LMFDB - Embedded newform 25.34.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,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, 34, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
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:	$172.457072203$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9680197848 x^{4} + 8052423720422 x^{3} + \cdots - 10\!\cdots\!50 $ x^6 - x^5 - 9680197848x^4 + 8052423720422x^3 + 24239866893261762265x^2 - 69081627028404093368325x - 10572274201725134136583265250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$77152.3$ 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)

$f(q)$	$=$	$q-178863. q^{2} -8.55112e7 q^{3} +2.34019e10 q^{4} +1.52948e13 q^{6} +8.09549e13 q^{7} -2.64931e15 q^{8} +1.75311e15 q^{9} +O(q^{10})$	\(q-178863. q^{2} -8.55112e7 q^{3} +2.34019e10 q^{4} +1.52948e13 q^{6} +8.09549e13 q^{7} -2.64931e15 q^{8} +1.75311e15 q^{9} +1.95800e17 q^{11} -2.00113e18 q^{12} +2.59207e18 q^{13} -1.44798e19 q^{14} +2.72841e20 q^{16} +1.52177e20 q^{17} -3.13565e20 q^{18} +1.39526e21 q^{19} -6.92255e21 q^{21} -3.50214e22 q^{22} +3.40316e22 q^{23} +2.26546e23 q^{24} -4.63625e23 q^{26} +3.25452e23 q^{27} +1.89450e24 q^{28} -1.49246e24 q^{29} -1.38398e24 q^{31} -2.60438e25 q^{32} -1.67431e25 q^{33} -2.72188e25 q^{34} +4.10261e25 q^{36} -1.15380e26 q^{37} -2.49559e26 q^{38} -2.21651e26 q^{39} -6.35087e25 q^{41} +1.23819e27 q^{42} +2.64294e26 q^{43} +4.58211e27 q^{44} -6.08698e27 q^{46} -1.03700e27 q^{47} -2.33310e28 q^{48} -1.17730e27 q^{49} -1.30128e28 q^{51} +6.06594e28 q^{52} -5.20280e28 q^{53} -5.82111e28 q^{54} -2.14475e29 q^{56} -1.19310e29 q^{57} +2.66946e29 q^{58} -6.17754e28 q^{59} -1.21654e29 q^{61} +2.47543e29 q^{62} +1.41923e29 q^{63} +2.31456e30 q^{64} +2.99472e30 q^{66} +2.87484e29 q^{67} +3.56123e30 q^{68} -2.91008e30 q^{69} -2.84409e30 q^{71} -4.64452e30 q^{72} +2.67045e30 q^{73} +2.06372e31 q^{74} +3.26517e31 q^{76} +1.58510e31 q^{77} +3.96451e31 q^{78} -7.84640e30 q^{79} -3.75754e31 q^{81} +1.13593e31 q^{82} -1.28723e31 q^{83} -1.62001e32 q^{84} -4.72724e31 q^{86} +1.27622e32 q^{87} -5.18736e32 q^{88} -1.56902e32 q^{89} +2.09841e32 q^{91} +7.96404e32 q^{92} +1.18346e32 q^{93} +1.85481e32 q^{94} +2.22703e33 q^{96} -4.84738e32 q^{97} +2.10574e32 q^{98} +3.43259e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 6615759249352 q^{6} - 19113832847500 q^{7} - 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) $ 6 * q - 147350 * q^2 - 26513900 * q^3 + 29520645652 * q^4 + 6615759249352 * q^6 - 19113832847500 * q^7 - 3069820115785800 * q^8 + 13602102583345438 * q^9	$ 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 6615759249352 q^{6} - 19113832847500 q^{7} - 30\!\cdots\!00 q^{8}+ \cdots + 16\!\cdots\!16 q^{99}+O(q^{100}) $ 6 * q - 147350 * q^2 - 26513900 * q^3 + 29520645652 * q^4 + 6615759249352 * q^6 - 19113832847500 * q^7 - 3069820115785800 * q^8 + 13602102583345438 * q^9 + 150760896555890192 * q^11 - 466351581756413200 * q^12 + 1403095636752804700 * q^13 - 7086110008989891456 * q^14 + 64511520005858668816 * q^16 - 134380842798611834300 * q^17 - 673397185005127949150 * q^18 + 1711584362599986612200 * q^19 - 10560397660826154148128 * q^21 - 2470897477250007236200 * q^22 - 6879744551224024319700 * q^23 + 211895016154723698861600 * q^24 - 361829246667436498168588 * q^26 + 340705501428703899968200 * q^27 + 1750376606004032278695200 * q^28 + 1305223406410727358015700 * q^29 + 10825321396800575904753352 * q^31 - 26818258713124955338861600 * q^32 - 34856079507682787436662800 * q^33 + 8872409666654531735490124 * q^34 + 168714411751774892911163396 * q^36 - 276757164463535626747584900 * q^37 - 835386866362613528909982200 * q^38 + 579964086232605925635188456 * q^39 + 448008579649522993395821932 * q^41 - 1478478813030145693383604800 * q^42 - 2250588086104897739543439500 * q^43 + 7171805342222267509050250864 * q^44 + 3493759290976330924493595072 * q^46 - 3830785379519133075460228700 * q^47 - 24576343390562635665291611200 * q^48 - 7173427073564666873529235258 * q^49 - 54920362805063671320868694888 * q^51 + 90553915669177954388890305000 * q^52 - 47034713551772209628037134900 * q^53 - 182647187168263097239229399600 * q^54 - 392573339390998146620750750400 * q^56 + 242119765146738617914766400400 * q^57 + 443272639260736798552560798700 * q^58 - 178315156221037727069533799800 * q^59 - 282317689060586014253208287308 * q^61 - 3477509804797272360008839200 * q^62 + 559259159226762324796386276900 * q^63 + 1937968534792541396434479607872 * q^64 + 5061208746155430260544773159264 * q^66 - 3357382217232044190774976063300 * q^67 - 3866973693935427075529380663400 * q^68 + 316127240816983184255653823136 * q^69 + 8451218031993742702656617170072 * q^71 - 8740278584811466598158058687400 * q^72 + 1719044326022105657749673125300 * q^73 + 20494727417173075429289542476484 * q^74 + 29410039922734837753629694458000 * q^76 + 1179300749517366199915257594000 * q^77 + 57229303014236704407408363530000 * q^78 - 22052505351402355443894747635600 * q^79 - 133163964889176760661905573719674 * q^81 + 156059027108947085834404172875300 * q^82 + 47087087002138304263127820978900 * q^83 - 235991611992224148517578838651776 * q^84 - 128823880621545855657554048105608 * q^86 + 175316396211912369693639217216600 * q^87 - 497433069891524019720739466805600 * q^88 - 336491358341169481948206213360900 * q^89 + 194633769402343866156602864483432 * q^91 + 419043430758613276035983032687200 * q^92 - 212928090391747529239858474972800 * q^93 + 1486141097168392212687292135345264 * q^94 + 3151728990173122672564203081529472 * q^96 - 2569321197832638009639208504856700 * q^97 - 6985460513399098756137635798950 * q^98 + 1660882302442227079414567162624016 * 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 $

$2$	−178863.	−1.92986	−0.964928	−	0.262516i	$-0.915448\pi$
$2$	−178863.	−1.92986	−0.964928	+	0.262516i	$0.915448\pi$
$3$	−8.55112e7	−1.14689	−0.573446	−	0.819243i	$-0.694394\pi$
$3$	−8.55112e7	−1.14689	−0.573446	+	0.819243i	$0.694394\pi$
$4$	2.34019e10	2.72434
$5$	0	0
$5$	0	0
$6$	1.52948e13	2.21333
$7$	8.09549e13	0.920716	0.460358	−	0.887733i	$-0.347721\pi$
$7$	8.09549e13	0.920716	0.460358	+	0.887733i	$0.347721\pi$
$8$	−2.64931e15	−3.32773
$9$	1.75311e15	0.315360
$10$	0	0
$11$	1.95800e17	1.28480	0.642398	−	0.766371i	$-0.277939\pi$
$11$	1.95800e17	1.28480	0.642398	+	0.766371i	$0.277939\pi$
$12$	−2.00113e18	−3.12452
$13$	2.59207e18	1.08039	0.540197	−	0.841539i	$-0.318350\pi$
$13$	2.59207e18	1.08039	0.540197	+	0.841539i	$0.318350\pi$
$14$	−1.44798e19	−1.77685
$15$	0	0
$16$	2.72841e20	3.69769
$17$	1.52177e20	0.758475	0.379238	−	0.925299i	$-0.376186\pi$
$17$	1.52177e20	0.758475	0.379238	+	0.925299i	$0.376186\pi$
$18$	−3.13565e20	−0.608600
$19$	1.39526e21	1.10974	0.554868	−	0.831938i	$-0.312769\pi$
$19$	1.39526e21	1.10974	0.554868	+	0.831938i	$0.312769\pi$
$20$	0	0
$21$	−6.92255e21	−1.05596
$22$	−3.50214e22	−2.47947
$23$	3.40316e22	1.15711	0.578553	−	0.815645i	$-0.303618\pi$
$23$	3.40316e22	1.15711	0.578553	+	0.815645i	$0.303618\pi$
$24$	2.26546e23	3.81654
$25$	0	0
$26$	−4.63625e23	−2.08500
$27$	3.25452e23	0.785207
$28$	1.89450e24	2.50834
$29$	−1.49246e24	−1.10748	−0.553741	−	0.832689i	$-0.686800\pi$
$29$	−1.49246e24	−1.10748	−0.553741	+	0.832689i	$0.686800\pi$
$30$	0	0
$31$	−1.38398e24	−0.341714	−0.170857	−	0.985296i	$-0.554654\pi$
$31$	−1.38398e24	−0.341714	−0.170857	+	0.985296i	$0.554654\pi$
$32$	−2.60438e25	−3.80828
$33$	−1.67431e25	−1.47352
$34$	−2.72188e25	−1.46375
$35$	0	0
$36$	4.10261e25	0.859149
$37$	−1.15380e26	−1.53745	−0.768727	−	0.639577i	$-0.779109\pi$
$37$	−1.15380e26	−1.53745	−0.768727	+	0.639577i	$0.779109\pi$
$38$	−2.49559e26	−2.14163
$39$	−2.21651e26	−1.23909
$40$	0	0
$41$	−6.35087e25	−0.155561	−0.0777804	−	0.996971i	$-0.524783\pi$
$41$	−6.35087e25	−0.155561	−0.0777804	+	0.996971i	$0.524783\pi$
$42$	1.23819e27	2.03785
$43$	2.64294e26	0.295025	0.147512	−	0.989060i	$-0.452873\pi$
$43$	2.64294e26	0.295025	0.147512	+	0.989060i	$0.452873\pi$
$44$	4.58211e27	3.50022
$45$	0	0
$46$	−6.08698e27	−2.23305
$47$	−1.03700e27	−0.266788	−0.133394	−	0.991063i	$-0.542588\pi$
$47$	−1.03700e27	−0.266788	−0.133394	+	0.991063i	$0.542588\pi$
$48$	−2.33310e28	−4.24085
$49$	−1.17730e27	−0.152283
$50$	0	0
$51$	−1.30128e28	−0.869889
$52$	6.06594e28	2.94336
$53$	−5.20280e28	−1.84368	−0.921839	−	0.387574i	$-0.873313\pi$
$53$	−5.20280e28	−1.84368	−0.921839	+	0.387574i	$0.873313\pi$
$54$	−5.82111e28	−1.51534
$55$	0	0
$56$	−2.14475e29	−3.06389
$57$	−1.19310e29	−1.27275
$58$	2.66946e29	2.13728
$59$	−6.17754e28	−0.373042	−0.186521	−	0.982451i	$-0.559721\pi$
$59$	−6.17754e28	−0.373042	−0.186521	+	0.982451i	$0.559721\pi$
$60$	0	0
$61$	−1.21654e29	−0.423822	−0.211911	−	0.977289i	$-0.567969\pi$
$61$	−1.21654e29	−0.423822	−0.211911	+	0.977289i	$0.567969\pi$
$62$	2.47543e29	0.659458
$63$	1.41923e29	0.290357
$64$	2.31456e30	3.65174
$65$	0	0
$66$	2.99472e30	2.84369
$67$	2.87484e29	0.213000	0.106500	−	0.994313i	$-0.466036\pi$
$67$	2.87484e29	0.213000	0.106500	+	0.994313i	$0.466036\pi$
$68$	3.56123e30	2.06634
$69$	−2.91008e30	−1.32707
$70$	0	0
$71$	−2.84409e30	−0.809432	−0.404716	−	0.914442i	$-0.632630\pi$
$71$	−2.84409e30	−0.809432	−0.404716	+	0.914442i	$0.632630\pi$
$72$	−4.64452e30	−1.04943
$73$	2.67045e30	0.480570	0.240285	−	0.970702i	$-0.422759\pi$
$73$	2.67045e30	0.480570	0.240285	+	0.970702i	$0.422759\pi$
$74$	2.06372e31	2.96706
$75$	0	0
$76$	3.26517e31	3.02330
$77$	1.58510e31	1.18293
$78$	3.96451e31	2.39127
$79$	−7.84640e30	−0.383551	−0.191776	−	0.981439i	$-0.561425\pi$
$79$	−7.84640e30	−0.383551	−0.191776	+	0.981439i	$0.561425\pi$
$80$	0	0
$81$	−3.75754e31	−1.21591
$82$	1.13593e31	0.300210
$83$	−1.28723e31	−0.278527	−0.139263	−	0.990255i	$-0.544473\pi$
$83$	−1.28723e31	−0.278527	−0.139263	+	0.990255i	$0.544473\pi$
$84$	−1.62001e32	−2.87680
$85$	0	0
$86$	−4.72724e31	−0.569355
$87$	1.27622e32	1.27016
$88$	−5.18736e32	−4.27545
$89$	−1.56902e32	−1.07323	−0.536616	−	0.843826i	$-0.680298\pi$
$89$	−1.56902e32	−1.07323	−0.536616	+	0.843826i	$0.680298\pi$
$90$	0	0
$91$	2.09841e32	0.994735
$92$	7.96404e32	3.15235
$93$	1.18346e32	0.391909
$94$	1.85481e32	0.514862
$95$	0	0
$96$	2.22703e33	4.36769
$97$	−4.84738e32	−0.801259	−0.400630	−	0.916240i	$-0.631209\pi$
$97$	−4.84738e32	−0.801259	−0.400630	+	0.916240i	$0.631209\pi$
$98$	2.10574e32	0.293883
$99$	3.43259e32	0.405174
$100$	0	0
$101$	2.51128e32	0.213105	0.106552	−	0.994307i	$-0.466019\pi$
$101$	2.51128e32	0.213105	0.106552	+	0.994307i	$0.466019\pi$
$102$	2.32751e33	1.67876
$103$	2.60164e33	1.59747	0.798737	−	0.601681i	$-0.205502\pi$
$103$	2.60164e33	1.59747	0.798737	+	0.601681i	$0.205502\pi$
$104$	−6.86720e33	−3.59525
$105$	0	0
$106$	9.30586e33	3.55803
$107$	−3.74478e33	−1.22629	−0.613146	−	0.789970i	$-0.710096\pi$
$107$	−3.74478e33	−1.22629	−0.613146	+	0.789970i	$0.710096\pi$
$108$	7.61619e33	2.13917
$109$	−2.76732e33	−0.667609	−0.333805	−	0.942642i	$-0.608333\pi$
$109$	−2.76732e33	−0.667609	−0.333805	+	0.942642i	$0.608333\pi$
$110$	0	0
$111$	9.86628e33	1.76329
$112$	2.20879e34	3.40452
$113$	−1.26307e34	−1.68125	−0.840626	−	0.541617i	$-0.817812\pi$
$113$	−1.26307e34	−1.68125	−0.840626	+	0.541617i	$0.817812\pi$
$114$	2.13401e34	2.45622
$115$	0	0
$116$	−3.49265e34	−3.01716
$117$	4.54418e33	0.340713
$118$	1.10493e34	0.719917
$119$	1.23195e34	0.698340
$120$	0	0
$121$	1.51127e34	0.650703
$122$	2.17593e34	0.817915
$123$	5.43071e33	0.178411
$124$	−3.23878e34	−0.930945
$125$	0	0
$126$	−2.53847e34	−0.560348
$127$	2.24824e33	0.0435594	0.0217797	−	0.999763i	$-0.493067\pi$
$127$	2.24824e33	0.0435594	0.0217797	+	0.999763i	$0.493067\pi$
$128$	−1.90275e35	−3.23905
$129$	−2.26001e34	−0.338361
$130$	0	0
$131$	7.19207e34	0.835368	0.417684	−	0.908592i	$-0.362842\pi$
$131$	7.19207e34	0.835368	0.417684	+	0.908592i	$0.362842\pi$
$132$	−3.91821e35	−4.01438
$133$	1.12953e35	1.02175
$134$	−5.14202e34	−0.411059
$135$	0	0
$136$	−4.03163e35	−2.52400
$137$	−2.56636e35	−1.42373	−0.711867	−	0.702314i	$-0.752150\pi$
$137$	−2.56636e35	−1.42373	−0.711867	+	0.702314i	$0.752150\pi$
$138$	5.20505e35	2.56106
$139$	7.81097e34	0.341162	0.170581	−	0.985344i	$-0.445436\pi$
$139$	7.81097e34	0.341162	0.170581	+	0.985344i	$0.445436\pi$
$140$	0	0
$141$	8.86755e34	0.305977
$142$	5.08701e35	1.56209
$143$	5.07529e35	1.38809
$144$	4.78320e35	1.16611
$145$	0	0
$146$	−4.77643e35	−0.927431
$147$	1.00672e35	0.174652
$148$	−2.70011e36	−4.18855
$149$	−1.40823e35	−0.195479	−0.0977397	−	0.995212i	$-0.531161\pi$
$149$	−1.40823e35	−0.195479	−0.0977397	+	0.995212i	$0.531161\pi$
$150$	0	0
$151$	4.46232e35	0.497097	0.248548	−	0.968619i	$-0.420046\pi$
$151$	4.46232e35	0.497097	0.248548	+	0.968619i	$0.420046\pi$
$152$	−3.69647e36	−3.69290
$153$	2.66782e35	0.239193
$154$	−2.83515e36	−2.28289
$155$	0	0
$156$	−5.18706e36	−3.37571
$157$	−7.61070e35	−0.445739	−0.222869	−	0.974848i	$-0.571542\pi$
$157$	−7.61070e35	−0.445739	−0.222869	+	0.974848i	$0.571542\pi$
$158$	1.40343e36	0.740199
$159$	4.44897e36	2.11450
$160$	0	0
$161$	2.75502e36	1.06537
$162$	6.72084e36	2.34653
$163$	−1.95336e36	−0.616152	−0.308076	−	0.951362i	$-0.599685\pi$
$163$	−1.95336e36	−0.616152	−0.308076	+	0.951362i	$0.599685\pi$
$164$	−1.48623e36	−0.423800
$165$	0	0
$166$	2.30237e36	0.537516
$167$	−2.87170e36	−0.607180	−0.303590	−	0.952803i	$-0.598185\pi$
$167$	−2.87170e36	−0.607180	−0.303590	+	0.952803i	$0.598185\pi$
$168$	1.83400e37	3.51395
$169$	9.62710e35	0.167249
$170$	0	0
$171$	2.44604e36	0.349967
$172$	6.18499e36	0.803748
$173$	−1.61105e37	−1.90261	−0.951303	−	0.308258i	$-0.900254\pi$
$173$	−1.61105e37	−1.90261	−0.951303	+	0.308258i	$0.900254\pi$
$174$	−2.28269e37	−2.45123
$175$	0	0
$176$	5.34225e37	4.75078
$177$	5.28249e36	0.427839
$178$	2.80639e37	2.07118
$179$	9.06671e33	0.000610063 0	0.000305031	−	1.00000i	$-0.499903\pi$
$179$	9.06671e33	0.000610063 0	0.000305031		1.00000i	$0.499903\pi$
$180$	0	0
$181$	1.89723e36	0.106273	0.0531364	−	0.998587i	$-0.483078\pi$
$181$	1.89723e36	0.106273	0.0531364	+	0.998587i	$0.483078\pi$
$182$	−3.75327e37	−1.91969
$183$	1.04028e37	0.486078
$184$	−9.01602e37	−3.85053
$185$	0	0
$186$	−2.11677e37	−0.756327
$187$	2.97963e37	0.974487
$188$	−2.42679e37	−0.726821
$189$	2.63469e37	0.722953
$190$	0	0
$191$	−6.88314e37	−1.58758	−0.793790	−	0.608192i	$-0.791895\pi$
$191$	−6.88314e37	−1.58758	−0.793790	+	0.608192i	$0.791895\pi$
$192$	−1.97921e38	−4.18815
$193$	−5.10528e37	−0.991571	−0.495786	−	0.868445i	$-0.665120\pi$
$193$	−5.10528e37	−0.991571	−0.495786	+	0.868445i	$0.665120\pi$
$194$	8.67015e37	1.54631
$195$	0	0
$196$	−2.75510e37	−0.414869
$197$	6.02889e37	0.834727	0.417364	−	0.908740i	$-0.362954\pi$
$197$	6.02889e37	0.834727	0.417364	+	0.908740i	$0.362954\pi$
$198$	−6.13963e37	−0.781927
$199$	−1.42678e38	−1.67218	−0.836089	−	0.548594i	$-0.815163\pi$
$199$	−1.42678e38	−1.67218	−0.836089	+	0.548594i	$0.815163\pi$
$200$	0	0
$201$	−2.45831e37	−0.244288
$202$	−4.49175e37	−0.411261
$203$	−1.20822e38	−1.01968
$204$	−3.04525e38	−2.36987
$205$	0	0
$206$	−4.65337e38	−3.08289
$207$	5.96610e37	0.364905
$208$	7.07225e38	3.99496
$209$	2.73192e38	1.42579
$210$	0	0
$211$	3.27612e38	1.46116	0.730582	−	0.682825i	$-0.239249\pi$
$211$	3.27612e38	1.46116	0.730582	+	0.682825i	$0.239249\pi$
$212$	−1.21755e39	−5.02280
$213$	2.43201e38	0.928331
$214$	6.69801e38	2.36656
$215$	0	0
$216$	−8.62222e38	−2.61296
$217$	−1.12040e38	−0.314621
$218$	4.94971e38	1.28839
$219$	−2.28353e38	−0.551162
$220$	0	0
$221$	3.94453e38	0.819451
$222$	−1.76471e39	−3.40290
$223$	3.22330e38	0.577126	0.288563	−	0.957461i	$-0.406823\pi$
$223$	3.22330e38	0.577126	0.288563	+	0.957461i	$0.406823\pi$
$224$	−2.10837e39	−3.50634
$225$	0	0
$226$	2.25916e39	3.24457
$227$	6.02003e38	0.803845	0.401922	−	0.915674i	$-0.368342\pi$
$227$	6.02003e38	0.803845	0.401922	+	0.915674i	$0.368342\pi$
$228$	−2.79209e39	−3.46740
$229$	−3.71091e38	−0.428741	−0.214370	−	0.976752i	$-0.568770\pi$
$229$	−3.71091e38	−0.428741	−0.214370	+	0.976752i	$0.568770\pi$
$230$	0	0
$231$	−1.35544e39	−1.35670
$232$	3.95400e39	3.68540
$233$	3.81211e38	0.330973	0.165486	−	0.986212i	$-0.447081\pi$
$233$	3.81211e38	0.330973	0.165486	+	0.986212i	$0.447081\pi$
$234$	−8.12784e38	−0.657527
$235$	0	0
$236$	−1.44566e39	−1.01629
$237$	6.70955e38	0.439892
$238$	−2.20349e39	−1.34770
$239$	8.52350e38	0.486466	0.243233	−	0.969968i	$-0.421792\pi$
$239$	8.52350e38	0.486466	0.243233	+	0.969968i	$0.421792\pi$
$240$	0	0
$241$	3.41820e39	1.70027	0.850133	−	0.526568i	$-0.176522\pi$
$241$	3.41820e39	1.70027	0.850133	+	0.526568i	$0.176522\pi$
$242$	−2.70309e39	−1.25576
$243$	1.40391e39	0.609308
$244$	−2.84693e39	−1.15464
$245$	0	0
$246$	−9.71351e38	−0.344308
$247$	3.61661e39	1.19895
$248$	3.66660e39	1.13713
$249$	1.10072e39	0.319440
$250$	0	0
$251$	2.52321e39	0.641706	0.320853	−	0.947129i	$-0.396030\pi$
$251$	2.52321e39	0.641706	0.320853	+	0.947129i	$0.396030\pi$
$252$	3.32126e39	0.791032
$253$	6.66340e39	1.48665
$254$	−4.02127e38	−0.0840633
$255$	0	0
$256$	1.41511e40	2.59915
$257$	−4.18511e39	−0.720793	−0.360396	−	0.932799i	$-0.617359\pi$
$257$	−4.18511e39	−0.720793	−0.360396	+	0.932799i	$0.617359\pi$
$258$	4.04232e39	0.652988
$259$	−9.34058e39	−1.41556
$260$	0	0
$261$	−2.61645e39	−0.349256
$262$	−1.28639e40	−1.61214
$263$	−1.15657e40	−1.36114	−0.680570	−	0.732683i	$-0.738268\pi$
$263$	−1.15657e40	−1.36114	−0.680570	+	0.732683i	$0.738268\pi$
$264$	4.43577e40	4.90348
$265$	0	0
$266$	−2.02031e40	−1.97183
$267$	1.34169e40	1.23088
$268$	6.72768e39	0.580284
$269$	−7.21991e39	−0.585624	−0.292812	−	0.956170i	$-0.594591\pi$
$269$	−7.21991e39	−0.585624	−0.292812	+	0.956170i	$0.594591\pi$
$270$	0	0
$271$	2.28804e40	1.64237	0.821183	−	0.570665i	$-0.193315\pi$
$271$	2.28804e40	1.64237	0.821183	+	0.570665i	$0.193315\pi$
$272$	4.15202e40	2.80461
$273$	−1.79438e40	−1.14085
$274$	4.59026e40	2.74760
$275$	0	0
$276$	−6.81015e40	−3.61540
$277$	−2.67522e40	−1.33796	−0.668981	−	0.743279i	$-0.733269\pi$
$277$	−2.67522e40	−1.33796	−0.668981	+	0.743279i	$0.733269\pi$
$278$	−1.39709e40	−0.658394
$279$	−2.42627e39	−0.107763
$280$	0	0
$281$	−2.51780e40	−0.993955	−0.496977	−	0.867763i	$-0.665557\pi$
$281$	−2.51780e40	−0.993955	−0.496977	+	0.867763i	$0.665557\pi$
$282$	−1.58607e40	−0.590490
$283$	−4.17854e40	−1.46740	−0.733699	−	0.679475i	$-0.762208\pi$
$283$	−4.17854e40	−1.46740	−0.733699	+	0.679475i	$0.762208\pi$
$284$	−6.65571e40	−2.20517
$285$	0	0
$286$	−9.07780e40	−2.67880
$287$	−5.14135e39	−0.143227
$288$	−4.56575e40	−1.20098
$289$	−1.70967e40	−0.424715
$290$	0	0
$291$	4.14505e40	0.918958
$292$	6.24936e40	1.30924
$293$	1.81801e40	0.359981	0.179991	−	0.983668i	$-0.442393\pi$
$293$	1.81801e40	0.359981	0.179991	+	0.983668i	$0.442393\pi$
$294$	−1.80064e40	−0.337052
$295$	0	0
$296$	3.05677e41	5.11623
$297$	6.37236e40	1.00883
$298$	2.51880e40	0.377247
$299$	8.82124e40	1.25013
$300$	0	0
$301$	2.13959e40	0.271634
$302$	−7.98142e40	−0.959325
$303$	−2.14743e40	−0.244408
$304$	3.80684e41	4.10346
$305$	0	0
$306$	−4.77174e40	−0.461608
$307$	1.04678e40	0.0959564	0.0479782	−	0.998848i	$-0.484722\pi$
$307$	1.04678e40	0.0959564	0.0479782	+	0.998848i	$0.484722\pi$
$308$	3.70944e41	3.22271
$309$	−2.22470e41	−1.83213
$310$	0	0
$311$	1.01794e41	0.753660	0.376830	−	0.926282i	$-0.377014\pi$
$311$	1.01794e41	0.753660	0.376830	+	0.926282i	$0.377014\pi$
$312$	5.87223e41	4.12337
$313$	2.12567e41	1.41584	0.707921	−	0.706292i	$-0.249633\pi$
$313$	2.12567e41	1.41584	0.707921	+	0.706292i	$0.249633\pi$
$314$	1.36127e41	0.860212
$315$	0	0
$316$	−1.83621e41	−1.04492
$317$	−5.12986e40	−0.277094	−0.138547	−	0.990356i	$-0.544243\pi$
$317$	−5.12986e40	−0.277094	−0.138547	+	0.990356i	$0.544243\pi$
$318$	−7.95755e41	−4.08067
$319$	−2.92225e41	−1.42289
$320$	0	0
$321$	3.20220e41	1.40642
$322$	−4.92771e41	−2.05600
$323$	2.12326e41	0.841708
$324$	−8.79336e41	−3.31255
$325$	0	0
$326$	3.49384e41	1.18908
$327$	2.36637e41	0.765676
$328$	1.68254e41	0.517664
$329$	−8.39506e40	−0.245636
$330$	0	0
$331$	−4.71143e41	−1.24736	−0.623679	−	0.781681i	$-0.714363\pi$
$331$	−4.71143e41	−1.24736	−0.623679	+	0.781681i	$0.714363\pi$
$332$	−3.01236e41	−0.758802
$333$	−2.02274e41	−0.484852
$334$	5.13640e41	1.17177
$335$	0	0
$336$	−1.88876e42	−3.90462
$337$	−8.62495e40	−0.169771	−0.0848854	−	0.996391i	$-0.527052\pi$
$337$	−8.62495e40	−0.169771	−0.0848854	+	0.996391i	$0.527052\pi$
$338$	−1.72193e41	−0.322767
$339$	1.08007e42	1.92821
$340$	0	0
$341$	−2.70984e41	−0.439033
$342$	−4.37505e41	−0.675386
$343$	−7.21170e41	−1.06092
$344$	−7.00197e41	−0.981762
$345$	0	0
$346$	2.88157e42	3.67175
$347$	−2.78000e41	−0.337760	−0.168880	−	0.985637i	$-0.554015\pi$
$347$	−2.78000e41	−0.337760	−0.168880	+	0.985637i	$0.554015\pi$
$348$	2.98661e42	3.46036
$349$	−1.12911e42	−1.24772	−0.623860	−	0.781536i	$-0.714437\pi$
$349$	−1.12911e42	−1.24772	−0.623860	+	0.781536i	$0.714437\pi$
$350$	0	0
$351$	8.43594e41	0.848333
$352$	−5.09938e42	−4.89287
$353$	−1.75490e42	−1.60683	−0.803413	−	0.595422i	$-0.796985\pi$
$353$	−1.75490e42	−1.60683	−0.803413	+	0.595422i	$0.796985\pi$
$354$	−9.44841e41	−0.825667
$355$	0	0
$356$	−3.67181e42	−2.92385
$357$	−1.05345e42	−0.800920
$358$	−1.62170e39	−0.00117733
$359$	−2.42990e42	−1.68473	−0.842365	−	0.538907i	$-0.818837\pi$
$359$	−2.42990e42	−1.68473	−0.842365	+	0.538907i	$0.818837\pi$
$360$	0	0
$361$	3.65974e41	0.231516
$362$	−3.39343e41	−0.205091
$363$	−1.29230e42	−0.746286
$364$	4.91068e42	2.71000
$365$	0	0
$366$	−1.86067e42	−0.938060
$367$	2.37509e42	1.14470	0.572349	−	0.820010i	$-0.306032\pi$
$367$	2.37509e42	1.14470	0.572349	+	0.820010i	$0.306032\pi$
$368$	9.28523e42	4.27862
$369$	−1.11338e41	−0.0490577
$370$	0	0
$371$	−4.21192e42	−1.69750
$372$	2.76952e42	1.06769
$373$	−1.58778e42	−0.585592	−0.292796	−	0.956175i	$-0.594586\pi$
$373$	−1.58778e42	−0.585592	−0.292796	+	0.956175i	$0.594586\pi$
$374$	−5.32944e42	−1.88062
$375$	0	0
$376$	2.74734e42	0.887797
$377$	−3.86858e42	−1.19652
$378$	−4.71248e42	−1.39519
$379$	−2.74032e42	−0.776703	−0.388351	−	0.921511i	$-0.626955\pi$
$379$	−2.74032e42	−0.776703	−0.388351	+	0.921511i	$0.626955\pi$
$380$	0	0
$381$	−1.92250e41	−0.0499579
$382$	1.23114e43	3.06380
$383$	−3.57273e42	−0.851570	−0.425785	−	0.904824i	$-0.640002\pi$
$383$	−3.57273e42	−0.851570	−0.425785	+	0.904824i	$0.640002\pi$
$384$	1.62706e43	3.71483
$385$	0	0
$386$	9.13144e42	1.91359
$387$	4.63336e41	0.0930391
$388$	−1.13438e43	−2.18290
$389$	−2.24258e42	−0.413599	−0.206799	−	0.978383i	$-0.566305\pi$
$389$	−2.24258e42	−0.413599	−0.206799	+	0.978383i	$0.566305\pi$
$390$	0	0
$391$	5.17882e42	0.877636
$392$	3.11902e42	0.506755
$393$	−6.15003e42	−0.958077
$394$	−1.07834e43	−1.61090
$395$	0	0
$396$	8.03292e42	1.10383
$397$	8.69665e41	0.114633	0.0573164	−	0.998356i	$-0.481746\pi$
$397$	8.69665e41	0.114633	0.0573164	+	0.998356i	$0.481746\pi$
$398$	2.55198e43	3.22706
$399$	−9.65875e42	−1.17184
$400$	0	0
$401$	1.79590e41	0.0200632	0.0100316	−	0.999950i	$-0.496807\pi$
$401$	1.79590e41	0.0200632	0.0100316	+	0.999950i	$0.496807\pi$
$402$	4.39700e42	0.471440
$403$	−3.58738e42	−0.369185
$404$	5.87688e42	0.580569
$405$	0	0
$406$	2.16106e43	1.96783
$407$	−2.25915e43	−1.97532
$408$	3.44750e43	2.89475
$409$	1.72895e43	1.39427	0.697136	−	0.716939i	$-0.254457\pi$
$409$	1.72895e43	1.39427	0.697136	+	0.716939i	$0.254457\pi$
$410$	0	0
$411$	2.19453e43	1.63287
$412$	6.08834e43	4.35206
$413$	−5.00103e42	−0.343466
$414$	−1.06711e43	−0.704214
$415$	0	0
$416$	−6.75073e43	−4.11444
$417$	−6.67926e42	−0.391276
$418$	−4.88639e43	−2.75156
$419$	−3.07423e43	−1.66420	−0.832099	−	0.554628i	$-0.812861\pi$
$419$	−3.07423e43	−1.66420	−0.832099	+	0.554628i	$0.812861\pi$
$420$	0	0
$421$	−1.46291e43	−0.732090	−0.366045	−	0.930597i	$-0.619288\pi$
$421$	−1.46291e43	−0.732090	−0.366045	+	0.930597i	$0.619288\pi$
$422$	−5.85975e43	−2.81983
$423$	−1.81798e42	−0.0841343
$424$	1.37838e44	6.13526
$425$	0	0
$426$	−4.34997e43	−1.79154
$427$	−9.84848e42	−0.390220
$428$	−8.76349e43	−3.34083
$429$	−4.33994e43	−1.59198
$430$	0	0
$431$	3.24328e43	1.10182	0.550909	−	0.834565i	$-0.314281\pi$
$431$	3.24328e43	1.10182	0.550909	+	0.834565i	$0.314281\pi$
$432$	8.87967e43	2.90345
$433$	2.61817e42	0.0824040	0.0412020	−	0.999151i	$-0.486881\pi$
$433$	2.61817e42	0.0824040	0.0412020	+	0.999151i	$0.486881\pi$
$434$	2.00398e43	0.607174
$435$	0	0
$436$	−6.47606e43	−1.81880
$437$	4.74828e43	1.28408
$438$	4.08439e43	1.06366
$439$	−6.39695e43	−1.60438	−0.802192	−	0.597066i	$-0.796333\pi$
$439$	−6.39695e43	−1.60438	−0.802192	+	0.597066i	$0.796333\pi$
$440$	0	0
$441$	−2.06393e42	−0.0480239
$442$	−7.05530e43	−1.58142
$443$	−1.30321e43	−0.281418	−0.140709	−	0.990051i	$-0.544938\pi$
$443$	−1.30321e43	−0.281418	−0.140709	+	0.990051i	$0.544938\pi$
$444$	2.30890e44	4.80381
$445$	0	0
$446$	−5.76528e43	−1.11377
$447$	1.20420e43	0.224194
$448$	1.87375e44	3.36221
$449$	−9.56472e43	−1.65428	−0.827138	−	0.561999i	$-0.810032\pi$
$449$	−9.56472e43	−1.65428	−0.827138	+	0.561999i	$0.810032\pi$
$450$	0	0
$451$	−1.24350e43	−0.199864
$452$	−2.95582e44	−4.58030
$453$	−3.81578e43	−0.570116
$454$	−1.07676e44	−1.55130
$455$	0	0
$456$	3.16090e44	4.23536
$457$	3.78578e42	0.0489258	0.0244629	−	0.999701i	$-0.492212\pi$
$457$	3.78578e42	0.0489258	0.0244629	+	0.999701i	$0.492212\pi$
$458$	6.63743e43	0.827408
$459$	4.95262e43	0.595560
$460$	0	0
$461$	7.04190e43	0.788179	0.394089	−	0.919072i	$-0.371060\pi$
$461$	7.04190e43	0.788179	0.394089	+	0.919072i	$0.371060\pi$
$462$	2.42437e44	2.61823
$463$	−1.41714e44	−1.47682	−0.738409	−	0.674353i	$-0.764423\pi$
$463$	−1.41714e44	−1.47682	−0.738409	+	0.674353i	$0.764423\pi$
$464$	−4.07206e44	−4.09513
$465$	0	0
$466$	−6.81843e43	−0.638729
$467$	1.83277e44	1.65721	0.828606	−	0.559831i	$-0.189134\pi$
$467$	1.83277e44	1.65721	0.828606	+	0.559831i	$0.189134\pi$
$468$	1.06343e44	0.928219
$469$	2.32732e43	0.196112
$470$	0	0
$471$	6.50801e43	0.511214
$472$	1.63662e44	1.24138
$473$	5.17490e43	0.379047
$474$	−1.20009e44	−0.848928
$475$	0	0
$476$	2.88299e44	1.90252
$477$	−9.12106e43	−0.581423
$478$	−1.52454e44	−0.938809
$479$	−6.67837e43	−0.397314	−0.198657	−	0.980069i	$-0.563658\pi$
$479$	−6.67837e43	−0.397314	−0.198657	+	0.980069i	$0.563658\pi$
$480$	0	0
$481$	−2.99073e44	−1.66105
$482$	−6.11389e44	−3.28127
$483$	−2.35586e44	−1.22186
$484$	3.53666e44	1.77274
$485$	0	0
$486$	−2.51108e44	−1.17588
$487$	1.75263e44	0.793345	0.396673	−	0.917960i	$-0.370165\pi$
$487$	1.75263e44	0.793345	0.396673	+	0.917960i	$0.370165\pi$
$488$	3.22299e44	1.41036
$489$	1.67035e44	0.706659
$490$	0	0
$491$	3.92240e44	1.55134	0.775670	−	0.631139i	$-0.217412\pi$
$491$	3.92240e44	1.55134	0.775670	+	0.631139i	$0.217412\pi$
$492$	1.27089e44	0.486053
$493$	−2.27118e44	−0.839998
$494$	−6.46876e44	−2.31380
$495$	0	0
$496$	−3.77608e44	−1.26355
$497$	−2.30243e44	−0.745257
$498$	−1.96878e44	−0.616473
$499$	7.64433e43	0.231569	0.115785	−	0.993274i	$-0.463062\pi$
$499$	7.64433e43	0.231569	0.115785	+	0.993274i	$0.463062\pi$
$500$	0	0
$501$	2.45563e44	0.696370
$502$	−4.51307e44	−1.23840
$503$	4.88916e44	1.29826	0.649132	−	0.760676i	$-0.275132\pi$
$503$	4.88916e44	1.29826	0.649132	+	0.760676i	$0.275132\pi$
$504$	−3.75997e44	−0.966230
$505$	0	0
$506$	−1.19183e45	−2.86901
$507$	−8.23225e43	−0.191817
$508$	5.26132e43	0.118671
$509$	−3.35020e44	−0.731522	−0.365761	−	0.930709i	$-0.619191\pi$
$509$	−3.35020e44	−0.731522	−0.365761	+	0.930709i	$0.619191\pi$
$510$	0	0
$511$	2.16186e44	0.442469
$512$	−8.96657e44	−1.77694
$513$	4.54089e44	0.871374
$514$	7.48560e44	1.39103
$515$	0	0
$516$	−5.28886e44	−0.921812
$517$	−2.03046e44	−0.342768
$518$	1.67068e45	2.73182
$519$	1.37763e45	2.18208
$520$	0	0
$521$	−5.22367e44	−0.776521	−0.388261	−	0.921550i	$-0.626924\pi$
$521$	−5.22367e44	−0.776521	−0.388261	+	0.921550i	$0.626924\pi$
$522$	4.67985e44	0.674014
$523$	1.10438e45	1.54113	0.770566	−	0.637360i	$-0.219974\pi$
$523$	1.10438e45	1.54113	0.770566	+	0.637360i	$0.219974\pi$
$524$	1.68308e45	2.27583
$525$	0	0
$526$	2.06868e45	2.62680
$527$	−2.10610e44	−0.259182
$528$	−4.56822e45	−5.44863
$529$	2.93144e44	0.338893
$530$	0	0
$531$	−1.08299e44	−0.117643
$532$	2.64332e45	2.78360
$533$	−1.64619e44	−0.168067
$534$	−2.39978e45	−2.37542
$535$	0	0
$536$	−7.61634e44	−0.708806
$537$	−7.75305e41	−0.000699676 0
$538$	1.29137e45	1.13017
$539$	−2.30515e44	−0.195652
$540$	0	0
$541$	−1.40716e45	−1.12354	−0.561772	−	0.827292i	$-0.689880\pi$
$541$	−1.40716e45	−1.12354	−0.561772	+	0.827292i	$0.689880\pi$
$542$	−4.09244e45	−3.16953
$543$	−1.62234e44	−0.121883
$544$	−3.96326e45	−2.88849
$545$	0	0
$546$	3.20947e45	2.20168
$547$	1.00599e45	0.669579	0.334789	−	0.942293i	$-0.391335\pi$
$547$	1.00599e45	0.669579	0.334789	+	0.942293i	$0.391335\pi$
$548$	−6.00578e45	−3.87874
$549$	−2.13272e44	−0.133657
$550$	0	0
$551$	−2.08237e45	−1.22901
$552$	7.70971e45	4.41614
$553$	−6.35205e44	−0.353142
$554$	4.78498e45	2.58207
$555$	0	0
$556$	1.82792e45	0.929442
$557$	−6.35386e44	−0.313637	−0.156818	−	0.987627i	$-0.550124\pi$
$557$	−6.35386e44	−0.313637	−0.156818	+	0.987627i	$0.550124\pi$
$558$	4.33969e44	0.207967
$559$	6.85070e44	0.318743
$560$	0	0
$561$	−2.54792e45	−1.11763
$562$	4.50340e45	1.91819
$563$	1.73714e45	0.718534	0.359267	−	0.933235i	$-0.383027\pi$
$563$	1.73714e45	0.718534	0.359267	+	0.933235i	$0.383027\pi$
$564$	2.07518e45	0.833584
$565$	0	0
$566$	7.47384e45	2.83187
$567$	−3.04191e45	−1.11951
$568$	7.53487e45	2.69357
$569$	3.27076e45	1.13579	0.567894	−	0.823102i	$-0.307759\pi$
$569$	3.27076e45	1.13579	0.567894	+	0.823102i	$0.307759\pi$
$570$	0	0
$571$	2.07979e45	0.681591	0.340795	−	0.940137i	$-0.389304\pi$
$571$	2.07979e45	0.681591	0.340795	+	0.940137i	$0.389304\pi$
$572$	1.18771e46	3.78162
$573$	5.88585e45	1.82078
$574$	9.19595e44	0.276408
$575$	0	0
$576$	4.05768e45	1.15161
$577$	2.30164e45	0.634800	0.317400	−	0.948292i	$-0.397190\pi$
$577$	2.30164e45	0.634800	0.317400	+	0.948292i	$0.397190\pi$
$578$	3.05796e45	0.819639
$579$	4.36559e45	1.13722
$580$	0	0
$581$	−1.04207e45	−0.256444
$582$	−7.41395e45	−1.77346
$583$	−1.01871e46	−2.36875
$584$	−7.07484e45	−1.59921
$585$	0	0
$586$	−3.25174e45	−0.694712
$587$	−1.99372e45	−0.414128	−0.207064	−	0.978327i	$-0.566391\pi$
$587$	−1.99372e45	−0.414128	−0.207064	+	0.978327i	$0.566391\pi$
$588$	2.35592e45	0.475810
$589$	−1.93101e45	−0.379213
$590$	0	0
$591$	−5.15538e45	−0.957341
$592$	−3.14804e46	−5.68503
$593$	6.54556e45	1.14959	0.574797	−	0.818296i	$-0.305081\pi$
$593$	6.54556e45	1.14959	0.574797	+	0.818296i	$0.305081\pi$
$594$	−1.13978e46	−1.94690
$595$	0	0
$596$	−3.29553e45	−0.532553
$597$	1.22006e46	1.91781
$598$	−1.57779e46	−2.41257
$599$	1.89735e45	0.282231	0.141115	−	0.989993i	$-0.454931\pi$
$599$	1.89735e45	0.282231	0.141115	+	0.989993i	$0.454931\pi$
$600$	0	0
$601$	−8.66013e45	−1.21926	−0.609629	−	0.792687i	$-0.708681\pi$
$601$	−8.66013e45	−1.21926	−0.609629	+	0.792687i	$0.708681\pi$
$602$	−3.82693e45	−0.524214
$603$	5.03991e44	0.0671718
$604$	1.04427e46	1.35426
$605$	0	0
$606$	3.84095e45	0.471672
$607$	−8.81789e45	−1.05378	−0.526892	−	0.849932i	$-0.676643\pi$
$607$	−8.81789e45	−1.05378	−0.526892	+	0.849932i	$0.676643\pi$
$608$	−3.63378e46	−4.22619
$609$	1.03317e46	1.16946
$610$	0	0
$611$	−2.68799e45	−0.288236
$612$	6.24322e45	0.651643
$613$	1.91712e46	1.94783	0.973915	−	0.226912i	$-0.0728630\pi$
$613$	1.91712e46	1.94783	0.973915	+	0.226912i	$0.0728630\pi$
$614$	−1.87231e45	−0.185182
$615$	0	0
$616$	−4.19942e46	−3.93648
$617$	1.53369e46	1.39969	0.699844	−	0.714295i	$-0.253253\pi$
$617$	1.53369e46	1.39969	0.699844	+	0.714295i	$0.253253\pi$
$618$	3.97915e46	3.53574
$619$	8.04204e45	0.695778	0.347889	−	0.937536i	$-0.386899\pi$
$619$	8.04204e45	0.695778	0.347889	+	0.937536i	$0.386899\pi$
$620$	0	0
$621$	1.10756e46	0.908568
$622$	−1.82071e46	−1.45446
$623$	−1.27020e46	−0.988142
$624$	−6.04757e46	−4.58179
$625$	0	0
$626$	−3.80203e46	−2.73237
$627$	−2.33610e46	−1.63522
$628$	−1.78105e46	−1.21434
$629$	−1.75582e46	−1.16612
$630$	0	0
$631$	2.52921e46	1.59405	0.797023	−	0.603949i	$-0.206407\pi$
$631$	2.52921e46	1.59405	0.797023	+	0.603949i	$0.206407\pi$
$632$	2.07875e46	1.27635
$633$	−2.80145e46	−1.67580
$634$	9.17540e45	0.534752
$635$	0	0
$636$	1.04114e47	5.76061
$637$	−3.05163e45	−0.164525
$638$	5.22682e46	2.74597
$639$	−4.98599e45	−0.255263
$640$	0	0
$641$	2.51177e46	1.22130	0.610651	−	0.791900i	$-0.290908\pi$
$641$	2.51177e46	1.22130	0.610651	+	0.791900i	$0.290908\pi$
$642$	−5.72755e46	−2.71419
$643$	1.47547e46	0.681473	0.340736	−	0.940159i	$-0.389324\pi$
$643$	1.47547e46	0.681473	0.340736	+	0.940159i	$0.389324\pi$
$644$	6.44728e46	2.90242
$645$	0	0
$646$	−3.79772e46	−1.62437
$647$	4.64548e46	1.93691	0.968457	−	0.249182i	$-0.0801617\pi$
$647$	4.64548e46	1.93691	0.968457	+	0.249182i	$0.0801617\pi$
$648$	9.95488e46	4.04621
$649$	−1.20957e46	−0.479283
$650$	0	0
$651$	9.58069e45	0.360837
$652$	−4.57124e46	−1.67861
$653$	−3.12135e46	−1.11757	−0.558786	−	0.829312i	$-0.688733\pi$
$653$	−3.12135e46	−1.11757	−0.558786	+	0.829312i	$0.688733\pi$
$654$	−4.23255e46	−1.47764
$655$	0	0
$656$	−1.73278e46	−0.575215
$657$	4.68158e45	0.151553
$658$	1.50156e46	0.474041
$659$	1.16512e46	0.358724	0.179362	−	0.983783i	$-0.442597\pi$
$659$	1.16512e46	0.358724	0.179362	+	0.983783i	$0.442597\pi$
$660$	0	0
$661$	−1.14126e46	−0.334241	−0.167121	−	0.985936i	$-0.553447\pi$
$661$	−1.14126e46	−0.334241	−0.167121	+	0.985936i	$0.553447\pi$
$662$	8.42699e46	2.40722
$663$	−3.37302e46	−0.939822
$664$	3.41026e46	0.926861
$665$	0	0
$666$	3.61792e46	0.935694
$667$	−5.07909e46	−1.28147
$668$	−6.72033e46	−1.65417
$669$	−2.75628e46	−0.661901
$670$	0	0
$671$	−2.38199e46	−0.544525
$672$	1.80289e47	4.02140
$673$	−4.26138e45	−0.0927475	−0.0463737	−	0.998924i	$-0.514767\pi$
$673$	−4.26138e45	−0.0927475	−0.0463737	+	0.998924i	$0.514767\pi$
$674$	1.54268e46	0.327633
$675$	0	0
$676$	2.25292e46	0.455644
$677$	6.45770e46	1.27457	0.637287	−	0.770627i	$-0.280057\pi$
$677$	6.45770e46	1.27457	0.637287	+	0.770627i	$0.280057\pi$
$678$	−1.93183e47	−3.72117
$679$	−3.92419e46	−0.737732
$680$	0	0
$681$	−5.14780e46	−0.921923
$682$	4.84690e46	0.847270
$683$	−3.35691e46	−0.572794	−0.286397	−	0.958111i	$-0.592458\pi$
$683$	−3.35691e46	−0.572794	−0.286397	+	0.958111i	$0.592458\pi$
$684$	5.72419e46	0.953430
$685$	0	0
$686$	1.28990e47	2.04743
$687$	3.17324e46	0.491719
$688$	7.21105e46	1.09091
$689$	−1.34860e47	−1.99190
$690$	0	0
$691$	−4.55000e46	−0.640654	−0.320327	−	0.947307i	$-0.603793\pi$
$691$	−4.55000e46	−0.640654	−0.320327	+	0.947307i	$0.603793\pi$
$692$	−3.77017e47	−5.18334
$693$	2.77885e46	0.373050
$694$	4.97238e46	0.651828
$695$	0	0
$696$	−3.38111e47	−4.22676
$697$	−9.66456e45	−0.117989
$698$	2.01956e47	2.40792
$699$	−3.25978e46	−0.379590
$700$	0	0
$701$	−1.37611e47	−1.52864	−0.764320	−	0.644837i	$-0.776925\pi$
$701$	−1.37611e47	−1.52864	−0.764320	+	0.644837i	$0.776925\pi$
$702$	−1.50888e47	−1.63716
$703$	−1.60985e47	−1.70617
$704$	4.53193e47	4.69174
$705$	0	0
$706$	3.13885e47	3.10094
$707$	2.03301e46	0.196209
$708$	1.23620e47	1.16558
$709$	−1.72099e47	−1.58531	−0.792656	−	0.609670i	$-0.791302\pi$
$709$	−1.72099e47	−1.58531	−0.792656	+	0.609670i	$0.791302\pi$
$710$	0	0
$711$	−1.37556e46	−0.120957
$712$	4.15682e47	3.57143
$713$	−4.70991e46	−0.395399
$714$	1.88423e47	1.54566
$715$	0	0
$716$	2.12178e44	0.00166202
$717$	−7.28855e46	−0.557924
$718$	4.34619e47	3.25128
$719$	1.00489e47	0.734667	0.367334	−	0.930089i	$-0.380271\pi$
$719$	1.00489e47	0.734667	0.367334	+	0.930089i	$0.380271\pi$
$720$	0	0
$721$	2.10616e47	1.47082
$722$	−6.54591e46	−0.446793
$723$	−2.92295e47	−1.95002
$724$	4.43987e46	0.289524
$725$	0	0
$726$	2.31145e47	1.44022
$727$	−1.79204e47	−1.09151	−0.545757	−	0.837944i	$-0.683758\pi$
$727$	−1.79204e47	−1.09151	−0.545757	+	0.837944i	$0.683758\pi$
$728$	−5.55934e47	−3.31021
$729$	8.88336e46	0.517098
$730$	0	0
$731$	4.02195e46	0.223769
$732$	2.43445e47	1.32424
$733$	−1.91032e46	−0.101599	−0.0507996	−	0.998709i	$-0.516177\pi$
$733$	−1.91032e46	−0.101599	−0.0507996	+	0.998709i	$0.516177\pi$
$734$	−4.24816e47	−2.20910
$735$	0	0
$736$	−8.86310e47	−4.40658
$737$	5.62895e46	0.273662
$738$	1.99141e46	0.0946742
$739$	2.81727e47	1.30977	0.654886	−	0.755728i	$-0.272717\pi$
$739$	2.81727e47	1.30977	0.654886	+	0.755728i	$0.272717\pi$
$740$	0	0
$741$	−3.09261e47	−1.37507
$742$	7.53355e47	3.27593
$743$	5.77441e46	0.245580	0.122790	−	0.992433i	$-0.460816\pi$
$743$	5.77441e46	0.245580	0.122790	+	0.992433i	$0.460816\pi$
$744$	−3.13535e47	−1.30417
$745$	0	0
$746$	2.83995e47	1.13011
$747$	−2.25665e46	−0.0878363
$748$	6.97290e47	2.65483
$749$	−3.03158e47	−1.12907
$750$	0	0
$751$	2.71539e47	0.967772	0.483886	−	0.875131i	$-0.339225\pi$
$751$	2.71539e47	0.967772	0.483886	+	0.875131i	$0.339225\pi$
$752$	−2.82938e47	−0.986498
$753$	−2.15762e47	−0.735968
$754$	6.91944e47	2.30910
$755$	0	0
$756$	6.16568e47	1.96957
$757$	−2.34370e47	−0.732521	−0.366260	−	0.930512i	$-0.619362\pi$
$757$	−2.34370e47	−0.732521	−0.366260	+	0.930512i	$0.619362\pi$
$758$	4.90141e47	1.49892
$759$	−5.69796e47	−1.70502
$760$	0	0
$761$	−3.85769e47	−1.10530	−0.552651	−	0.833413i	$-0.686384\pi$
$761$	−3.85769e47	−1.10530	−0.552651	+	0.833413i	$0.686384\pi$
$762$	3.43863e46	0.0964115
$763$	−2.24028e47	−0.614679
$764$	−1.61079e48	−4.32511
$765$	0	0
$766$	6.39028e47	1.64341
$767$	−1.60126e47	−0.403032
$768$	−1.21008e48	−2.98094
$769$	5.88677e47	1.41936	0.709679	−	0.704525i	$-0.248840\pi$
$769$	5.88677e47	1.41936	0.709679	+	0.704525i	$0.248840\pi$
$770$	0	0
$771$	3.57874e47	0.826671
$772$	−1.19473e48	−2.70138
$773$	4.68346e47	1.03659	0.518293	−	0.855203i	$-0.326568\pi$
$773$	4.68346e47	1.03659	0.518293	+	0.855203i	$0.326568\pi$
$774$	−8.28736e46	−0.179552
$775$	0	0
$776$	1.28422e48	2.66637
$777$	7.98724e47	1.62349
$778$	4.01113e47	0.798185
$779$	−8.86111e46	−0.172631
$780$	0	0
$781$	−5.56874e47	−1.03996
$782$	−9.26297e47	−1.69371
$783$	−4.85725e47	−0.869604
$784$	−3.21215e47	−0.563094
$785$	0	0
$786$	1.10001e48	1.84895
$787$	3.57150e47	0.587851	0.293926	−	0.955828i	$-0.405038\pi$
$787$	3.57150e47	0.587851	0.293926	+	0.955828i	$0.405038\pi$
$788$	1.41087e48	2.27408
$789$	9.88999e47	1.56108
$790$	0	0
$791$	−1.02252e48	−1.54795
$792$	−9.09400e47	−1.34831
$793$	−3.15336e47	−0.457895
$794$	−1.55551e47	−0.221225
$795$	0	0
$796$	−3.33895e48	−4.55558
$797$	3.36343e47	0.449490	0.224745	−	0.974418i	$-0.427845\pi$
$797$	3.36343e47	0.449490	0.224745	+	0.974418i	$0.427845\pi$
$798$	1.72759e48	2.26148
$799$	−1.57808e47	−0.202352
$800$	0	0
$801$	−2.75066e47	−0.338455
$802$	−3.21219e46	−0.0387190
$803$	5.22875e47	0.617435
$804$	−5.75292e47	−0.665523
$805$	0	0
$806$	6.41649e47	0.712474
$807$	6.17383e47	0.671647
$808$	−6.65316e47	−0.709154
$809$	8.08353e47	0.844210	0.422105	−	0.906547i	$-0.361291\pi$
$809$	8.08353e47	0.844210	0.422105	+	0.906547i	$0.361291\pi$
$810$	0	0
$811$	−1.18729e48	−1.19045	−0.595225	−	0.803559i	$-0.702937\pi$
$811$	−1.18729e48	−1.19045	−0.595225	+	0.803559i	$0.702937\pi$
$812$	−2.82747e48	−2.77795
$813$	−1.95653e48	−1.88362
$814$	4.04077e48	3.81207
$815$	0	0
$816$	−3.55044e48	−3.21658
$817$	3.68759e47	0.327400
$818$	−3.09244e48	−2.69074
$819$	3.67874e47	0.313700
$820$	0	0
$821$	−1.55006e48	−1.26966	−0.634829	−	0.772653i	$-0.718929\pi$
$821$	−1.55006e48	−1.26966	−0.634829	+	0.772653i	$0.718929\pi$
$822$	−3.92519e48	−3.15120
$823$	−2.91534e47	−0.229399	−0.114700	−	0.993400i	$-0.536591\pi$
$823$	−2.91534e47	−0.229399	−0.114700	+	0.993400i	$0.536591\pi$
$824$	−6.89256e48	−5.31596
$825$	0	0
$826$	8.94497e47	0.662839
$827$	1.33839e48	0.972166	0.486083	−	0.873913i	$-0.338425\pi$
$827$	1.33839e48	0.972166	0.486083	+	0.873913i	$0.338425\pi$
$828$	1.39618e48	0.994126
$829$	−2.06685e47	−0.144264	−0.0721321	−	0.997395i	$-0.522980\pi$
$829$	−2.06685e47	−0.144264	−0.0721321	+	0.997395i	$0.522980\pi$
$830$	0	0
$831$	2.28762e48	1.53450
$832$	5.99952e48	3.94531
$833$	−1.79157e47	−0.115502
$834$	1.19467e48	0.755106
$835$	0	0
$836$	6.39322e48	3.88433
$837$	−4.50419e47	−0.268316
$838$	5.49865e48	3.21166
$839$	−1.80225e48	−1.03215	−0.516075	−	0.856544i	$-0.672607\pi$
$839$	−1.80225e48	−1.03215	−0.516075	+	0.856544i	$0.672607\pi$
$840$	0	0
$841$	4.11374e47	0.226518
$842$	2.61661e48	1.41283
$843$	2.15300e48	1.13996
$844$	7.66674e48	3.98071
$845$	0	0
$846$	3.25169e47	0.162367
$847$	1.22345e48	0.599113
$848$	−1.41954e49	−6.81735
$849$	3.57312e48	1.68295
$850$	0	0
$851$	−3.92656e48	−1.77900
$852$	5.69138e48	2.52909
$853$	3.50343e48	1.52699	0.763493	−	0.645816i	$-0.223483\pi$
$853$	3.50343e48	1.52699	0.763493	+	0.645816i	$0.223483\pi$
$854$	1.76153e48	0.753068
$855$	0	0
$856$	9.92107e48	4.08076
$857$	−4.03540e48	−1.62818	−0.814091	−	0.580737i	$-0.802764\pi$
$857$	−4.03540e48	−1.62818	−0.814091	+	0.580737i	$0.802764\pi$
$858$	7.76254e48	3.07230
$859$	−4.93399e46	−0.0191563	−0.00957813	−	0.999954i	$-0.503049\pi$
$859$	−4.93399e46	−0.0191563	−0.00957813	+	0.999954i	$0.503049\pi$
$860$	0	0
$861$	4.39643e47	0.164266
$862$	−5.80102e48	−2.12635
$863$	5.86818e47	0.211021	0.105510	−	0.994418i	$-0.466352\pi$
$863$	5.86818e47	0.211021	0.105510	+	0.994418i	$0.466352\pi$
$864$	−8.47598e48	−2.99029
$865$	0	0
$866$	−4.68294e47	−0.159028
$867$	1.46196e48	0.487103
$868$	−2.62195e48	−0.857136
$869$	−1.53633e48	−0.492786
$870$	0	0
$871$	7.45180e47	0.230124
$872$	7.33149e48	2.22162
$873$	−8.49797e47	−0.252686
$874$	−8.49291e48	−2.47809
$875$	0	0
$876$	−5.34390e48	−1.50155
$877$	5.15342e48	1.42103	0.710514	−	0.703683i	$-0.248463\pi$
$877$	5.15342e48	1.42103	0.710514	+	0.703683i	$0.248463\pi$
$878$	1.14418e49	3.09623
$879$	−1.55460e48	−0.412860
$880$	0	0
$881$	7.21570e48	1.84576	0.922882	−	0.385084i	$-0.125827\pi$
$881$	7.21570e48	1.84576	0.922882	+	0.385084i	$0.125827\pi$
$882$	3.69159e47	0.0926791
$883$	−7.21502e48	−1.77781	−0.888906	−	0.458089i	$-0.848534\pi$
$883$	−7.21502e48	−1.77781	−0.888906	+	0.458089i	$0.848534\pi$
$884$	9.23096e48	2.23246
$885$	0	0
$886$	2.33095e48	0.543097
$887$	2.04483e48	0.467647	0.233824	−	0.972279i	$-0.424876\pi$
$887$	2.04483e48	0.467647	0.233824	+	0.972279i	$0.424876\pi$
$888$	−2.61388e49	−5.86776
$889$	1.82006e47	0.0401058
$890$	0	0
$891$	−7.35728e48	−1.56220
$892$	7.54314e48	1.57229
$893$	−1.44689e48	−0.296064
$894$	−2.15386e48	−0.432661
$895$	0	0
$896$	−1.54037e49	−2.98224
$897$	−7.54315e48	−1.43376
$898$	1.71077e49	3.19251
$899$	2.06554e48	0.378442
$900$	0	0
$901$	−7.91745e48	−1.39838
$902$	2.22416e48	0.385708
$903$	−1.82959e48	−0.311535
$904$	3.34626e49	5.59475
$905$	0	0
$906$	6.82501e48	1.10024
$907$	−4.33823e48	−0.686739	−0.343370	−	0.939200i	$-0.611568\pi$
$907$	−4.33823e48	−0.686739	−0.343370	+	0.939200i	$0.611568\pi$
$908$	1.40880e49	2.18995
$909$	4.40255e47	0.0672048
$910$	0	0
$911$	−1.54797e48	−0.227882	−0.113941	−	0.993488i	$-0.536348\pi$
$911$	−1.54797e48	−0.227882	−0.113941	+	0.993488i	$0.536348\pi$
$912$	−3.25528e49	−4.70623
$913$	−2.52040e48	−0.357850
$914$	−6.77134e47	−0.0944196
$915$	0	0
$916$	−8.68424e48	−1.16804
$917$	5.82234e48	0.769136
$918$	−8.85839e48	−1.14935
$919$	4.44681e48	0.566686	0.283343	−	0.959019i	$-0.408557\pi$
$919$	4.44681e48	0.566686	0.283343	+	0.959019i	$0.408557\pi$
$920$	0	0
$921$	−8.95118e47	−0.110052
$922$	−1.25953e49	−1.52107
$923$	−7.37208e48	−0.874505
$924$	−3.17199e49	−3.69610
$925$	0	0
$926$	2.53474e49	2.85005
$927$	4.56096e48	0.503780
$928$	3.88694e49	4.21760
$929$	7.81292e48	0.832826	0.416413	−	0.909176i	$-0.363287\pi$
$929$	7.81292e48	0.832826	0.416413	+	0.909176i	$0.363287\pi$
$930$	0	0
$931$	−1.64263e48	−0.168994
$932$	8.92105e48	0.901682
$933$	−8.70453e48	−0.864367
$934$	−3.27813e49	−3.19818
$935$	0	0
$936$	−1.20389e49	−1.13380
$937$	−1.29441e49	−1.19776	−0.598880	−	0.800839i	$-0.704387\pi$
$937$	−1.29441e49	−1.19776	−0.598880	+	0.800839i	$0.704387\pi$
$938$	−4.16271e48	−0.378469
$939$	−1.81769e49	−1.62382
$940$	0	0
$941$	−5.82381e47	−0.0502318	−0.0251159	−	0.999685i	$-0.507995\pi$
$941$	−5.82381e47	−0.0502318	−0.0251159	+	0.999685i	$0.507995\pi$
$942$	−1.16404e49	−0.986569
$943$	−2.16130e48	−0.180000
$944$	−1.68549e49	−1.37939
$945$	0	0
$946$	−9.25596e48	−0.731505
$947$	−1.87865e49	−1.45905	−0.729526	−	0.683953i	$-0.760259\pi$
$947$	−1.87865e49	−1.45905	−0.729526	+	0.683953i	$0.760259\pi$
$948$	1.57016e49	1.19842
$949$	6.92200e48	0.519205
$950$	0	0
$951$	4.38661e48	0.317797
$952$	−3.26381e49	−2.32389
$953$	−1.71040e49	−1.19692	−0.598459	−	0.801154i	$-0.704220\pi$
$953$	−1.71040e49	−1.19692	−0.598459	+	0.801154i	$0.704220\pi$
$954$	1.63142e49	1.12206
$955$	0	0
$956$	1.99466e49	1.32530
$957$	2.49885e49	1.63190
$958$	1.19451e49	0.766759
$959$	−2.07760e49	−1.31085
$960$	0	0
$961$	−1.44881e49	−0.883232
$962$	5.34930e49	3.20559
$963$	−6.56500e48	−0.386724
$964$	7.99925e49	4.63210
$965$	0	0
$966$	4.21374e49	2.35801
$967$	3.31445e49	1.82337	0.911683	−	0.410893i	$-0.134783\pi$
$967$	3.31445e49	1.82337	0.911683	+	0.410893i	$0.134783\pi$
$968$	−4.00382e49	−2.16536
$969$	−1.81562e49	−0.965348
$970$	0	0
$971$	−1.48405e49	−0.762662	−0.381331	−	0.924439i	$-0.624534\pi$
$971$	−1.48405e49	−0.762662	−0.381331	+	0.924439i	$0.624534\pi$
$972$	3.28542e49	1.65996
$973$	6.32337e48	0.314113
$974$	−3.13480e49	−1.53104
$975$	0	0
$976$	−3.31922e49	−1.56716
$977$	7.11883e47	0.0330482	0.0165241	−	0.999863i	$-0.494740\pi$
$977$	7.11883e47	0.0330482	0.0165241	+	0.999863i	$0.494740\pi$
$978$	−2.98762e49	−1.36375
$979$	−3.07215e49	−1.37889
$980$	0	0
$981$	−4.85141e48	−0.210538
$982$	−7.01570e49	−2.99386
$983$	−3.13902e49	−1.31723	−0.658614	−	0.752481i	$-0.728857\pi$
$983$	−3.13902e49	−1.31723	−0.658614	+	0.752481i	$0.728857\pi$
$984$	−1.43876e49	−0.593704
$985$	0	0
$986$	4.06230e49	1.62107
$987$	7.17872e48	0.281717
$988$	8.46356e49	3.26635
$989$	8.99436e48	0.341375
$990$	0	0
$991$	2.53674e49	0.931239	0.465619	−	0.884985i	$-0.345832\pi$
$991$	2.53674e49	0.931239	0.465619	+	0.884985i	$0.345832\pi$
$992$	3.60441e49	1.30134
$993$	4.02880e49	1.43058
$994$	4.11819e49	1.43824
$995$	0	0
$996$	2.57590e49	0.870263
$997$	−4.24313e48	−0.140999	−0.0704995	−	0.997512i	$-0.522459\pi$
$997$	−4.24313e48	−0.140999	−0.0704995	+	0.997512i	$0.522459\pi$
$998$	−1.36729e49	−0.446895
$999$	−3.75506e49	−1.20722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.c.1.1		6
5.2	odd	4		25.34.b.c.24.1		12
5.3	odd	4		25.34.b.c.24.12		12
5.4	even	2		5.34.a.b.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.6	✓	6	5.4	even	2
25.34.a.c.1.1		6	1.1	even	1	trivial
25.34.b.c.24.1		12	5.2	odd	4
25.34.b.c.24.12		12	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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-178863. q^{2} -8.55112e7 q^{3} +2.34019e10 q^{4} +1.52948e13 q^{6} +8.09549e13 q^{7} -2.64931e15 q^{8} +1.75311e15 q^{9} +O(q^{10})\)	\(q-178863. q^{2} -8.55112e7 q^{3} +2.34019e10 q^{4} +1.52948e13 q^{6} +8.09549e13 q^{7} -2.64931e15 q^{8} +1.75311e15 q^{9} +1.95800e17 q^{11} -2.00113e18 q^{12} +2.59207e18 q^{13} -1.44798e19 q^{14} +2.72841e20 q^{16} +1.52177e20 q^{17} -3.13565e20 q^{18} +1.39526e21 q^{19} -6.92255e21 q^{21} -3.50214e22 q^{22} +3.40316e22 q^{23} +2.26546e23 q^{24} -4.63625e23 q^{26} +3.25452e23 q^{27} +1.89450e24 q^{28} -1.49246e24 q^{29} -1.38398e24 q^{31} -2.60438e25 q^{32} -1.67431e25 q^{33} -2.72188e25 q^{34} +4.10261e25 q^{36} -1.15380e26 q^{37} -2.49559e26 q^{38} -2.21651e26 q^{39} -6.35087e25 q^{41} +1.23819e27 q^{42} +2.64294e26 q^{43} +4.58211e27 q^{44} -6.08698e27 q^{46} -1.03700e27 q^{47} -2.33310e28 q^{48} -1.17730e27 q^{49} -1.30128e28 q^{51} +6.06594e28 q^{52} -5.20280e28 q^{53} -5.82111e28 q^{54} -2.14475e29 q^{56} -1.19310e29 q^{57} +2.66946e29 q^{58} -6.17754e28 q^{59} -1.21654e29 q^{61} +2.47543e29 q^{62} +1.41923e29 q^{63} +2.31456e30 q^{64} +2.99472e30 q^{66} +2.87484e29 q^{67} +3.56123e30 q^{68} -2.91008e30 q^{69} -2.84409e30 q^{71} -4.64452e30 q^{72} +2.67045e30 q^{73} +2.06372e31 q^{74} +3.26517e31 q^{76} +1.58510e31 q^{77} +3.96451e31 q^{78} -7.84640e30 q^{79} -3.75754e31 q^{81} +1.13593e31 q^{82} -1.28723e31 q^{83} -1.62001e32 q^{84} -4.72724e31 q^{86} +1.27622e32 q^{87} -5.18736e32 q^{88} -1.56902e32 q^{89} +2.09841e32 q^{91} +7.96404e32 q^{92} +1.18346e32 q^{93} +1.85481e32 q^{94} +2.22703e33 q^{96} -4.84738e32 q^{97} +2.10574e32 q^{98} +3.43259e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 6615759249352 q^{6} - 19113832847500 q^{7} - 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 6 * q - 147350 * q^2 - 26513900 * q^3 + 29520645652 * q^4 + 6615759249352 * q^6 - 19113832847500 * q^7 - 3069820115785800 * q^8 + 13602102583345438 * q^9	\( 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 6615759249352 q^{6} - 19113832847500 q^{7} - 30\!\cdots\!00 q^{8}+ \cdots + 16\!\cdots\!16 q^{99}+O(q^{100}) \) 6 * q - 147350 * q^2 - 26513900 * q^3 + 29520645652 * q^4 + 6615759249352 * q^6 - 19113832847500 * q^7 - 3069820115785800 * q^8 + 13602102583345438 * q^9 + 150760896555890192 * q^11 - 466351581756413200 * q^12 + 1403095636752804700 * q^13 - 7086110008989891456 * q^14 + 64511520005858668816 * q^16 - 134380842798611834300 * q^17 - 673397185005127949150 * q^18 + 1711584362599986612200 * q^19 - 10560397660826154148128 * q^21 - 2470897477250007236200 * q^22 - 6879744551224024319700 * q^23 + 211895016154723698861600 * q^24 - 361829246667436498168588 * q^26 + 340705501428703899968200 * q^27 + 1750376606004032278695200 * q^28 + 1305223406410727358015700 * q^29 + 10825321396800575904753352 * q^31 - 26818258713124955338861600 * q^32 - 34856079507682787436662800 * q^33 + 8872409666654531735490124 * q^34 + 168714411751774892911163396 * q^36 - 276757164463535626747584900 * q^37 - 835386866362613528909982200 * q^38 + 579964086232605925635188456 * q^39 + 448008579649522993395821932 * q^41 - 1478478813030145693383604800 * q^42 - 2250588086104897739543439500 * q^43 + 7171805342222267509050250864 * q^44 + 3493759290976330924493595072 * q^46 - 3830785379519133075460228700 * q^47 - 24576343390562635665291611200 * q^48 - 7173427073564666873529235258 * q^49 - 54920362805063671320868694888 * q^51 + 90553915669177954388890305000 * q^52 - 47034713551772209628037134900 * q^53 - 182647187168263097239229399600 * q^54 - 392573339390998146620750750400 * q^56 + 242119765146738617914766400400 * q^57 + 443272639260736798552560798700 * q^58 - 178315156221037727069533799800 * q^59 - 282317689060586014253208287308 * q^61 - 3477509804797272360008839200 * q^62 + 559259159226762324796386276900 * q^63 + 1937968534792541396434479607872 * q^64 + 5061208746155430260544773159264 * q^66 - 3357382217232044190774976063300 * q^67 - 3866973693935427075529380663400 * q^68 + 316127240816983184255653823136 * q^69 + 8451218031993742702656617170072 * q^71 - 8740278584811466598158058687400 * q^72 + 1719044326022105657749673125300 * q^73 + 20494727417173075429289542476484 * q^74 + 29410039922734837753629694458000 * q^76 + 1179300749517366199915257594000 * q^77 + 57229303014236704407408363530000 * q^78 - 22052505351402355443894747635600 * q^79 - 133163964889176760661905573719674 * q^81 + 156059027108947085834404172875300 * q^82 + 47087087002138304263127820978900 * q^83 - 235991611992224148517578838651776 * q^84 - 128823880621545855657554048105608 * q^86 + 175316396211912369693639217216600 * q^87 - 497433069891524019720739466805600 * q^88 - 336491358341169481948206213360900 * q^89 + 194633769402343866156602864483432 * q^91 + 419043430758613276035983032687200 * q^92 - 212928090391747529239858474972800 * q^93 + 1486141097168392212687292135345264 * q^94 + 3151728990173122672564203081529472 * q^96 - 2569321197832638009639208504856700 * q^97 - 6985460513399098756137635798950 * q^98 + 1660882302442227079414567162624016 * q^99

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