9} -6.82681e17 q^{11} +1.16917e19 q^{12} +1.17949e19 q^{13} +1.31515e20 q^{14} +1.93496e21 q^{16} +1.33083e21 q^{17} +8.65483e21 q^{18} -3.58945e22 q^{19} -6.13565e22 q^{21} +2.26359e23 q^{22} -6.92195e23 q^{23} -2.11429e24 q^{24} -3.91088e24 q^{26} -1.17772e25 q^{27} -2.99785e25 q^{28} -5.67568e25 q^{29} +1.02960e26 q^{31} -1.71955e26 q^{32} -1.05604e26 q^{33} -4.41267e26 q^{34} -1.97284e27 q^{36} -4.50412e27 q^{37} +1.19017e28 q^{38} +1.82456e27 q^{39} -6.23104e27 q^{41} +2.03442e28 q^{42} +2.75822e27 q^{43} -5.15977e28 q^{44} +2.29513e29 q^{46} -1.41103e29 q^{47} +2.99320e29 q^{48} -2.21495e29 q^{49} +2.05867e29 q^{51} +8.91472e29 q^{52} +2.48503e30 q^{53} +3.90500e30 q^{54} +5.42123e30 q^{56} -5.55255e30 q^{57} +1.88190e31 q^{58} +5.47495e30 q^{59} +2.30979e31 q^{61} -3.41386e31 q^{62} +1.03532e31 q^{63} -9.46893e30 q^{64} +3.50156e31 q^{66} -1.55814e31 q^{67} +1.00585e32 q^{68} -1.07076e32 q^{69} -1.13262e32 q^{71} +3.56763e32 q^{72} -3.23524e32 q^{73} +1.49345e33 q^{74} -2.71294e33 q^{76} +2.70778e32 q^{77} -6.04976e32 q^{78} -1.44166e32 q^{79} -5.15885e32 q^{81} +2.06605e33 q^{82} -3.50421e33 q^{83} -4.63739e33 q^{84} -9.14551e32 q^{86} -8.77975e33 q^{87} +9.33079e33 q^{88} +9.37543e33 q^{89} -4.67833e33 q^{91} -5.23168e34 q^{92} +1.59269e34 q^{93} +4.67858e34 q^{94} -2.65998e34 q^{96} -3.59603e33 q^{97} +7.34419e34 q^{98} +1.78195e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 139656 q^{2} + 104875308 q^{3} + 34841262144 q^{4} - 4786530564384 q^{6} - 878422149346056 q^{7} - 22\!\cdots\!00 q^{8}+ \cdots + 15\!\cdots\!51 q^{9}+O(q^{10}) \) 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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