LMFDB - Embedded newform 25.34.a.c.1.2

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			1.2
Root			$54181.8$ 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)

$f(q)$	$=$	$q-132922. q^{2} +1.17526e8 q^{3} +9.07819e9 q^{4} -1.56217e13 q^{6} +1.34853e13 q^{7} -6.49000e13 q^{8} +8.25322e15 q^{9} +O(q^{10})$	\(q-132922. q^{2} +1.17526e8 q^{3} +9.07819e9 q^{4} -1.56217e13 q^{6} +1.34853e13 q^{7} -6.49000e13 q^{8} +8.25322e15 q^{9} -7.96470e16 q^{11} +1.06692e18 q^{12} +1.16823e18 q^{13} -1.79249e18 q^{14} -6.93545e19 q^{16} -3.27833e20 q^{17} -1.09703e21 q^{18} +2.21358e21 q^{19} +1.58487e21 q^{21} +1.05868e22 q^{22} -3.93052e22 q^{23} -7.62742e21 q^{24} -1.55283e23 q^{26} +3.16633e23 q^{27} +1.22422e23 q^{28} +1.59428e24 q^{29} +2.07133e24 q^{31} +9.77619e24 q^{32} -9.36057e24 q^{33} +4.35761e25 q^{34} +7.49243e25 q^{36} +4.76387e25 q^{37} -2.94233e26 q^{38} +1.37297e26 q^{39} -6.39281e26 q^{41} -2.10663e26 q^{42} +2.16469e26 q^{43} -7.23051e26 q^{44} +5.22451e27 q^{46} -7.45743e27 q^{47} -8.15093e27 q^{48} -7.54914e27 q^{49} -3.85288e28 q^{51} +1.06055e28 q^{52} -1.70592e28 q^{53} -4.20873e28 q^{54} -8.75196e26 q^{56} +2.60153e29 q^{57} -2.11913e29 q^{58} -5.91397e28 q^{59} +2.18117e29 q^{61} -2.75325e29 q^{62} +1.11297e29 q^{63} -7.03715e29 q^{64} +1.24422e30 q^{66} -2.21631e30 q^{67} -2.97613e30 q^{68} -4.61937e30 q^{69} +2.87498e30 q^{71} -5.35634e29 q^{72} +3.41825e30 q^{73} -6.33220e30 q^{74} +2.00953e31 q^{76} -1.07406e30 q^{77} -1.82498e31 q^{78} +5.87385e30 q^{79} -8.66769e30 q^{81} +8.49743e31 q^{82} +2.11211e31 q^{83} +1.43877e31 q^{84} -2.87734e31 q^{86} +1.87368e32 q^{87} +5.16909e30 q^{88} -2.67672e32 q^{89} +1.57540e31 q^{91} -3.56821e32 q^{92} +2.43435e32 q^{93} +9.91253e32 q^{94} +1.14895e33 q^{96} -1.07066e31 q^{97} +1.00344e33 q^{98} -6.57344e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−132922.	−1.43417	−0.717085	−	0.696986i	$-0.754524\pi$
$2$	−132922.	−1.43417	−0.717085	+	0.696986i	$0.754524\pi$
$3$	1.17526e8	1.57627	0.788137	−	0.615499i	$-0.211046\pi$
$3$	1.17526e8	1.57627	0.788137	+	0.615499i	$0.211046\pi$
$4$	9.07819e9	1.05684
$5$	0	0
$5$	0	0
$6$	−1.56217e13	−2.26064
$7$	1.34853e13	0.153371	0.0766854	−	0.997055i	$-0.475566\pi$
$7$	1.34853e13	0.153371	0.0766854	+	0.997055i	$0.475566\pi$
$8$	−6.49000e13	−0.0815192
$9$	8.25322e15	1.48464
$10$	0	0
$11$	−7.96470e16	−0.522625	−0.261313	−	0.965254i	$-0.584155\pi$
$11$	−7.96470e16	−0.522625	−0.261313	+	0.965254i	$0.584155\pi$
$12$	1.06692e18	1.66587
$13$	1.16823e18	0.486928	0.243464	−	0.969910i	$-0.421716\pi$
$13$	1.16823e18	0.486928	0.243464	+	0.969910i	$0.421716\pi$
$14$	−1.79249e18	−0.219960
$15$	0	0
$16$	−6.93545e19	−0.939928
$17$	−3.27833e20	−1.63398	−0.816988	−	0.576654i	$-0.804358\pi$
$17$	−3.27833e20	−1.63398	−0.816988	+	0.576654i	$0.804358\pi$
$18$	−1.09703e21	−2.12923
$19$	2.21358e21	1.76060	0.880301	−	0.474416i	$-0.157341\pi$
$19$	2.21358e21	1.76060	0.880301	+	0.474416i	$0.157341\pi$
$20$	0	0
$21$	1.58487e21	0.241755
$22$	1.05868e22	0.749533
$23$	−3.93052e22	−1.33641	−0.668207	−	0.743975i	$-0.732938\pi$
$23$	−3.93052e22	−1.33641	−0.668207	+	0.743975i	$0.732938\pi$
$24$	−7.62742e21	−0.128497
$25$	0	0
$26$	−1.55283e23	−0.698337
$27$	3.16633e23	0.763930
$28$	1.22422e23	0.162089
$29$	1.59428e24	1.18303	0.591516	−	0.806293i	$-0.298530\pi$
$29$	1.59428e24	1.18303	0.591516	+	0.806293i	$0.298530\pi$
$30$	0	0
$31$	2.07133e24	0.511425	0.255712	−	0.966753i	$-0.417690\pi$
$31$	2.07133e24	0.511425	0.255712	+	0.966753i	$0.417690\pi$
$32$	9.77619e24	1.42954
$33$	−9.36057e24	−0.823801
$34$	4.35761e25	2.34340
$35$	0	0
$36$	7.49243e25	1.56903
$37$	4.76387e25	0.634792	0.317396	−	0.948293i	$-0.397192\pi$
$37$	4.76387e25	0.634792	0.317396	+	0.948293i	$0.397192\pi$
$38$	−2.94233e26	−2.52500
$39$	1.37297e26	0.767532
$40$	0	0
$41$	−6.39281e26	−1.56588	−0.782940	−	0.622097i	$-0.786281\pi$
$41$	−6.39281e26	−1.56588	−0.782940	+	0.622097i	$0.786281\pi$
$42$	−2.10663e26	−0.346717
$43$	2.16469e26	0.241639	0.120819	−	0.992674i	$-0.461448\pi$
$43$	2.16469e26	0.241639	0.120819	+	0.992674i	$0.461448\pi$
$44$	−7.23051e26	−0.552331
$45$	0	0
$46$	5.22451e27	1.91664
$47$	−7.45743e27	−1.91856	−0.959278	−	0.282462i	$-0.908849\pi$
$47$	−7.45743e27	−1.91856	−0.959278	+	0.282462i	$0.908849\pi$
$48$	−8.15093e27	−1.48159
$49$	−7.54914e27	−0.976477
$50$	0	0
$51$	−3.85288e28	−2.57560
$52$	1.06055e28	0.514605
$53$	−1.70592e28	−0.604513	−0.302257	−	0.953227i	$-0.597740\pi$
$53$	−1.70592e28	−0.604513	−0.302257	+	0.953227i	$0.597740\pi$
$54$	−4.20873e28	−1.09560
$55$	0	0
$56$	−8.75196e26	−0.0125027
$57$	2.60153e29	2.77519
$58$	−2.11913e29	−1.69667
$59$	−5.91397e28	−0.357126	−0.178563	−	0.983928i	$-0.557145\pi$
$59$	−5.91397e28	−0.357126	−0.178563	+	0.983928i	$0.557145\pi$
$60$	0	0
$61$	2.18117e29	0.759884	0.379942	−	0.925010i	$-0.375944\pi$
$61$	2.18117e29	0.759884	0.379942	+	0.925010i	$0.375944\pi$
$62$	−2.75325e29	−0.733470
$63$	1.11297e29	0.227701
$64$	−7.03715e29	−1.11027
$65$	0	0
$66$	1.24422e30	1.18147
$67$	−2.21631e30	−1.64209	−0.821044	−	0.570865i	$-0.806608\pi$
$67$	−2.21631e30	−1.64209	−0.821044	+	0.570865i	$0.806608\pi$
$68$	−2.97613e30	−1.72685
$69$	−4.61937e30	−2.10656
$70$	0	0
$71$	2.87498e30	0.818223	0.409112	−	0.912484i	$-0.365839\pi$
$71$	2.87498e30	0.818223	0.409112	+	0.912484i	$0.365839\pi$
$72$	−5.35634e29	−0.121027
$73$	3.41825e30	0.615143	0.307571	−	0.951525i	$-0.400484\pi$
$73$	3.41825e30	0.615143	0.307571	+	0.951525i	$0.400484\pi$
$74$	−6.33220e30	−0.910398
$75$	0	0
$76$	2.00953e31	1.86068
$77$	−1.07406e30	−0.0801555
$78$	−1.82498e31	−1.10077
$79$	5.87385e30	0.287128	0.143564	−	0.989641i	$-0.454144\pi$
$79$	5.87385e30	0.287128	0.143564	+	0.989641i	$0.454144\pi$
$80$	0	0
$81$	−8.66769e30	−0.280479
$82$	8.49743e31	2.24574
$83$	2.11211e31	0.457013	0.228507	−	0.973542i	$-0.426616\pi$
$83$	2.11211e31	0.457013	0.228507	+	0.973542i	$0.426616\pi$
$84$	1.43877e31	0.255496
$85$	0	0
$86$	−2.87734e31	−0.346551
$87$	1.87368e32	1.86478
$88$	5.16909e30	0.0426040
$89$	−2.67672e32	−1.83092	−0.915458	−	0.402413i	$-0.868172\pi$
$89$	−2.67672e32	−1.83092	−0.915458	+	0.402413i	$0.868172\pi$
$90$	0	0
$91$	1.57540e31	0.0746806
$92$	−3.56821e32	−1.41238
$93$	2.43435e32	0.806146
$94$	9.91253e32	2.75153
$95$	0	0
$96$	1.14895e33	2.25334
$97$	−1.07066e31	−0.0176977	−0.00884885	−	0.999961i	$-0.502817\pi$
$97$	−1.07066e31	−0.0176977	−0.00884885	+	0.999961i	$0.502817\pi$
$98$	1.00344e33	1.40043
$99$	−6.57344e32	−0.775911
$100$	0	0
$101$	1.55093e33	1.31610	0.658051	−	0.752974i	$-0.271381\pi$
$101$	1.55093e33	1.31610	0.658051	+	0.752974i	$0.271381\pi$
$102$	5.12131e33	3.69384
$103$	−6.99665e32	−0.429612	−0.214806	−	0.976657i	$-0.568912\pi$
$103$	−6.99665e32	−0.429612	−0.214806	+	0.976657i	$0.568912\pi$
$104$	−7.58184e31	−0.0396940
$105$	0	0
$106$	2.26753e33	0.866974
$107$	6.35208e32	0.208010	0.104005	−	0.994577i	$-0.466834\pi$
$107$	6.35208e32	0.208010	0.104005	+	0.994577i	$0.466834\pi$
$108$	2.87445e33	0.807352
$109$	2.09396e33	0.505163	0.252581	−	0.967576i	$-0.418720\pi$
$109$	2.09396e33	0.505163	0.252581	+	0.967576i	$0.418720\pi$
$110$	0	0
$111$	5.59876e33	1.00061
$112$	−9.35266e32	−0.144158
$113$	−7.28662e33	−0.969910	−0.484955	−	0.874539i	$-0.661164\pi$
$113$	−7.28662e33	−0.969910	−0.484955	+	0.874539i	$0.661164\pi$
$114$	−3.45799e34	−3.98009
$115$	0	0
$116$	1.44731e34	1.25028
$117$	9.64169e33	0.722914
$118$	7.86094e33	0.512179
$119$	−4.42093e33	−0.250604
$120$	0	0
$121$	−1.68815e34	−0.726863
$122$	−2.89924e34	−1.08980
$123$	−7.51320e34	−2.46826
$124$	1.88040e34	0.540495
$125$	0	0
$126$	−1.47938e34	−0.326562
$127$	4.47086e34	0.866222	0.433111	−	0.901341i	$-0.357416\pi$
$127$	4.47086e34	0.866222	0.433111	+	0.901341i	$0.357416\pi$
$128$	9.56208e33	0.162775
$129$	2.54407e34	0.380889
$130$	0	0
$131$	−2.63964e34	−0.306597	−0.153298	−	0.988180i	$-0.548990\pi$
$131$	−2.63964e34	−0.306597	−0.153298	+	0.988180i	$0.548990\pi$
$132$	−8.49770e34	−0.870626
$133$	2.98508e34	0.270025
$134$	2.94595e35	2.35503
$135$	0	0
$136$	2.12764e34	0.133201
$137$	−1.03805e35	−0.575874	−0.287937	−	0.957649i	$-0.592969\pi$
$137$	−1.03805e35	−0.575874	−0.287937	+	0.957649i	$0.592969\pi$
$138$	6.14014e35	3.02116
$139$	−1.77157e34	−0.0773774	−0.0386887	−	0.999251i	$-0.512318\pi$
$139$	−1.77157e34	−0.0773774	−0.0386887	+	0.999251i	$0.512318\pi$
$140$	0	0
$141$	−8.76440e35	−3.02417
$142$	−3.82147e35	−1.17347
$143$	−9.30464e34	−0.254481
$144$	−5.72398e35	−1.39546
$145$	0	0
$146$	−4.54358e35	−0.882219
$147$	−8.87218e35	−1.53920
$148$	4.32473e35	0.670874
$149$	9.39618e35	1.30430	0.652151	−	0.758089i	$-0.273867\pi$
$149$	9.39618e35	1.30430	0.652151	+	0.758089i	$0.273867\pi$
$150$	0	0
$151$	4.46650e35	0.497563	0.248781	−	0.968560i	$-0.419970\pi$
$151$	4.46650e35	0.497563	0.248781	+	0.968560i	$0.419970\pi$
$152$	−1.43661e35	−0.143523
$153$	−2.70568e36	−2.42587
$154$	1.42766e35	0.114956
$155$	0	0
$156$	1.24641e36	0.811159
$157$	7.30629e35	0.427910	0.213955	−	0.976843i	$-0.431365\pi$
$157$	7.30629e35	0.427910	0.213955	+	0.976843i	$0.431365\pi$
$158$	−7.80761e35	−0.411791
$159$	−2.00489e36	−0.952879
$160$	0	0
$161$	−5.30043e35	−0.204967
$162$	1.15212e36	0.402254
$163$	2.77089e35	0.0874026	0.0437013	−	0.999045i	$-0.486085\pi$
$163$	2.77089e35	0.0874026	0.0437013	+	0.999045i	$0.486085\pi$
$164$	−5.80352e36	−1.65489
$165$	0	0
$166$	−2.80745e36	−0.655434
$167$	−5.22919e36	−1.10564	−0.552818	−	0.833302i	$-0.686448\pi$
$167$	−5.22919e36	−1.10564	−0.552818	+	0.833302i	$0.686448\pi$
$168$	−1.02858e35	−0.0197077
$169$	−4.39136e36	−0.762901
$170$	0	0
$171$	1.82692e37	2.61386
$172$	1.96515e36	0.255374
$173$	5.38814e36	0.636324	0.318162	−	0.948036i	$-0.396934\pi$
$173$	5.38814e36	0.636324	0.318162	+	0.948036i	$0.396934\pi$
$174$	−2.49053e37	−2.67441
$175$	0	0
$176$	5.52388e36	0.491230
$177$	−6.95044e36	−0.562928
$178$	3.55794e37	2.62584
$179$	2.52793e37	1.70094	0.850472	−	0.526020i	$-0.176316\pi$
$179$	2.52793e37	1.70094	0.850472	+	0.526020i	$0.176316\pi$
$180$	0	0
$181$	1.65835e36	0.0928924	0.0464462	−	0.998921i	$-0.485210\pi$
$181$	1.65835e36	0.0928924	0.0464462	+	0.998921i	$0.485210\pi$
$182$	−2.09404e36	−0.107105
$183$	2.56343e37	1.19779
$184$	2.55091e36	0.108943
$185$	0	0
$186$	−3.23577e37	−1.15615
$187$	2.61109e37	0.853957
$188$	−6.77000e37	−2.02761
$189$	4.26989e36	0.117165
$190$	0	0
$191$	6.04480e37	1.39422	0.697110	−	0.716964i	$-0.254469\pi$
$191$	6.04480e37	1.39422	0.697110	+	0.716964i	$0.254469\pi$
$192$	−8.27046e37	−1.75009
$193$	−6.49082e36	−0.126068	−0.0630339	−	0.998011i	$-0.520078\pi$
$193$	−6.49082e36	−0.126068	−0.0630339	+	0.998011i	$0.520078\pi$
$194$	1.42313e36	0.0253815
$195$	0	0
$196$	−6.85326e37	−1.03198
$197$	−9.24040e37	−1.27938	−0.639688	−	0.768635i	$-0.720936\pi$
$197$	−9.24040e37	−1.27938	−0.639688	+	0.768635i	$0.720936\pi$
$198$	8.73752e37	1.11279
$199$	−1.09203e38	−1.27985	−0.639925	−	0.768437i	$-0.721035\pi$
$199$	−1.09203e38	−1.27985	−0.639925	+	0.768437i	$0.721035\pi$
$200$	0	0
$201$	−2.60473e38	−2.58838
$202$	−2.06152e38	−1.88751
$203$	2.14993e37	0.181443
$204$	−3.49772e38	−2.72200
$205$	0	0
$206$	9.30006e37	0.616136
$207$	−3.24395e38	−1.98410
$208$	−8.10223e37	−0.457677
$209$	−1.76305e38	−0.920134
$210$	0	0
$211$	−6.11672e37	−0.272808	−0.136404	−	0.990653i	$-0.543555\pi$
$211$	−6.11672e37	−0.272808	−0.136404	+	0.990653i	$0.543555\pi$
$212$	−1.54866e38	−0.638874
$213$	3.37884e38	1.28974
$214$	−8.44328e37	−0.298321
$215$	0	0
$216$	−2.05495e37	−0.0622750
$217$	2.79325e37	0.0784377
$218$	−2.78332e38	−0.724489
$219$	4.01731e38	0.969634
$220$	0	0
$221$	−3.82986e38	−0.795629
$222$	−7.44196e38	−1.43504
$223$	−9.45280e38	−1.69251	−0.846253	−	0.532781i	$-0.821147\pi$
$223$	−9.45280e38	−1.69251	−0.846253	+	0.532781i	$0.821147\pi$
$224$	1.31835e38	0.219249
$225$	0	0
$226$	9.68548e38	1.39102
$227$	−4.90469e38	−0.654914	−0.327457	−	0.944866i	$-0.606192\pi$
$227$	−4.90469e38	−0.654914	−0.327457	+	0.944866i	$0.606192\pi$
$228$	2.36172e39	2.93294
$229$	−4.57241e38	−0.528275	−0.264137	−	0.964485i	$-0.585087\pi$
$229$	−4.57241e38	−0.528275	−0.264137	+	0.964485i	$0.585087\pi$
$230$	0	0
$231$	−1.26230e38	−0.126347
$232$	−1.03468e38	−0.0964398
$233$	8.69571e38	0.754975	0.377487	−	0.926015i	$-0.376788\pi$
$233$	8.69571e38	0.754975	0.377487	+	0.926015i	$0.376788\pi$
$234$	−1.28159e39	−1.03678
$235$	0	0
$236$	−5.36882e38	−0.377425
$237$	6.90328e38	0.452593
$238$	5.87637e38	0.359409
$239$	−1.38618e39	−0.791140	−0.395570	−	0.918436i	$-0.629453\pi$
$239$	−1.38618e39	−0.791140	−0.395570	+	0.918436i	$0.629453\pi$
$240$	0	0
$241$	−2.94732e39	−1.46604	−0.733019	−	0.680208i	$-0.761890\pi$
$241$	−2.94732e39	−1.46604	−0.733019	+	0.680208i	$0.761890\pi$
$242$	2.24392e39	1.04244
$243$	−2.77886e39	−1.20604
$244$	1.98011e39	0.803076
$245$	0	0
$246$	9.98665e39	3.53990
$247$	2.58598e39	0.857286
$248$	−1.34430e38	−0.0416910
$249$	2.48228e39	0.720379
$250$	0	0
$251$	−5.17168e39	−1.31527	−0.657636	−	0.753336i	$-0.728444\pi$
$251$	−5.17168e39	−1.31527	−0.657636	+	0.753336i	$0.728444\pi$
$252$	1.01038e39	0.240644
$253$	3.13055e39	0.698444
$254$	−5.94273e39	−1.24231
$255$	0	0
$256$	4.77386e39	0.876820
$257$	4.09624e39	0.705488	0.352744	−	0.935720i	$-0.385249\pi$
$257$	4.09624e39	0.705488	0.352744	+	0.935720i	$0.385249\pi$
$258$	−3.38162e39	−0.546260
$259$	6.42422e38	0.0973585
$260$	0	0
$261$	1.31579e40	1.75638
$262$	3.50865e39	0.439712
$263$	−2.59968e39	−0.305950	−0.152975	−	0.988230i	$-0.548885\pi$
$263$	−2.59968e39	−0.305950	−0.152975	+	0.988230i	$0.548885\pi$
$264$	6.07501e38	0.0671556
$265$	0	0
$266$	−3.96781e39	−0.387262
$267$	−3.14584e40	−2.88603
$268$	−2.01201e40	−1.73543
$269$	7.20422e39	0.584351	0.292176	−	0.956365i	$-0.405621\pi$
$269$	7.20422e39	0.584351	0.292176	+	0.956365i	$0.405621\pi$
$270$	0	0
$271$	−1.89743e40	−1.36199	−0.680993	−	0.732290i	$-0.738451\pi$
$271$	−1.89743e40	−1.36199	−0.680993	+	0.732290i	$0.738451\pi$
$272$	2.27367e40	1.53582
$273$	1.85150e39	0.117717
$274$	1.37979e40	0.825901
$275$	0	0
$276$	−4.19356e40	−2.22629
$277$	−3.08340e40	−1.54211	−0.771053	−	0.636771i	$-0.780270\pi$
$277$	−3.08340e40	−1.54211	−0.771053	+	0.636771i	$0.780270\pi$
$278$	2.35480e39	0.110972
$279$	1.70952e40	0.759283
$280$	0	0
$281$	−1.56575e40	−0.618112	−0.309056	−	0.951044i	$-0.600013\pi$
$281$	−1.56575e40	−0.618112	−0.309056	+	0.951044i	$0.600013\pi$
$282$	1.16498e41	4.33718
$283$	−7.24188e39	−0.254317	−0.127158	−	0.991882i	$-0.540586\pi$
$283$	−7.24188e39	−0.254317	−0.127158	+	0.991882i	$0.540586\pi$
$284$	2.60996e40	0.864732
$285$	0	0
$286$	1.23679e40	0.364968
$287$	−8.62090e39	−0.240160
$288$	8.06850e40	2.12235
$289$	6.72202e40	1.66988
$290$	0	0
$291$	−1.25830e39	−0.0278964
$292$	3.10315e40	0.650108
$293$	−7.67091e40	−1.51891	−0.759453	−	0.650562i	$-0.774533\pi$
$293$	−7.67091e40	−1.51891	−0.759453	+	0.650562i	$0.774533\pi$
$294$	1.17930e41	2.20747
$295$	0	0
$296$	−3.09175e39	−0.0517477
$297$	−2.52188e40	−0.399249
$298$	−1.24895e41	−1.87059
$299$	−4.59177e40	−0.650737
$300$	0	0
$301$	2.91915e39	0.0370604
$302$	−5.93694e40	−0.713589
$303$	1.82274e41	2.07454
$304$	−1.53522e41	−1.65484
$305$	0	0
$306$	3.59643e41	3.47911
$307$	1.29298e41	1.18525	0.592625	−	0.805478i	$-0.298091\pi$
$307$	1.29298e41	1.18525	0.592625	+	0.805478i	$0.298091\pi$
$308$	−9.75056e39	−0.0847116
$309$	−8.22286e40	−0.677186
$310$	0	0
$311$	−5.39990e40	−0.399797	−0.199898	−	0.979817i	$-0.564061\pi$
$311$	−5.39990e40	−0.399797	−0.199898	+	0.979817i	$0.564061\pi$
$312$	−8.91061e39	−0.0625686
$313$	−1.08588e41	−0.723270	−0.361635	−	0.932320i	$-0.617781\pi$
$313$	−1.08588e41	−0.723270	−0.361635	+	0.932320i	$0.617781\pi$
$314$	−9.71163e40	−0.613696
$315$	0	0
$316$	5.33240e40	0.303449
$317$	1.38129e41	0.746117	0.373059	−	0.927808i	$-0.378309\pi$
$317$	1.38129e41	0.746117	0.373059	+	0.927808i	$0.378309\pi$
$318$	2.66493e41	1.36659
$319$	−1.26979e41	−0.618282
$320$	0	0
$321$	7.46533e40	0.327881
$322$	7.04541e40	0.293957
$323$	−7.25686e41	−2.87678
$324$	−7.86869e40	−0.296422
$325$	0	0
$326$	−3.68311e40	−0.125350
$327$	2.46094e41	0.796275
$328$	4.14894e40	0.127649
$329$	−1.00566e41	−0.294251
$330$	0	0
$331$	−4.29457e41	−1.13699	−0.568496	−	0.822686i	$-0.692474\pi$
$331$	−4.29457e41	−1.13699	−0.568496	+	0.822686i	$0.692474\pi$
$332$	1.91742e41	0.482990
$333$	3.93172e41	0.942439
$334$	6.95072e41	1.58567
$335$	0	0
$336$	−1.09918e41	−0.227232
$337$	−6.97107e41	−1.37216	−0.686082	−	0.727524i	$-0.740671\pi$
$337$	−6.97107e41	−1.37216	−0.686082	+	0.727524i	$0.740671\pi$
$338$	5.83706e41	1.09413
$339$	−8.56364e41	−1.52885
$340$	0	0
$341$	−1.64975e41	−0.267284
$342$	−2.42837e42	−3.74872
$343$	−2.06057e41	−0.303134
$344$	−1.40489e40	−0.0196982
$345$	0	0
$346$	−7.16200e41	−0.912596
$347$	−7.56830e41	−0.919522	−0.459761	−	0.888043i	$-0.652065\pi$
$347$	−7.56830e41	−0.919522	−0.459761	+	0.888043i	$0.652065\pi$
$348$	1.70096e42	1.97078
$349$	4.06051e41	0.448705	0.224353	−	0.974508i	$-0.427973\pi$
$349$	4.06051e41	0.448705	0.224353	+	0.974508i	$0.427973\pi$
$350$	0	0
$351$	3.69901e41	0.371979
$352$	−7.78644e41	−0.747111
$353$	1.97994e42	1.81288	0.906439	−	0.422336i	$-0.138790\pi$
$353$	1.97994e42	1.81288	0.906439	+	0.422336i	$0.138790\pi$
$354$	9.23863e41	0.807335
$355$	0	0
$356$	−2.42998e42	−1.93499
$357$	−5.19573e41	−0.395022
$358$	−3.36016e42	−2.43944
$359$	−6.70289e41	−0.464733	−0.232366	−	0.972628i	$-0.574647\pi$
$359$	−6.70289e41	−0.464733	−0.232366	+	0.972628i	$0.574647\pi$
$360$	0	0
$361$	3.31917e42	2.09972
$362$	−2.20431e41	−0.133223
$363$	−1.98401e42	−1.14574
$364$	1.43018e41	0.0789255
$365$	0	0
$366$	−3.40736e42	−1.71783
$367$	1.36571e42	0.658215	0.329108	−	0.944292i	$-0.393252\pi$
$367$	1.36571e42	0.658215	0.329108	+	0.944292i	$0.393252\pi$
$368$	2.72599e42	1.25613
$369$	−5.27613e42	−2.32477
$370$	0	0
$371$	−2.30048e41	−0.0927147
$372$	2.20995e42	0.851968
$373$	−3.32617e41	−0.122673	−0.0613364	−	0.998117i	$-0.519536\pi$
$373$	−3.32617e41	−0.122673	−0.0613364	+	0.998117i	$0.519536\pi$
$374$	−3.47071e42	−1.22472
$375$	0	0
$376$	4.83988e41	0.156399
$377$	1.86249e42	0.576051
$378$	−5.67560e41	−0.168034
$379$	1.32387e42	0.375230	0.187615	−	0.982243i	$-0.439924\pi$
$379$	1.32387e42	0.375230	0.187615	+	0.982243i	$0.439924\pi$
$380$	0	0
$381$	5.25440e42	1.36540
$382$	−8.03484e42	−1.99955
$383$	−5.38010e42	−1.28236	−0.641181	−	0.767390i	$-0.721555\pi$
$383$	−5.38010e42	−1.28236	−0.641181	+	0.767390i	$0.721555\pi$
$384$	1.12379e42	0.256578
$385$	0	0
$386$	8.62770e41	0.180803
$387$	1.78657e42	0.358747
$388$	−9.71963e40	−0.0187036
$389$	−6.93155e42	−1.27839	−0.639193	−	0.769046i	$-0.720731\pi$
$389$	−6.93155e42	−1.27839	−0.639193	+	0.769046i	$0.720731\pi$
$390$	0	0
$391$	1.28856e43	2.18367
$392$	4.89939e41	0.0796017
$393$	−3.10225e42	−0.483281
$394$	1.22825e43	1.83484
$395$	0	0
$396$	−5.96750e42	−0.820015
$397$	9.33530e42	1.23051	0.615254	−	0.788329i	$-0.289053\pi$
$397$	9.33530e42	1.23051	0.615254	+	0.788329i	$0.289053\pi$
$398$	1.45154e43	1.83552
$399$	3.50824e42	0.425634
$400$	0	0
$401$	3.40931e42	0.380877	0.190438	−	0.981699i	$-0.439009\pi$
$401$	3.40931e42	0.380877	0.190438	+	0.981699i	$0.439009\pi$
$402$	3.46225e43	3.71218
$403$	2.41980e42	0.249027
$404$	1.40796e43	1.39091
$405$	0	0
$406$	−2.85772e42	−0.260219
$407$	−3.79428e42	−0.331758
$408$	2.50052e42	0.209961
$409$	3.12051e42	0.251646	0.125823	−	0.992053i	$-0.459843\pi$
$409$	3.12051e42	0.251646	0.125823	+	0.992053i	$0.459843\pi$
$410$	0	0
$411$	−1.21997e43	−0.907736
$412$	−6.35170e42	−0.454031
$413$	−7.97517e41	−0.0547727
$414$	4.31190e43	2.84553
$415$	0	0
$416$	1.14209e43	0.696081
$417$	−2.08205e42	−0.121968
$418$	2.34347e43	1.31963
$419$	−3.20466e43	−1.73480	−0.867402	−	0.497608i	$-0.834212\pi$
$419$	−3.20466e43	−1.73480	−0.867402	+	0.497608i	$0.834212\pi$
$420$	0	0
$421$	5.44061e42	0.272266	0.136133	−	0.990691i	$-0.456533\pi$
$421$	5.44061e42	0.272266	0.136133	+	0.990691i	$0.456533\pi$
$422$	8.13043e42	0.391253
$423$	−6.15478e43	−2.84837
$424$	1.10714e42	0.0492794
$425$	0	0
$426$	−4.49120e43	−1.84971
$427$	2.94137e42	0.116544
$428$	5.76654e42	0.219833
$429$	−1.09353e43	−0.401132
$430$	0	0
$431$	−3.50771e43	−1.19165	−0.595826	−	0.803114i	$-0.703175\pi$
$431$	−3.50771e43	−1.19165	−0.595826	+	0.803114i	$0.703175\pi$
$432$	−2.19599e43	−0.718039
$433$	−4.30567e43	−1.35516	−0.677580	−	0.735449i	$-0.736971\pi$
$433$	−4.30567e43	−1.35516	−0.677580	+	0.735449i	$0.736971\pi$
$434$	−3.71284e42	−0.112493
$435$	0	0
$436$	1.90094e43	0.533876
$437$	−8.70054e43	−2.35289
$438$	−5.33988e43	−1.39062
$439$	−1.81689e43	−0.455685	−0.227843	−	0.973698i	$-0.573167\pi$
$439$	−1.81689e43	−0.455685	−0.227843	+	0.973698i	$0.573167\pi$
$440$	0	0
$441$	−6.23047e43	−1.44972
$442$	5.09071e43	1.14107
$443$	2.81575e43	0.608040	0.304020	−	0.952666i	$-0.401671\pi$
$443$	2.81575e43	0.608040	0.304020	+	0.952666i	$0.401671\pi$
$444$	5.08267e43	1.05748
$445$	0	0
$446$	1.25648e44	2.42734
$447$	1.10429e44	2.05594
$448$	−9.48981e42	−0.170283
$449$	2.21288e43	0.382731	0.191365	−	0.981519i	$-0.438708\pi$
$449$	2.21288e43	0.382731	0.191365	+	0.981519i	$0.438708\pi$
$450$	0	0
$451$	5.09169e43	0.818368
$452$	−6.61493e43	−1.02504
$453$	5.24928e43	0.784295
$454$	6.51938e43	0.939258
$455$	0	0
$456$	−1.68839e43	−0.226231
$457$	6.39404e43	0.826339	0.413169	−	0.910654i	$-0.364422\pi$
$457$	6.39404e43	0.826339	0.413169	+	0.910654i	$0.364422\pi$
$458$	6.07772e43	0.757636
$459$	−1.03803e44	−1.24824
$460$	0	0
$461$	8.79013e42	0.0983853	0.0491926	−	0.998789i	$-0.484335\pi$
$461$	8.79013e42	0.0983853	0.0491926	+	0.998789i	$0.484335\pi$
$462$	1.67787e43	0.181203
$463$	1.18763e44	1.23764	0.618821	−	0.785532i	$-0.287611\pi$
$463$	1.18763e44	1.23764	0.618821	+	0.785532i	$0.287611\pi$
$464$	−1.10570e44	−1.11196
$465$	0	0
$466$	−1.15585e44	−1.08276
$467$	−1.78679e44	−1.61564	−0.807819	−	0.589431i	$-0.799352\pi$
$467$	−1.78679e44	−1.61564	−0.807819	+	0.589431i	$0.799352\pi$
$468$	8.75291e43	0.764005
$469$	−2.98876e43	−0.251849
$470$	0	0
$471$	8.58677e43	0.674504
$472$	3.83817e42	0.0291126
$473$	−1.72411e43	−0.126287
$474$	−9.17595e43	−0.649095
$475$	0	0
$476$	−4.01341e43	−0.264849
$477$	−1.40793e44	−0.897486
$478$	1.84253e44	1.13463
$479$	1.06259e44	0.632165	0.316082	−	0.948732i	$-0.397632\pi$
$479$	1.06259e44	0.632165	0.316082	+	0.948732i	$0.397632\pi$
$480$	0	0
$481$	5.56531e43	0.309098
$482$	3.91762e44	2.10255
$483$	−6.22936e43	−0.323084
$484$	−1.53254e44	−0.768178
$485$	0	0
$486$	3.69370e44	1.72967
$487$	−1.85504e44	−0.839700	−0.419850	−	0.907593i	$-0.637917\pi$
$487$	−1.85504e44	−0.839700	−0.419850	+	0.907593i	$0.637917\pi$
$488$	−1.41558e43	−0.0619451
$489$	3.25651e43	0.137771
$490$	0	0
$491$	8.88210e43	0.351294	0.175647	−	0.984453i	$-0.443798\pi$
$491$	8.88210e43	0.351294	0.175647	+	0.984453i	$0.443798\pi$
$492$	−6.82062e44	−2.60855
$493$	−5.22657e44	−1.93305
$494$	−3.43733e44	−1.22949
$495$	0	0
$496$	−1.43656e44	−0.480703
$497$	3.87700e43	0.125492
$498$	−3.29948e44	−1.03314
$499$	2.77853e44	0.841699	0.420849	−	0.907131i	$-0.361732\pi$
$499$	2.77853e44	0.841699	0.420849	+	0.907131i	$0.361732\pi$
$500$	0	0
$501$	−6.14564e44	−1.74279
$502$	6.87428e44	1.88632
$503$	−8.80760e41	−0.00233876	−0.00116938	−	0.999999i	$-0.500372\pi$
$503$	−8.80760e41	−0.00233876	−0.00116938	+	0.999999i	$0.500372\pi$
$504$	−7.22319e42	−0.0185620
$505$	0	0
$506$	−4.16117e44	−1.00169
$507$	−5.16097e44	−1.20254
$508$	4.05873e44	0.915459
$509$	−8.68803e44	−1.89705	−0.948523	−	0.316709i	$-0.897422\pi$
$509$	−8.68803e44	−1.89705	−0.948523	+	0.316709i	$0.897422\pi$
$510$	0	0
$511$	4.60961e43	0.0943450
$512$	−7.16687e44	−1.42028
$513$	7.00892e44	1.34498
$514$	−5.44479e44	−1.01179
$515$	0	0
$516$	2.30956e44	0.402539
$517$	5.93962e44	1.00269
$518$	−8.53917e43	−0.139629
$519$	6.33245e44	1.00302
$520$	0	0
$521$	−2.56437e44	−0.381205	−0.190602	−	0.981667i	$-0.561044\pi$
$521$	−2.56437e44	−0.381205	−0.190602	+	0.981667i	$0.561044\pi$
$522$	−1.74897e45	−2.51894
$523$	6.37079e43	0.0889028	0.0444514	−	0.999012i	$-0.485846\pi$
$523$	6.37079e43	0.0889028	0.0444514	+	0.999012i	$0.485846\pi$
$524$	−2.39631e44	−0.324024
$525$	0	0
$526$	3.45554e44	0.438784
$527$	−6.79052e44	−0.835657
$528$	6.49197e44	0.774314
$529$	6.79897e44	0.786004
$530$	0	0
$531$	−4.88093e44	−0.530204
$532$	2.70991e44	0.285373
$533$	−7.46830e44	−0.762471
$534$	4.18149e45	4.13905
$535$	0	0
$536$	1.43839e44	0.133862
$537$	2.97097e45	2.68116
$538$	−9.57595e44	−0.838059
$539$	6.01267e44	0.510332
$540$	0	0
$541$	−1.56706e45	−1.25121	−0.625605	−	0.780140i	$-0.715148\pi$
$541$	−1.56706e45	−1.25121	−0.625605	+	0.780140i	$0.715148\pi$
$542$	2.52209e45	1.95332
$543$	1.94899e44	0.146424
$544$	−3.20496e45	−2.33583
$545$	0	0
$546$	−2.46104e44	−0.168826
$547$	2.05395e45	1.36710	0.683548	−	0.729905i	$-0.260436\pi$
$547$	2.05395e45	1.36710	0.683548	+	0.729905i	$0.260436\pi$
$548$	−9.42359e44	−0.608607
$549$	1.80017e45	1.12816
$550$	0	0
$551$	3.52906e45	2.08285
$552$	2.99797e44	0.171725
$553$	7.92107e43	0.0440371
$554$	4.09851e45	2.21164
$555$	0	0
$556$	−1.60827e44	−0.0817756
$557$	−3.02985e44	−0.149558	−0.0747792	−	0.997200i	$-0.523825\pi$
$557$	−3.02985e44	−0.149558	−0.0747792	+	0.997200i	$0.523825\pi$
$558$	−2.27231e45	−1.08894
$559$	2.52887e44	0.117661
$560$	0	0
$561$	3.06871e45	1.34607
$562$	2.08122e45	0.886478
$563$	2.25447e45	0.932514	0.466257	−	0.884649i	$-0.345602\pi$
$563$	2.25447e45	0.932514	0.466257	+	0.884649i	$0.345602\pi$
$564$	−7.95649e45	−3.19607
$565$	0	0
$566$	9.62602e44	0.364733
$567$	−1.16886e44	−0.0430173
$568$	−1.86586e44	−0.0667009
$569$	−3.27232e45	−1.13633	−0.568163	−	0.822916i	$-0.692346\pi$
$569$	−3.27232e45	−1.13633	−0.568163	+	0.822916i	$0.692346\pi$
$570$	0	0
$571$	3.07381e45	1.00735	0.503675	−	0.863893i	$-0.331981\pi$
$571$	3.07381e45	1.00735	0.503675	+	0.863893i	$0.331981\pi$
$572$	−8.44693e44	−0.268946
$573$	7.10419e45	2.19768
$574$	1.14590e45	0.344431
$575$	0	0
$576$	−5.80792e45	−1.64835
$577$	6.81899e43	0.0188070	0.00940349	−	0.999956i	$-0.497007\pi$
$577$	6.81899e43	0.0188070	0.00940349	+	0.999956i	$0.497007\pi$
$578$	−8.93501e45	−2.39489
$579$	−7.62838e44	−0.198718
$580$	0	0
$581$	2.84825e44	0.0700926
$582$	1.67255e44	0.0400082
$583$	1.35871e45	0.315934
$584$	−2.21844e44	−0.0501460
$585$	0	0
$586$	1.01963e46	2.17837
$587$	8.96797e45	1.86280	0.931398	−	0.364002i	$-0.118590\pi$
$587$	8.96797e45	1.86280	0.931398	+	0.364002i	$0.118590\pi$
$588$	−8.05433e45	−1.62669
$589$	4.58506e45	0.900416
$590$	0	0
$591$	−1.08598e46	−2.01665
$592$	−3.30395e45	−0.596659
$593$	3.75910e45	0.660209	0.330104	−	0.943944i	$-0.392916\pi$
$593$	3.75910e45	0.660209	0.330104	+	0.943944i	$0.392916\pi$
$594$	3.35213e45	0.572590
$595$	0	0
$596$	8.53004e45	1.37844
$597$	−1.28342e46	−2.01740
$598$	6.10345e45	0.933268
$599$	8.80446e45	1.30966	0.654832	−	0.755774i	$-0.272739\pi$
$599$	8.80446e45	1.30966	0.654832	+	0.755774i	$0.272739\pi$
$600$	0	0
$601$	−4.53048e45	−0.637846	−0.318923	−	0.947781i	$-0.603321\pi$
$601$	−4.53048e45	−0.637846	−0.318923	+	0.947781i	$0.603321\pi$
$602$	−3.88018e44	−0.0531508
$603$	−1.82917e46	−2.43791
$604$	4.05477e45	0.525844
$605$	0	0
$606$	−2.42281e46	−2.97524
$607$	−1.02463e46	−1.22448	−0.612242	−	0.790671i	$-0.709732\pi$
$607$	−1.02463e46	−1.22448	−0.612242	+	0.790671i	$0.709732\pi$
$608$	2.16404e46	2.51684
$609$	2.52672e45	0.286003
$610$	0	0
$611$	−8.71203e45	−0.934199
$612$	−2.45627e46	−2.56376
$613$	4.85425e45	0.493201	0.246601	−	0.969117i	$-0.420686\pi$
$613$	4.85425e45	0.493201	0.246601	+	0.969117i	$0.420686\pi$
$614$	−1.71865e46	−1.69985
$615$	0	0
$616$	6.97068e43	0.00653421
$617$	1.62668e46	1.48455	0.742277	−	0.670093i	$-0.233746\pi$
$617$	1.62668e46	1.48455	0.742277	+	0.670093i	$0.233746\pi$
$618$	1.09300e46	0.971200
$619$	−2.50157e45	−0.216430	−0.108215	−	0.994128i	$-0.534514\pi$
$619$	−2.50157e45	−0.216430	−0.108215	+	0.994128i	$0.534514\pi$
$620$	0	0
$621$	−1.24453e46	−1.02093
$622$	7.17763e45	0.573376
$623$	−3.60964e45	−0.280809
$624$	−9.52220e45	−0.721425
$625$	0	0
$626$	1.44337e46	1.03729
$627$	−2.07204e46	−1.45038
$628$	6.63279e45	0.452233
$629$	−1.56175e46	−1.03723
$630$	0	0
$631$	6.94339e45	0.437610	0.218805	−	0.975769i	$-0.429784\pi$
$631$	6.94339e45	0.437610	0.218805	+	0.975769i	$0.429784\pi$
$632$	−3.81213e44	−0.0234065
$633$	−7.18871e45	−0.430021
$634$	−1.83603e46	−1.07006
$635$	0	0
$636$	−1.82008e46	−1.00704
$637$	−8.81916e45	−0.475474
$638$	1.68783e46	0.886721
$639$	2.37278e46	1.21477
$640$	0	0
$641$	4.34529e45	0.211282	0.105641	−	0.994404i	$-0.466311\pi$
$641$	4.34529e45	0.211282	0.105641	+	0.994404i	$0.466311\pi$
$642$	−9.92303e45	−0.470236
$643$	−2.56764e46	−1.18591	−0.592956	−	0.805235i	$-0.702039\pi$
$643$	−2.56764e46	−1.18591	−0.592956	+	0.805235i	$0.702039\pi$
$644$	−4.81183e45	−0.216618
$645$	0	0
$646$	9.64592e46	4.12579
$647$	1.55928e46	0.650136	0.325068	−	0.945691i	$-0.394613\pi$
$647$	1.55928e46	0.650136	0.325068	+	0.945691i	$0.394613\pi$
$648$	5.62533e44	0.0228644
$649$	4.71030e45	0.186643
$650$	0	0
$651$	3.28279e45	0.123639
$652$	2.51547e45	0.0923706
$653$	−1.54838e45	−0.0554384	−0.0277192	−	0.999616i	$-0.508824\pi$
$653$	−1.54838e45	−0.0554384	−0.0277192	+	0.999616i	$0.508824\pi$
$654$	−3.27112e46	−1.14199
$655$	0	0
$656$	4.43370e46	1.47182
$657$	2.82115e46	0.913267
$658$	1.33673e46	0.422005
$659$	−1.05260e46	−0.324080	−0.162040	−	0.986784i	$-0.551807\pi$
$659$	−1.05260e46	−0.324080	−0.162040	+	0.986784i	$0.551807\pi$
$660$	0	0
$661$	−1.48865e46	−0.435981	−0.217990	−	0.975951i	$-0.569950\pi$
$661$	−1.48865e46	−0.435981	−0.217990	+	0.975951i	$0.569950\pi$
$662$	5.70840e46	1.63064
$663$	−4.50107e46	−1.25413
$664$	−1.37076e45	−0.0372554
$665$	0	0
$666$	−5.22611e46	−1.35162
$667$	−6.26634e46	−1.58102
$668$	−4.74716e46	−1.16848
$669$	−1.11095e47	−2.66786
$670$	0	0
$671$	−1.73724e46	−0.397134
$672$	1.54940e46	0.345597
$673$	2.78172e46	0.605432	0.302716	−	0.953081i	$-0.402107\pi$
$673$	2.78172e46	0.605432	0.302716	+	0.953081i	$0.402107\pi$
$674$	9.26605e46	1.96791
$675$	0	0
$676$	−3.98656e46	−0.806265
$677$	9.09948e45	0.179599	0.0897995	−	0.995960i	$-0.471377\pi$
$677$	9.09948e45	0.179599	0.0897995	+	0.995960i	$0.471377\pi$
$678$	1.13829e47	2.19262
$679$	−1.44381e44	−0.00271431
$680$	0	0
$681$	−5.76426e46	−1.03233
$682$	2.19288e46	0.383330
$683$	−2.07397e46	−0.353883	−0.176942	−	0.984221i	$-0.556620\pi$
$683$	−2.07397e46	−0.353883	−0.176942	+	0.984221i	$0.556620\pi$
$684$	1.65851e47	2.76244
$685$	0	0
$686$	2.73894e46	0.434746
$687$	−5.37376e46	−0.832707
$688$	−1.50131e46	−0.227123
$689$	−1.99291e46	−0.294354
$690$	0	0
$691$	7.80876e46	1.09950	0.549749	−	0.835330i	$-0.314723\pi$
$691$	7.80876e46	1.09950	0.549749	+	0.835330i	$0.314723\pi$
$692$	4.89146e46	0.672493
$693$	−8.86448e45	−0.119002
$694$	1.00599e47	1.31875
$695$	0	0
$696$	−1.21602e46	−0.152016
$697$	2.09578e47	2.55861
$698$	−5.39729e46	−0.643519
$699$	1.02197e47	1.19005
$700$	0	0
$701$	−7.28838e46	−0.809624	−0.404812	−	0.914400i	$-0.632663\pi$
$701$	−7.28838e46	−0.809624	−0.404812	+	0.914400i	$0.632663\pi$
$702$	−4.91678e46	−0.533480
$703$	1.05452e47	1.11761
$704$	5.60488e46	0.580253
$705$	0	0
$706$	−2.63176e47	−2.59997
$707$	2.09147e46	0.201852
$708$	−6.30974e46	−0.594926
$709$	4.67334e46	0.430491	0.215246	−	0.976560i	$-0.430945\pi$
$709$	4.67334e46	0.430491	0.215246	+	0.976560i	$0.430945\pi$
$710$	0	0
$711$	4.84782e46	0.426283
$712$	1.73719e46	0.149255
$713$	−8.14142e46	−0.683476
$714$	6.90624e46	0.566528
$715$	0	0
$716$	2.29490e47	1.79763
$717$	−1.62911e47	−1.24705
$718$	8.90958e46	0.666506
$719$	−1.27931e47	−0.935299	−0.467649	−	0.883914i	$-0.654899\pi$
$719$	−1.27931e47	−0.935299	−0.467649	+	0.883914i	$0.654899\pi$
$720$	0	0
$721$	−9.43520e45	−0.0658899
$722$	−4.41189e47	−3.01135
$723$	−3.46385e47	−2.31088
$724$	1.50548e46	0.0981725
$725$	0	0
$726$	2.63718e47	1.64318
$727$	1.68652e47	1.02724	0.513621	−	0.858017i	$-0.328304\pi$
$727$	1.68652e47	1.02724	0.513621	+	0.858017i	$0.328304\pi$
$728$	−1.02243e45	−0.00608790
$729$	−2.78403e47	−1.62057
$730$	0	0
$731$	−7.09659e46	−0.394832
$732$	2.32713e47	1.26587
$733$	−3.19951e47	−1.70164	−0.850821	−	0.525456i	$-0.823895\pi$
$733$	−3.19951e47	−1.70164	−0.850821	+	0.525456i	$0.823895\pi$
$734$	−1.81532e47	−0.943992
$735$	0	0
$736$	−3.84255e47	−1.91045
$737$	1.76523e47	0.858196
$738$	7.01311e47	3.33412
$739$	−1.33356e47	−0.619980	−0.309990	−	0.950740i	$-0.600326\pi$
$739$	−1.33356e47	−0.619980	−0.309990	+	0.950740i	$0.600326\pi$
$740$	0	0
$741$	3.03919e47	1.35132
$742$	3.05783e46	0.132969
$743$	−3.22840e46	−0.137300	−0.0686502	−	0.997641i	$-0.521869\pi$
$743$	−3.22840e46	−0.137300	−0.0686502	+	0.997641i	$0.521869\pi$
$744$	−1.57989e46	−0.0657164
$745$	0	0
$746$	4.42119e46	0.175934
$747$	1.74317e47	0.678502
$748$	2.37040e47	0.902497
$749$	8.56597e45	0.0319027
$750$	0	0
$751$	2.39672e46	0.0854196	0.0427098	−	0.999088i	$-0.486401\pi$
$751$	2.39672e46	0.0854196	0.0427098	+	0.999088i	$0.486401\pi$
$752$	5.17206e47	1.80331
$753$	−6.07806e47	−2.07323
$754$	−2.47565e47	−0.826154
$755$	0	0
$756$	3.87628e46	0.123824
$757$	6.92584e46	0.216466	0.108233	−	0.994126i	$-0.465481\pi$
$757$	6.92584e46	0.216466	0.108233	+	0.994126i	$0.465481\pi$
$758$	−1.75970e47	−0.538143
$759$	3.67919e47	1.10094
$760$	0	0
$761$	−4.97287e47	−1.42482	−0.712411	−	0.701763i	$-0.752397\pi$
$761$	−4.97287e47	−1.42482	−0.712411	+	0.701763i	$0.752397\pi$
$762$	−6.98423e47	−1.95822
$763$	2.82377e46	0.0774773
$764$	5.48759e47	1.47347
$765$	0	0
$766$	7.15131e47	1.83912
$767$	−6.90891e46	−0.173895
$768$	5.61051e47	1.38211
$769$	2.89778e47	0.698683	0.349342	−	0.936995i	$-0.386405\pi$
$769$	2.89778e47	0.698683	0.349342	+	0.936995i	$0.386405\pi$
$770$	0	0
$771$	4.81414e47	1.11204
$772$	−5.89249e46	−0.133234
$773$	5.10656e47	1.13023	0.565115	−	0.825012i	$-0.308832\pi$
$773$	5.10656e47	1.13023	0.565115	+	0.825012i	$0.308832\pi$
$774$	−2.37473e47	−0.514504
$775$	0	0
$776$	6.94857e44	0.00144270
$777$	7.55010e46	0.153464
$778$	9.21352e47	1.83342
$779$	−1.41510e48	−2.75689
$780$	0	0
$781$	−2.28983e47	−0.427624
$782$	−1.71277e48	−3.13175
$783$	5.04799e47	0.903753
$784$	5.23567e47	0.917819
$785$	0	0
$786$	4.12356e47	0.693107
$787$	−3.90010e47	−0.641938	−0.320969	−	0.947090i	$-0.604009\pi$
$787$	−3.90010e47	−0.641938	−0.320969	+	0.947090i	$0.604009\pi$
$788$	−8.38862e47	−1.35210
$789$	−3.05529e47	−0.482261
$790$	0	0
$791$	−9.82622e46	−0.148756
$792$	4.26617e46	0.0632517
$793$	2.54812e47	0.370009
$794$	−1.24086e48	−1.76476
$795$	0	0
$796$	−9.91367e47	−1.35260
$797$	−6.38986e47	−0.853943	−0.426972	−	0.904265i	$-0.640420\pi$
$797$	−6.38986e47	−0.853943	−0.426972	+	0.904265i	$0.640420\pi$
$798$	−4.66320e47	−0.610431
$799$	2.44479e48	3.13488
$800$	0	0
$801$	−2.20916e48	−2.71826
$802$	−4.53171e47	−0.546242
$803$	−2.72253e47	−0.321489
$804$	−2.36463e48	−2.73551
$805$	0	0
$806$	−3.21644e47	−0.357147
$807$	8.46680e47	0.921098
$808$	−1.00655e47	−0.107288
$809$	−3.00339e47	−0.313661	−0.156831	−	0.987626i	$-0.550128\pi$
$809$	−3.00339e47	−0.313661	−0.156831	+	0.987626i	$0.550128\pi$
$810$	0	0
$811$	−1.57205e48	−1.57624	−0.788121	−	0.615521i	$-0.788946\pi$
$811$	−1.57205e48	−1.57624	−0.788121	+	0.615521i	$0.788946\pi$
$812$	1.95175e47	0.191756
$813$	−2.22997e48	−2.14686
$814$	5.04341e47	0.475797
$815$	0	0
$816$	2.67215e48	2.42088
$817$	4.79172e47	0.425430
$818$	−4.14782e47	−0.360903
$819$	1.30021e47	0.110874
$820$	0	0
$821$	2.23751e48	1.83275	0.916374	−	0.400324i	$-0.131102\pi$
$821$	2.23751e48	1.83275	0.916374	+	0.400324i	$0.131102\pi$
$822$	1.62160e48	1.30185
$823$	5.02472e47	0.395380	0.197690	−	0.980265i	$-0.436656\pi$
$823$	5.02472e47	0.395380	0.197690	+	0.980265i	$0.436656\pi$
$824$	4.54083e46	0.0350216
$825$	0	0
$826$	1.06007e47	0.0785533
$827$	−1.52395e48	−1.10695	−0.553475	−	0.832865i	$-0.686699\pi$
$827$	−1.52395e48	−1.10695	−0.553475	+	0.832865i	$0.686699\pi$
$828$	−2.94492e48	−2.09688
$829$	7.14872e47	0.498975	0.249487	−	0.968378i	$-0.419738\pi$
$829$	7.14872e47	0.498975	0.249487	+	0.968378i	$0.419738\pi$
$830$	0	0
$831$	−3.62379e48	−2.43078
$832$	−8.22104e47	−0.540620
$833$	2.47486e48	1.59554
$834$	2.76749e47	0.174923
$835$	0	0
$836$	−1.60053e48	−0.972436
$837$	6.55851e47	0.390693
$838$	4.25968e48	2.48800
$839$	2.41800e48	1.38479	0.692394	−	0.721519i	$-0.256556\pi$
$839$	2.41800e48	1.38479	0.692394	+	0.721519i	$0.256556\pi$
$840$	0	0
$841$	7.25637e47	0.399563
$842$	−7.23174e47	−0.390475
$843$	−1.84015e48	−0.974315
$844$	−5.55287e47	−0.288315
$845$	0	0
$846$	8.18103e48	4.08505
$847$	−2.27652e47	−0.111480
$848$	1.18313e48	0.568199
$849$	−8.51107e47	−0.400873
$850$	0	0
$851$	−1.87245e48	−0.848345
$852$	3.06737e48	1.36306
$853$	−5.58595e47	−0.243466	−0.121733	−	0.992563i	$-0.538845\pi$
$853$	−5.58595e47	−0.243466	−0.121733	+	0.992563i	$0.538845\pi$
$854$	−3.90972e47	−0.167144
$855$	0	0
$856$	−4.12250e46	−0.0169568
$857$	7.99378e47	0.322529	0.161264	−	0.986911i	$-0.448443\pi$
$857$	7.99378e47	0.322529	0.161264	+	0.986911i	$0.448443\pi$
$858$	1.45354e48	0.575290
$859$	3.21299e48	1.24745	0.623723	−	0.781646i	$-0.285619\pi$
$859$	3.21299e48	1.24745	0.623723	+	0.781646i	$0.285619\pi$
$860$	0	0
$861$	−1.01318e48	−0.378559
$862$	4.66251e48	1.70903
$863$	−2.15382e48	−0.774519	−0.387259	−	0.921971i	$-0.626578\pi$
$863$	−2.15382e48	−0.774519	−0.387259	+	0.921971i	$0.626578\pi$
$864$	3.09546e48	1.09206
$865$	0	0
$866$	5.72316e48	1.94353
$867$	7.90010e48	2.63219
$868$	2.53577e47	0.0828962
$869$	−4.67835e47	−0.150060
$870$	0	0
$871$	−2.58917e48	−0.799578
$872$	−1.35898e47	−0.0411805
$873$	−8.83637e46	−0.0262748
$874$	1.15649e49	3.37445
$875$	0	0
$876$	3.64700e48	1.02475
$877$	−4.36089e48	−1.20249	−0.601245	−	0.799064i	$-0.705329\pi$
$877$	−4.36089e48	−1.20249	−0.601245	+	0.799064i	$0.705329\pi$
$878$	2.41504e48	0.653530
$879$	−9.01528e48	−2.39421
$880$	0	0
$881$	−4.71885e48	−1.20707	−0.603537	−	0.797335i	$-0.706242\pi$
$881$	−4.71885e48	−1.20707	−0.603537	+	0.797335i	$0.706242\pi$
$882$	8.28163e48	2.07914
$883$	2.47214e48	0.609146	0.304573	−	0.952489i	$-0.401486\pi$
$883$	2.47214e48	0.609146	0.304573	+	0.952489i	$0.401486\pi$
$884$	−3.47682e48	−0.840853
$885$	0	0
$886$	−3.74274e48	−0.872033
$887$	6.65983e48	1.52308	0.761542	−	0.648116i	$-0.224443\pi$
$887$	6.65983e48	1.52308	0.761542	+	0.648116i	$0.224443\pi$
$888$	−3.63360e47	−0.0815686
$889$	6.02908e47	0.132853
$890$	0	0
$891$	6.90355e47	0.146585
$892$	−8.58144e48	−1.78871
$893$	−1.65076e49	−3.37781
$894$	−1.46784e49	−2.94856
$895$	0	0
$896$	1.28948e47	0.0249650
$897$	−5.39651e48	−1.02574
$898$	−2.94139e48	−0.548901
$899$	3.30227e48	0.605032
$900$	0	0
$901$	5.59256e48	0.987760
$902$	−6.76795e48	−1.17368
$903$	3.43075e47	0.0584173
$904$	4.72902e47	0.0790663
$905$	0	0
$906$	−6.97743e48	−1.12481
$907$	−4.30056e48	−0.680777	−0.340388	−	0.940285i	$-0.610559\pi$
$907$	−4.30056e48	−0.680777	−0.340388	+	0.940285i	$0.610559\pi$
$908$	−4.45257e48	−0.692140
$909$	1.28002e49	1.95394
$910$	0	0
$911$	−2.43257e48	−0.358106	−0.179053	−	0.983839i	$-0.557303\pi$
$911$	−2.43257e48	−0.358106	−0.179053	+	0.983839i	$0.557303\pi$
$912$	−1.80427e49	−2.60848
$913$	−1.68224e48	−0.238847
$914$	−8.49906e48	−1.18511
$915$	0	0
$916$	−4.15093e48	−0.558303
$917$	−3.55963e47	−0.0470230
$918$	1.37976e49	1.79019
$919$	1.59035e48	0.202669	0.101334	−	0.994852i	$-0.467689\pi$
$919$	1.59035e48	0.202669	0.101334	+	0.994852i	$0.467689\pi$
$920$	0	0
$921$	1.51959e49	1.86828
$922$	−1.16840e48	−0.141101
$923$	3.35865e48	0.398416
$924$	−1.14594e48	−0.133529
$925$	0	0
$926$	−1.57862e49	−1.77499
$927$	−5.77449e48	−0.637820
$928$	1.55859e49	1.69119
$929$	−1.48456e49	−1.58248	−0.791239	−	0.611507i	$-0.790564\pi$
$929$	−1.48456e49	−1.58248	−0.791239	+	0.611507i	$0.790564\pi$
$930$	0	0
$931$	−1.67106e49	−1.71919
$932$	7.89414e48	0.797888
$933$	−6.34627e48	−0.630190
$934$	2.37502e49	2.31710
$935$	0	0
$936$	−6.25746e47	−0.0589314
$937$	1.00831e49	0.933020	0.466510	−	0.884516i	$-0.345511\pi$
$937$	1.00831e49	0.933020	0.466510	+	0.884516i	$0.345511\pi$
$938$	3.97271e48	0.361193
$939$	−1.27619e49	−1.14007
$940$	0	0
$941$	9.04832e48	0.780440	0.390220	−	0.920722i	$-0.372399\pi$
$941$	9.04832e48	0.780440	0.390220	+	0.920722i	$0.372399\pi$
$942$	−1.14137e49	−0.967353
$943$	2.51271e49	2.09266
$944$	4.10161e48	0.335673
$945$	0	0
$946$	2.29172e48	0.181116
$947$	9.36347e48	0.727214	0.363607	−	0.931552i	$-0.381545\pi$
$947$	9.36347e48	0.727214	0.363607	+	0.931552i	$0.381545\pi$
$948$	6.26693e48	0.478319
$949$	3.99331e48	0.299530
$950$	0	0
$951$	1.62337e49	1.17609
$952$	2.86919e47	0.0204291
$953$	−1.92193e49	−1.34494	−0.672472	−	0.740123i	$-0.734767\pi$
$953$	−1.92193e49	−1.34494	−0.672472	+	0.740123i	$0.734767\pi$
$954$	1.87144e49	1.28715
$955$	0	0
$956$	−1.25840e49	−0.836109
$957$	−1.49233e49	−0.974582
$958$	−1.41241e49	−0.906631
$959$	−1.39984e48	−0.0883223
$960$	0	0
$961$	−1.21131e49	−0.738444
$962$	−7.39750e48	−0.443298
$963$	5.24251e48	0.308820
$964$	−2.67563e49	−1.54937
$965$	0	0
$966$	8.28017e48	0.463358
$967$	1.11182e49	0.611642	0.305821	−	0.952089i	$-0.401069\pi$
$967$	1.11182e49	0.611642	0.305821	+	0.952089i	$0.401069\pi$
$968$	1.09561e48	0.0592533
$969$	−8.52867e49	−4.53460
$970$	0	0
$971$	1.55536e49	0.799308	0.399654	−	0.916666i	$-0.369130\pi$
$971$	1.55536e49	0.799308	0.399654	+	0.916666i	$0.369130\pi$
$972$	−2.52270e49	−1.27459
$973$	−2.38902e47	−0.0118674
$974$	2.46574e49	1.20427
$975$	0	0
$976$	−1.51274e49	−0.714236
$977$	2.43707e49	1.13138	0.565690	−	0.824618i	$-0.308610\pi$
$977$	2.43707e49	1.13138	0.565690	+	0.824618i	$0.308610\pi$
$978$	−4.32860e48	−0.197586
$979$	2.13193e49	0.956883
$980$	0	0
$981$	1.72819e49	0.749986
$982$	−1.18062e49	−0.503815
$983$	−1.27767e48	−0.0536148	−0.0268074	−	0.999641i	$-0.508534\pi$
$983$	−1.27767e48	−0.0536148	−0.0268074	+	0.999641i	$0.508534\pi$
$984$	4.87607e48	0.201210
$985$	0	0
$986$	6.94723e49	2.77231
$987$	−1.18191e49	−0.463820
$988$	2.34760e49	0.906015
$989$	−8.50838e48	−0.322930
$990$	0	0
$991$	−8.47131e48	−0.310982	−0.155491	−	0.987837i	$-0.549696\pi$
$991$	−8.47131e48	−0.310982	−0.155491	+	0.987837i	$0.549696\pi$
$992$	2.02497e49	0.731100
$993$	−5.04722e49	−1.79221
$994$	−5.15336e48	−0.179976
$995$	0	0
$996$	2.25346e49	0.761326
$997$	4.23201e49	1.40629	0.703147	−	0.711045i	$-0.251778\pi$
$997$	4.23201e49	1.40629	0.703147	+	0.711045i	$0.251778\pi$
$998$	−3.69327e49	−1.20714
$999$	1.50840e49	0.484936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.c.1.2		6
5.2	odd	4		25.34.b.c.24.2		12
5.3	odd	4		25.34.b.c.24.11		12
5.4	even	2		5.34.a.b.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.5	✓	6	5.4	even	2
25.34.a.c.1.2		6	1.1	even	1	trivial
25.34.b.c.24.2		12	5.2	odd	4
25.34.b.c.24.11		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)

\(f(q)\)	\(=\)	\(q-132922. q^{2} +1.17526e8 q^{3} +9.07819e9 q^{4} -1.56217e13 q^{6} +1.34853e13 q^{7} -6.49000e13 q^{8} +8.25322e15 q^{9} +O(q^{10})\)	\(q-132922. q^{2} +1.17526e8 q^{3} +9.07819e9 q^{4} -1.56217e13 q^{6} +1.34853e13 q^{7} -6.49000e13 q^{8} +8.25322e15 q^{9} -7.96470e16 q^{11} +1.06692e18 q^{12} +1.16823e18 q^{13} -1.79249e18 q^{14} -6.93545e19 q^{16} -3.27833e20 q^{17} -1.09703e21 q^{18} +2.21358e21 q^{19} +1.58487e21 q^{21} +1.05868e22 q^{22} -3.93052e22 q^{23} -7.62742e21 q^{24} -1.55283e23 q^{26} +3.16633e23 q^{27} +1.22422e23 q^{28} +1.59428e24 q^{29} +2.07133e24 q^{31} +9.77619e24 q^{32} -9.36057e24 q^{33} +4.35761e25 q^{34} +7.49243e25 q^{36} +4.76387e25 q^{37} -2.94233e26 q^{38} +1.37297e26 q^{39} -6.39281e26 q^{41} -2.10663e26 q^{42} +2.16469e26 q^{43} -7.23051e26 q^{44} +5.22451e27 q^{46} -7.45743e27 q^{47} -8.15093e27 q^{48} -7.54914e27 q^{49} -3.85288e28 q^{51} +1.06055e28 q^{52} -1.70592e28 q^{53} -4.20873e28 q^{54} -8.75196e26 q^{56} +2.60153e29 q^{57} -2.11913e29 q^{58} -5.91397e28 q^{59} +2.18117e29 q^{61} -2.75325e29 q^{62} +1.11297e29 q^{63} -7.03715e29 q^{64} +1.24422e30 q^{66} -2.21631e30 q^{67} -2.97613e30 q^{68} -4.61937e30 q^{69} +2.87498e30 q^{71} -5.35634e29 q^{72} +3.41825e30 q^{73} -6.33220e30 q^{74} +2.00953e31 q^{76} -1.07406e30 q^{77} -1.82498e31 q^{78} +5.87385e30 q^{79} -8.66769e30 q^{81} +8.49743e31 q^{82} +2.11211e31 q^{83} +1.43877e31 q^{84} -2.87734e31 q^{86} +1.87368e32 q^{87} +5.16909e30 q^{88} -2.67672e32 q^{89} +1.57540e31 q^{91} -3.56821e32 q^{92} +2.43435e32 q^{93} +9.91253e32 q^{94} +1.14895e33 q^{96} -1.07066e31 q^{97} +1.00344e33 q^{98} -6.57344e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 6615759249352 q^{6} - 19113832847500 q^{7} - 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 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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