LMFDB - Embedded newform 25.32.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,32,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, 32, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 32 $
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:	$152.192832048$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 15839611600 x^{8} - 45590087880320 x^{7} + \cdots - 25\!\cdots\!32 $ x^10 - 5x^9 - 15839611600x^8 - 45590087880320x^7 + 85474769223363383360x^6 + 551294123417348135986144x^5 - 182909365166022938529687566720x^4 - 1829719117177160236327129855726080x^3 + 143308707060383591826312630378520185600x^2 + 1482064367555394481116858469439756676837120*x - 25794524289233029371900088892211194679153580032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{39}\cdot 3^{11}\cdot 5^{24} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$53026.3$ 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)

$f(q)$	$=$	$q-50468.3 q^{2} -3.54185e7 q^{3} +3.99569e8 q^{4} +1.78751e12 q^{6} -7.37897e12 q^{7} +8.82143e13 q^{8} +6.36795e14 q^{9} +O(q^{10})$	\(q-50468.3 q^{2} -3.54185e7 q^{3} +3.99569e8 q^{4} +1.78751e12 q^{6} -7.37897e12 q^{7} +8.82143e13 q^{8} +6.36795e14 q^{9} -2.56911e16 q^{11} -1.41521e16 q^{12} -1.59954e17 q^{13} +3.72404e17 q^{14} -5.31010e18 q^{16} +5.12967e18 q^{17} -3.21380e19 q^{18} +6.46616e19 q^{19} +2.61352e20 q^{21} +1.29658e21 q^{22} +1.49288e21 q^{23} -3.12442e21 q^{24} +8.07260e21 q^{26} -6.77267e20 q^{27} -2.94841e21 q^{28} -5.23737e22 q^{29} +2.77195e22 q^{31} +7.85529e22 q^{32} +9.09938e23 q^{33} -2.58886e23 q^{34} +2.54443e23 q^{36} +6.74592e23 q^{37} -3.26336e24 q^{38} +5.66532e24 q^{39} -6.66926e24 q^{41} -1.31900e25 q^{42} -2.14950e25 q^{43} -1.02653e25 q^{44} -7.53434e25 q^{46} +1.75727e25 q^{47} +1.88076e26 q^{48} -1.03326e26 q^{49} -1.81685e26 q^{51} -6.39125e25 q^{52} +3.62828e26 q^{53} +3.41806e25 q^{54} -6.50931e26 q^{56} -2.29022e27 q^{57} +2.64322e27 q^{58} -4.99188e27 q^{59} -7.77843e27 q^{61} -1.39896e27 q^{62} -4.69890e27 q^{63} +7.43891e27 q^{64} -4.59231e28 q^{66} -2.47542e28 q^{67} +2.04966e27 q^{68} -5.28757e28 q^{69} +8.55888e28 q^{71} +5.61745e28 q^{72} +7.99777e28 q^{73} -3.40455e28 q^{74} +2.58368e28 q^{76} +1.89574e29 q^{77} -2.85919e29 q^{78} -1.78848e29 q^{79} -3.69344e29 q^{81} +3.36586e29 q^{82} -8.73583e29 q^{83} +1.04428e29 q^{84} +1.08481e30 q^{86} +1.85500e30 q^{87} -2.26632e30 q^{88} -2.53778e30 q^{89} +1.18029e30 q^{91} +5.96510e29 q^{92} -9.81782e29 q^{93} -8.86867e29 q^{94} -2.78223e30 q^{96} +2.82605e30 q^{97} +5.21470e30 q^{98} -1.63599e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 25575 q^{2} - 2760800 q^{3} + 10269794805 q^{4} + 343311916045 q^{6} + 9887556005000 q^{7} - 3578006280975 q^{8} + 18\!\cdots\!20 q^{9}+O(q^{10}) $ 10 * q + 25575 * q^2 - 2760800 * q^3 + 10269794805 * q^4 + 343311916045 * q^6 + 9887556005000 * q^7 - 3578006280975 * q^8 + 1815779931749020 * q^9	$ 10 q + 25575 q^{2} - 2760800 q^{3} + 10269794805 q^{4} + 343311916045 q^{6} + 9887556005000 q^{7} - 3578006280975 q^{8} + 18\!\cdots\!20 q^{9}+ \cdots + 62\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q + 25575 * q^2 - 2760800 * q^3 + 10269794805 * q^4 + 343311916045 * q^6 + 9887556005000 * q^7 - 3578006280975 * q^8 + 1815779931749020 * q^9 + 7349131705193520 * q^11 + 125108909447979275 * q^12 + 297674226399950400 * q^13 + 1792715492267723010 * q^14 + 1334353718260535985 * q^16 + 9523258650276952350 * q^17 + 38495078920359601450 * q^18 + 46352372872867236000 * q^19 - 716978115331506024180 * q^21 + 1690458204465597900775 * q^22 + 631835006725227807600 * q^23 + 3814887329433293073975 * q^24 + 16428044934100377635820 * q^26 - 44922657529601683294400 * q^27 + 16025331740330522453150 * q^28 - 43862751388004829593400 * q^29 - 111398499239730790616480 * q^31 + 624015821508918585234825 * q^32 + 126250963868713519223150 * q^33 + 962162010656367444278285 * q^34 - 2512527250607526541928290 * q^36 + 5644924721128363757179300 * q^37 + 4826095859564212441518975 * q^38 + 7725309347826090604730840 * q^39 - 23954965467751578822345630 * q^41 + 52362312080978950024873350 * q^42 + 14566521950591051962026000 * q^43 + 72655345451170446851237985 * q^44 - 126418292060169078516582330 * q^46 + 324148178060325313916201400 * q^47 + 300309923927800698275303975 * q^48 + 623138091199598015722452130 * q^49 - 924948963841877288638346480 * q^51 + 1416823162531342539559652500 * q^52 + 238005597268840584357269700 * q^53 - 1295576658888572188253302625 * q^54 + 2899658525974131770370991350 * q^56 - 6226349620730017694505216050 * q^57 - 4306284916672849063070827600 * q^58 - 3033079573561674003346257600 * q^59 + 4231817029130863702119286620 * q^61 - 16098304855452311820307766850 * q^62 + 7361575042495709162746930800 * q^63 - 4758679453351220179885580495 * q^64 + 20941748361811791347567292965 * q^66 - 27305019543952980426556158400 * q^67 - 64404565186219577130468886425 * q^68 - 70710746528072109261961650660 * q^69 + 59422726898031051667669065720 * q^71 - 87856614695319178573207323450 * q^72 + 167783929989442631280479528850 * q^73 + 233886472625162831037933838410 * q^74 - 431165109277408954165767525175 * q^76 + 820800484268840888889286594500 * q^77 + 127124231267016797985074322500 * q^78 + 419830654198707399953568495400 * q^79 - 23178478329365819834057302790 * q^81 + 789038645466992754053523018275 * q^82 + 843536130899785235460491302800 * q^83 + 1533731687188227156859469497410 * q^84 - 880018109049133595082445679580 * q^86 - 2019500060946434885638438686200 * q^87 - 298284716872697736218771826075 * q^88 - 1486086045181702570536871131450 * q^89 + 7311774579005982050993260573520 * q^91 - 8592235976506062778549400808150 * q^92 - 4438442492661044963203969196100 * q^93 - 10230327657788093663700166076740 * q^94 + 6355286745483948239059480165295 * q^96 - 6882714708207174103260839260100 * q^97 + 4375208329490354177415738128475 * q^98 + 6243638896172887002986280271040 * 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 $

$2$	−50468.3	−1.08907	−0.544533	−	0.838740i	$-0.683293\pi$
$2$	−50468.3	−1.08907	−0.544533	+	0.838740i	$0.683293\pi$
$3$	−3.54185e7	−1.42512	−0.712558	−	0.701613i	$-0.752464\pi$
$3$	−3.54185e7	−1.42512	−0.712558	+	0.701613i	$0.752464\pi$
$4$	3.99569e8	0.186064
$5$	0	0
$5$	0	0
$6$	1.78751e12	1.55205
$7$	−7.37897e12	−0.587457	−0.293729	−	0.955889i	$-0.594896\pi$
$7$	−7.37897e12	−0.587457	−0.293729	+	0.955889i	$0.594896\pi$
$8$	8.82143e13	0.886430
$9$	6.36795e14	1.03096
$10$	0	0
$11$	−2.56911e16	−1.85437	−0.927183	−	0.374609i	$-0.877777\pi$
$11$	−2.56911e16	−1.85437	−0.927183	+	0.374609i	$0.877777\pi$
$12$	−1.41521e16	−0.265163
$13$	−1.59954e17	−0.866708	−0.433354	−	0.901224i	$-0.642670\pi$
$13$	−1.59954e17	−0.866708	−0.433354	+	0.901224i	$0.642670\pi$
$14$	3.72404e17	0.639780
$15$	0	0
$16$	−5.31010e18	−1.15144
$17$	5.12967e18	0.434642	0.217321	−	0.976100i	$-0.430268\pi$
$17$	5.12967e18	0.434642	0.217321	+	0.976100i	$0.430268\pi$
$18$	−3.21380e19	−1.12278
$19$	6.46616e19	0.977160	0.488580	−	0.872519i	$-0.337515\pi$
$19$	6.46616e19	0.977160	0.488580	+	0.872519i	$0.337515\pi$
$20$	0	0
$21$	2.61352e20	0.837195
$22$	1.29658e21	2.01953
$23$	1.49288e21	1.16747	0.583734	−	0.811945i	$-0.301591\pi$
$23$	1.49288e21	1.16747	0.583734	+	0.811945i	$0.301591\pi$
$24$	−3.12442e21	−1.26327
$25$	0	0
$26$	8.07260e21	0.943901
$27$	−6.77267e20	−0.0441186
$28$	−2.94841e21	−0.109304
$29$	−5.23737e22	−1.12705	−0.563527	−	0.826098i	$-0.690556\pi$
$29$	−5.23737e22	−1.12705	−0.563527	+	0.826098i	$0.690556\pi$
$30$	0	0
$31$	2.77195e22	0.212168	0.106084	−	0.994357i	$-0.466169\pi$
$31$	2.77195e22	0.212168	0.106084	+	0.994357i	$0.466169\pi$
$32$	7.85529e22	0.367568
$33$	9.09938e23	2.64269
$34$	−2.58886e23	−0.473353
$35$	0	0
$36$	2.54443e23	0.191824
$37$	6.74592e23	0.332594	0.166297	−	0.986076i	$-0.446819\pi$
$37$	6.74592e23	0.332594	0.166297	+	0.986076i	$0.446819\pi$
$38$	−3.26336e24	−1.06419
$39$	5.66532e24	1.23516
$40$	0	0
$41$	−6.66926e24	−0.669773	−0.334887	−	0.942258i	$-0.608698\pi$
$41$	−6.66926e24	−0.669773	−0.334887	+	0.942258i	$0.608698\pi$
$42$	−1.31900e25	−0.911761
$43$	−2.14950e25	−1.03175	−0.515876	−	0.856663i	$-0.672534\pi$
$43$	−2.14950e25	−1.03175	−0.515876	+	0.856663i	$0.672534\pi$
$44$	−1.02653e25	−0.345030
$45$	0	0
$46$	−7.53434e25	−1.27145
$47$	1.75727e25	0.212482	0.106241	−	0.994340i	$-0.466118\pi$
$47$	1.75727e25	0.212482	0.106241	+	0.994340i	$0.466118\pi$
$48$	1.88076e26	1.64094
$49$	−1.03326e26	−0.654894
$50$	0	0
$51$	−1.81685e26	−0.619415
$52$	−6.39125e25	−0.161263
$53$	3.62828e26	0.681436	0.340718	−	0.940166i	$-0.389330\pi$
$53$	3.62828e26	0.681436	0.340718	+	0.940166i	$0.389330\pi$
$54$	3.41806e25	0.0480481
$55$	0	0
$56$	−6.50931e26	−0.520740
$57$	−2.29022e27	−1.39257
$58$	2.64322e27	1.22744
$59$	−4.99188e27	−1.77852	−0.889258	−	0.457407i	$-0.848778\pi$
$59$	−4.99188e27	−1.77852	−0.889258	+	0.457407i	$0.848778\pi$
$60$	0	0
$61$	−7.77843e27	−1.65302	−0.826512	−	0.562918i	$-0.809679\pi$
$61$	−7.77843e27	−1.65302	−0.826512	+	0.562918i	$0.809679\pi$
$62$	−1.39896e27	−0.231064
$63$	−4.69890e27	−0.605644
$64$	7.43891e27	0.751138
$65$	0	0
$66$	−4.59231e28	−2.87806
$67$	−2.47542e28	−1.22883	−0.614413	−	0.788985i	$-0.710607\pi$
$67$	−2.47542e28	−1.22883	−0.614413	+	0.788985i	$0.710607\pi$
$68$	2.04966e27	0.0808710
$69$	−5.28757e28	−1.66378
$70$	0	0
$71$	8.55888e28	1.72947	0.864734	−	0.502229i	$-0.167487\pi$
$71$	8.55888e28	1.72947	0.864734	+	0.502229i	$0.167487\pi$
$72$	5.61745e28	0.913872
$73$	7.99777e28	1.05067	0.525333	−	0.850897i	$-0.323941\pi$
$73$	7.99777e28	1.05067	0.525333	+	0.850897i	$0.323941\pi$
$74$	−3.40455e28	−0.362217
$75$	0	0
$76$	2.58368e28	0.181814
$77$	1.89574e29	1.08936
$78$	−2.85919e29	−1.34517
$79$	−1.78848e29	−0.690661	−0.345330	−	0.938481i	$-0.612233\pi$
$79$	−1.78848e29	−0.690661	−0.345330	+	0.938481i	$0.612233\pi$
$80$	0	0
$81$	−3.69344e29	−0.968084
$82$	3.36586e29	0.729427
$83$	−8.73583e29	−1.56889	−0.784447	−	0.620196i	$-0.787053\pi$
$83$	−8.73583e29	−1.56889	−0.784447	+	0.620196i	$0.787053\pi$
$84$	1.04428e29	0.155772
$85$	0	0
$86$	1.08481e30	1.12365
$87$	1.85500e30	1.60618
$88$	−2.26632e30	−1.64377
$89$	−2.53778e30	−1.54493	−0.772464	−	0.635058i	$-0.780976\pi$
$89$	−2.53778e30	−1.54493	−0.772464	+	0.635058i	$0.780976\pi$
$90$	0	0
$91$	1.18029e30	0.509154
$92$	5.96510e29	0.217223
$93$	−9.81782e29	−0.302364
$94$	−8.86867e29	−0.231407
$95$	0	0
$96$	−2.78223e30	−0.523827
$97$	2.82605e30	0.453125	0.226563	−	0.973997i	$-0.427251\pi$
$97$	2.82605e30	0.453125	0.226563	+	0.973997i	$0.427251\pi$
$98$	5.21470e30	0.713222
$99$	−1.63599e31	−1.91177
$100$	0	0
$101$	−1.71242e31	−1.46767	−0.733834	−	0.679328i	$-0.762271\pi$
$101$	−1.71242e31	−1.46767	−0.733834	+	0.679328i	$0.762271\pi$
$102$	9.16935e30	0.674583
$103$	−1.58163e30	−0.100029	−0.0500146	−	0.998748i	$-0.515927\pi$
$103$	−1.58163e30	−0.100029	−0.0500146	+	0.998748i	$0.515927\pi$
$104$	−1.41102e31	−0.768276
$105$	0	0
$106$	−1.83113e31	−0.742128
$107$	−5.00191e31	−1.75262	−0.876310	−	0.481748i	$-0.840002\pi$
$107$	−5.00191e31	−1.75262	−0.876310	+	0.481748i	$0.840002\pi$
$108$	−2.70615e29	−0.00820887
$109$	−5.02620e30	−0.132169	−0.0660844	−	0.997814i	$-0.521051\pi$
$109$	−5.02620e30	−0.132169	−0.0660844	+	0.997814i	$0.521051\pi$
$110$	0	0
$111$	−2.38930e31	−0.473986
$112$	3.91831e31	0.676424
$113$	−4.36896e31	−0.657146	−0.328573	−	0.944479i	$-0.606568\pi$
$113$	−4.36896e31	−0.657146	−0.328573	+	0.944479i	$0.606568\pi$
$114$	1.15583e32	1.51660
$115$	0	0
$116$	−2.09269e31	−0.209704
$117$	−1.01858e32	−0.893539
$118$	2.51932e32	1.93692
$119$	−3.78517e31	−0.255333
$120$	0	0
$121$	4.68087e32	2.43867
$122$	3.92564e32	1.80025
$123$	2.36215e32	0.954505
$124$	1.10758e31	0.0394767
$125$	0	0
$126$	2.37145e32	0.659586
$127$	−7.87167e32	−1.93691	−0.968454	−	0.249191i	$-0.919835\pi$
$127$	−7.87167e32	−1.93691	−0.968454	+	0.249191i	$0.919835\pi$
$128$	−5.44121e32	−1.18561
$129$	7.61319e32	1.47037
$130$	0	0
$131$	4.96406e32	0.755322	0.377661	−	0.925944i	$-0.376728\pi$
$131$	4.96406e32	0.755322	0.377661	+	0.925944i	$0.376728\pi$
$132$	3.63583e32	0.491708
$133$	−4.77136e32	−0.574040
$134$	1.24931e33	1.33827
$135$	0	0
$136$	4.52511e32	0.385279
$137$	1.28980e33	0.980291	0.490146	−	0.871640i	$-0.336944\pi$
$137$	1.28980e33	0.980291	0.490146	+	0.871640i	$0.336944\pi$
$138$	2.66855e33	1.81196
$139$	−1.17433e33	−0.712952	−0.356476	−	0.934304i	$-0.616022\pi$
$139$	−1.17433e33	−0.712952	−0.356476	+	0.934304i	$0.616022\pi$
$140$	0	0
$141$	−6.22400e32	−0.302812
$142$	−4.31953e33	−1.88350
$143$	4.10938e33	1.60719
$144$	−3.38145e33	−1.18709
$145$	0	0
$146$	−4.03634e33	−1.14424
$147$	3.65965e33	0.933300
$148$	2.69546e32	0.0618837
$149$	−6.31685e33	−1.30651	−0.653256	−	0.757137i	$-0.726597\pi$
$149$	−6.31685e33	−1.30651	−0.653256	+	0.757137i	$0.726597\pi$
$150$	0	0
$151$	3.39621e33	0.571283	0.285642	−	0.958336i	$-0.407793\pi$
$151$	3.39621e33	0.571283	0.285642	+	0.958336i	$0.407793\pi$
$152$	5.70408e33	0.866184
$153$	3.26655e33	0.448097
$154$	−9.56746e33	−1.18639
$155$	0	0
$156$	2.26368e33	0.229818
$157$	1.12435e33	0.103385	0.0516925	−	0.998663i	$-0.483538\pi$
$157$	1.12435e33	0.103385	0.0516925	+	0.998663i	$0.483538\pi$
$158$	9.02617e33	0.752175
$159$	−1.28508e34	−0.971126
$160$	0	0
$161$	−1.10160e34	−0.685837
$162$	1.86402e34	1.05431
$163$	−1.80084e34	−0.925907	−0.462954	−	0.886383i	$-0.653210\pi$
$163$	−1.80084e34	−0.925907	−0.462954	+	0.886383i	$0.653210\pi$
$164$	−2.66483e33	−0.124620
$165$	0	0
$166$	4.40883e34	1.70863
$167$	1.75097e34	0.618262	0.309131	−	0.951019i	$-0.399962\pi$
$167$	1.75097e34	0.618262	0.309131	+	0.951019i	$0.399962\pi$
$168$	2.30550e34	0.742115
$169$	−8.47473e33	−0.248818
$170$	0	0
$171$	4.11762e34	1.00741
$172$	−8.58871e33	−0.191972
$173$	2.82466e34	0.577101	0.288550	−	0.957465i	$-0.406827\pi$
$173$	2.82466e34	0.577101	0.288550	+	0.957465i	$0.406827\pi$
$174$	−9.36187e34	−1.74924
$175$	0	0
$176$	1.36422e35	2.13520
$177$	1.76805e35	2.53459
$178$	1.28077e35	1.68253
$179$	−1.63675e34	−0.197134	−0.0985668	−	0.995130i	$-0.531426\pi$
$179$	−1.63675e34	−0.197134	−0.0985668	+	0.995130i	$0.531426\pi$
$180$	0	0
$181$	4.55817e33	0.0462139	0.0231069	−	0.999733i	$-0.492644\pi$
$181$	4.55817e33	0.0462139	0.0231069	+	0.999733i	$0.492644\pi$
$182$	−5.95675e34	−0.554502
$183$	2.75500e35	2.35575
$184$	1.31694e35	1.03488
$185$	0	0
$186$	4.95489e34	0.329294
$187$	−1.31787e35	−0.805984
$188$	7.02152e33	0.0395352
$189$	4.99754e33	0.0259178
$190$	0	0
$191$	−1.84946e35	−0.814755	−0.407377	−	0.913260i	$-0.633557\pi$
$191$	−1.84946e35	−0.814755	−0.407377	+	0.913260i	$0.633557\pi$
$192$	−2.63475e35	−1.07046
$193$	3.01732e35	1.13105	0.565527	−	0.824730i	$-0.308673\pi$
$193$	3.01732e35	1.13105	0.565527	+	0.824730i	$0.308673\pi$
$194$	−1.42626e35	−0.493483
$195$	0	0
$196$	−4.12859e34	−0.121852
$197$	−3.75808e35	−1.02504	−0.512519	−	0.858676i	$-0.671288\pi$
$197$	−3.75808e35	−1.02504	−0.512519	+	0.858676i	$0.671288\pi$
$198$	8.25659e35	2.08205
$199$	−2.95593e35	−0.689401	−0.344700	−	0.938713i	$-0.612020\pi$
$199$	−2.95593e35	−0.689401	−0.344700	+	0.938713i	$0.612020\pi$
$200$	0	0
$201$	8.76758e35	1.75122
$202$	8.64228e35	1.59839
$203$	3.86464e35	0.662096
$204$	−7.25957e34	−0.115251
$205$	0	0
$206$	7.98220e34	0.108938
$207$	9.50662e35	1.20361
$208$	8.49370e35	0.997965
$209$	−1.66123e36	−1.81201
$210$	0	0
$211$	8.80125e35	0.828259	0.414129	−	0.910218i	$-0.364086\pi$
$211$	8.80125e35	0.828259	0.414129	+	0.910218i	$0.364086\pi$
$212$	1.44975e35	0.126790
$213$	−3.03143e36	−2.46470
$214$	2.52438e36	1.90872
$215$	0	0
$216$	−5.97447e34	−0.0391081
$217$	−2.04541e35	−0.124639
$218$	2.53664e35	0.143940
$219$	−2.83269e36	−1.49732
$220$	0	0
$221$	−8.20510e35	−0.376707
$222$	1.20584e36	0.516201
$223$	−1.84633e36	−0.737196	−0.368598	−	0.929589i	$-0.620162\pi$
$223$	−1.84633e36	−0.737196	−0.368598	+	0.929589i	$0.620162\pi$
$224$	−5.79640e35	−0.215931
$225$	0	0
$226$	2.20494e36	0.715675
$227$	3.93136e36	1.19163	0.595816	−	0.803121i	$-0.296829\pi$
$227$	3.93136e36	1.19163	0.595816	+	0.803121i	$0.296829\pi$
$228$	−9.15099e35	−0.259106
$229$	1.69716e35	0.0449028	0.0224514	−	0.999748i	$-0.492853\pi$
$229$	1.69716e35	0.0449028	0.0224514	+	0.999748i	$0.492853\pi$
$230$	0	0
$231$	−6.71441e36	−1.55247
$232$	−4.62012e36	−0.999054
$233$	−7.56158e36	−1.52966	−0.764831	−	0.644231i	$-0.777178\pi$
$233$	−7.56158e36	−1.52966	−0.764831	+	0.644231i	$0.777178\pi$
$234$	5.14059e36	0.973122
$235$	0	0
$236$	−1.99460e36	−0.330917
$237$	6.33453e36	0.984272
$238$	1.91031e36	0.278075
$239$	−9.22168e36	−1.25789	−0.628945	−	0.777450i	$-0.716513\pi$
$239$	−9.22168e36	−1.25789	−0.628945	+	0.777450i	$0.716513\pi$
$240$	0	0
$241$	−4.75610e36	−0.570147	−0.285073	−	0.958506i	$-0.592018\pi$
$241$	−4.75610e36	−0.570147	−0.285073	+	0.958506i	$0.592018\pi$
$242$	−2.36236e37	−2.65587
$243$	1.34999e37	1.42375
$244$	−3.10802e36	−0.307568
$245$	0	0
$246$	−1.19214e37	−1.03952
$247$	−1.03429e37	−0.846912
$248$	2.44526e36	0.188072
$249$	3.09410e37	2.23586
$250$	0	0
$251$	−6.37631e36	−0.407030	−0.203515	−	0.979072i	$-0.565237\pi$
$251$	−6.37631e36	−0.407030	−0.203515	+	0.979072i	$0.565237\pi$
$252$	−1.87753e36	−0.112688
$253$	−3.83538e37	−2.16491
$254$	3.97270e37	2.10942
$255$	0	0
$256$	1.14859e37	0.540065
$257$	−1.08857e37	−0.481831	−0.240915	−	0.970546i	$-0.577448\pi$
$257$	−1.08857e37	−0.481831	−0.240915	+	0.970546i	$0.577448\pi$
$258$	−3.84225e37	−1.60133
$259$	−4.97780e36	−0.195385
$260$	0	0
$261$	−3.33514e37	−1.16194
$262$	−2.50528e37	−0.822596
$263$	6.84363e36	0.211823	0.105911	−	0.994376i	$-0.466224\pi$
$263$	6.84363e36	0.211823	0.105911	+	0.994376i	$0.466224\pi$
$264$	8.02696e37	2.34256
$265$	0	0
$266$	2.40803e37	0.625167
$267$	8.98842e37	2.20170
$268$	−9.89102e36	−0.228640
$269$	−3.81449e37	−0.832293	−0.416147	−	0.909297i	$-0.636620\pi$
$269$	−3.81449e37	−0.832293	−0.416147	+	0.909297i	$0.636620\pi$
$270$	0	0
$271$	9.16564e37	1.78295	0.891474	−	0.453072i	$-0.149672\pi$
$271$	9.16564e37	1.78295	0.891474	+	0.453072i	$0.149672\pi$
$272$	−2.72391e37	−0.500465
$273$	−4.18042e37	−0.725603
$274$	−6.50943e37	−1.06760
$275$	0	0
$276$	−2.11275e37	−0.309568
$277$	−5.62673e37	−0.779507	−0.389753	−	0.920919i	$-0.627440\pi$
$277$	−5.62673e37	−0.779507	−0.389753	+	0.920919i	$0.627440\pi$
$278$	5.92664e37	0.776451
$279$	1.76516e37	0.218736
$280$	0	0
$281$	−4.25587e37	−0.472107	−0.236053	−	0.971740i	$-0.575854\pi$
$281$	−4.25587e37	−0.472107	−0.236053	+	0.971740i	$0.575854\pi$
$282$	3.14115e37	0.329782
$283$	−1.21210e38	−1.20461	−0.602306	−	0.798266i	$-0.705751\pi$
$283$	−1.21210e38	−1.20461	−0.602306	+	0.798266i	$0.705751\pi$
$284$	3.41986e37	0.321791
$285$	0	0
$286$	−2.07394e38	−1.75034
$287$	4.92123e37	0.393463
$288$	5.00221e37	0.378947
$289$	−1.12975e38	−0.811087
$290$	0	0
$291$	−1.00094e38	−0.645756
$292$	3.19566e37	0.195491
$293$	−2.43751e38	−1.41416	−0.707080	−	0.707134i	$-0.749988\pi$
$293$	−2.43751e38	−1.41416	−0.707080	+	0.707134i	$0.749988\pi$
$294$	−1.84697e38	−1.01643
$295$	0	0
$296$	5.95087e37	0.294821
$297$	1.73997e37	0.0818120
$298$	3.18801e38	1.42288
$299$	−2.38792e38	−1.01185
$300$	0	0
$301$	1.58611e38	0.606111
$302$	−1.71401e38	−0.622165
$303$	6.06512e38	2.09160
$304$	−3.43360e38	−1.12515
$305$	0	0
$306$	−1.64857e38	−0.488007
$307$	2.30206e38	0.647845	0.323922	−	0.946084i	$-0.394998\pi$
$307$	2.30206e38	0.647845	0.323922	+	0.946084i	$0.394998\pi$
$308$	7.57477e37	0.202690
$309$	5.60188e37	0.142553
$310$	0	0
$311$	6.45531e38	1.48638	0.743192	−	0.669078i	$-0.233311\pi$
$311$	6.45531e38	1.48638	0.743192	+	0.669078i	$0.233311\pi$
$312$	4.99763e38	1.09488
$313$	2.25998e38	0.471159	0.235580	−	0.971855i	$-0.424301\pi$
$313$	2.25998e38	0.471159	0.235580	+	0.971855i	$0.424301\pi$
$314$	−5.67441e37	−0.112593
$315$	0	0
$316$	−7.14622e37	−0.128507
$317$	−3.33447e38	−0.570964	−0.285482	−	0.958384i	$-0.592154\pi$
$317$	−3.33447e38	−0.570964	−0.285482	+	0.958384i	$0.592154\pi$
$318$	6.48560e38	1.05762
$319$	1.34554e39	2.08997
$320$	0	0
$321$	1.77160e39	2.49769
$322$	5.55957e38	0.746922
$323$	3.31693e38	0.424714
$324$	−1.47578e38	−0.180125
$325$	0	0
$326$	9.08854e38	1.00837
$327$	1.78020e38	0.188356
$328$	−5.88324e38	−0.593707
$329$	−1.29669e38	−0.124824
$330$	0	0
$331$	5.21055e38	0.456614	0.228307	−	0.973589i	$-0.426681\pi$
$331$	5.21055e38	0.456614	0.228307	+	0.973589i	$0.426681\pi$
$332$	−3.49056e38	−0.291914
$333$	4.29577e38	0.342891
$334$	−8.83684e38	−0.673328
$335$	0	0
$336$	−1.38780e39	−0.963984
$337$	−1.07632e39	−0.713968	−0.356984	−	0.934110i	$-0.616195\pi$
$337$	−1.07632e39	−0.713968	−0.356984	+	0.934110i	$0.616195\pi$
$338$	4.27705e38	0.270979
$339$	1.54742e39	0.936510
$340$	0	0
$341$	−7.12143e38	−0.393436
$342$	−2.07810e39	−1.09714
$343$	1.92666e39	0.972180
$344$	−1.89616e39	−0.914576
$345$	0	0
$346$	−1.42556e39	−0.628500
$347$	4.50521e39	1.89937	0.949683	−	0.313213i	$-0.101405\pi$
$347$	4.50521e39	1.89937	0.949683	+	0.313213i	$0.101405\pi$
$348$	7.41199e38	0.298852
$349$	1.00452e39	0.387405	0.193703	−	0.981060i	$-0.437950\pi$
$349$	1.00452e39	0.387405	0.193703	+	0.981060i	$0.437950\pi$
$350$	0	0
$351$	1.08331e38	0.0382379
$352$	−2.01811e39	−0.681605
$353$	2.32272e39	0.750738	0.375369	−	0.926876i	$-0.377516\pi$
$353$	2.32272e39	0.750738	0.375369	+	0.926876i	$0.377516\pi$
$354$	−8.92304e39	−2.76034
$355$	0	0
$356$	−1.01402e39	−0.287455
$357$	1.34065e39	0.363880
$358$	8.26041e38	0.214691
$359$	7.12748e39	1.77408	0.887038	−	0.461696i	$-0.152759\pi$
$359$	7.12748e39	1.77408	0.887038	+	0.461696i	$0.152759\pi$
$360$	0	0
$361$	−1.97739e38	−0.0451576
$362$	−2.30043e38	−0.0503299
$363$	−1.65789e40	−3.47539
$364$	4.71609e38	0.0947350
$365$	0	0
$366$	−1.39040e40	−2.56557
$367$	−5.20594e39	−0.920821	−0.460411	−	0.887706i	$-0.652298\pi$
$367$	−5.20594e39	−0.920821	−0.460411	+	0.887706i	$0.652298\pi$
$368$	−7.92736e39	−1.34427
$369$	−4.24695e39	−0.690508
$370$	0	0
$371$	−2.67730e39	−0.400315
$372$	−3.92289e38	−0.0562589
$373$	−8.13982e39	−1.11977	−0.559884	−	0.828571i	$-0.689154\pi$
$373$	−8.13982e39	−1.11977	−0.559884	+	0.828571i	$0.689154\pi$
$374$	6.65105e39	0.877770
$375$	0	0
$376$	1.55017e39	0.188351
$377$	8.37738e39	0.976826
$378$	−2.52217e38	−0.0282262
$379$	−5.97264e38	−0.0641592	−0.0320796	−	0.999485i	$-0.510213\pi$
$379$	−5.97264e38	−0.0641592	−0.0320796	+	0.999485i	$0.510213\pi$
$380$	0	0
$381$	2.78803e40	2.76032
$382$	9.33390e39	0.887322
$383$	2.19654e39	0.200520	0.100260	−	0.994961i	$-0.468032\pi$
$383$	2.19654e39	0.200520	0.100260	+	0.994961i	$0.468032\pi$
$384$	1.92719e40	1.68963
$385$	0	0
$386$	−1.52279e40	−1.23179
$387$	−1.36879e40	−1.06369
$388$	1.12920e39	0.0843101
$389$	−7.52607e39	−0.539945	−0.269973	−	0.962868i	$-0.587015\pi$
$389$	−7.52607e39	−0.539945	−0.269973	+	0.962868i	$0.587015\pi$
$390$	0	0
$391$	7.65800e39	0.507430
$392$	−9.11485e39	−0.580518
$393$	−1.75820e40	−1.07642
$394$	1.89664e40	1.11633
$395$	0	0
$396$	−6.53692e39	−0.355712
$397$	9.21070e39	0.481992	0.240996	−	0.970526i	$-0.422526\pi$
$397$	9.21070e39	0.481992	0.240996	+	0.970526i	$0.422526\pi$
$398$	1.49181e40	0.750803
$399$	1.68994e40	0.818074
$400$	0	0
$401$	3.82642e39	0.171417	0.0857087	−	0.996320i	$-0.472685\pi$
$401$	3.82642e39	0.171417	0.0857087	+	0.996320i	$0.472685\pi$
$402$	−4.42485e40	−1.90719
$403$	−4.43384e39	−0.183887
$404$	−6.84228e39	−0.273080
$405$	0	0
$406$	−1.95042e40	−0.721066
$407$	−1.73310e40	−0.616751
$408$	−1.60272e40	−0.549068
$409$	3.63528e40	1.19902	0.599510	−	0.800367i	$-0.295362\pi$
$409$	3.63528e40	1.19902	0.599510	+	0.800367i	$0.295362\pi$
$410$	0	0
$411$	−4.56829e40	−1.39703
$412$	−6.31968e38	−0.0186118
$413$	3.68349e40	1.04480
$414$	−4.79783e40	−1.31081
$415$	0	0
$416$	−1.25648e40	−0.318574
$417$	4.15929e40	1.01604
$418$	8.38393e40	1.97340
$419$	9.79817e38	0.0222243	0.0111121	−	0.999938i	$-0.496463\pi$
$419$	9.79817e38	0.0222243	0.0111121	+	0.999938i	$0.496463\pi$
$420$	0	0
$421$	−5.79926e40	−1.22180	−0.610900	−	0.791708i	$-0.709192\pi$
$421$	−5.79926e40	−1.22180	−0.610900	+	0.791708i	$0.709192\pi$
$422$	−4.44184e40	−0.902028
$423$	1.11902e40	0.219060
$424$	3.20067e40	0.604045
$425$	0	0
$426$	1.52991e41	2.68421
$427$	5.73968e40	0.971082
$428$	−1.99861e40	−0.326099
$429$	−1.45548e41	−2.29044
$430$	0	0
$431$	1.23157e41	1.80327	0.901633	−	0.432502i	$-0.142369\pi$
$431$	1.23157e41	1.80327	0.901633	+	0.432502i	$0.142369\pi$
$432$	3.59636e39	0.0508001
$433$	−1.08651e41	−1.48072	−0.740360	−	0.672211i	$-0.765345\pi$
$433$	−1.08651e41	−1.48072	−0.740360	+	0.672211i	$0.765345\pi$
$434$	1.03229e40	0.135740
$435$	0	0
$436$	−2.00831e39	−0.0245918
$437$	9.65323e40	1.14080
$438$	1.42961e41	1.63068
$439$	−1.31452e41	−1.44732	−0.723662	−	0.690154i	$-0.757543\pi$
$439$	−1.31452e41	−1.44732	−0.723662	+	0.690154i	$0.757543\pi$
$440$	0	0
$441$	−6.57976e40	−0.675168
$442$	4.14098e40	0.410259
$443$	7.34404e40	0.702550	0.351275	−	0.936272i	$-0.385748\pi$
$443$	7.34404e40	0.702550	0.351275	+	0.936272i	$0.385748\pi$
$444$	−9.54691e39	−0.0881915
$445$	0	0
$446$	9.31810e40	0.802855
$447$	2.23733e41	1.86193
$448$	−5.48915e40	−0.441262
$449$	8.88276e39	0.0689810	0.0344905	−	0.999405i	$-0.489019\pi$
$449$	8.88276e39	0.0689810	0.0344905	+	0.999405i	$0.489019\pi$
$450$	0	0
$451$	1.71340e41	1.24200
$452$	−1.74570e40	−0.122271
$453$	−1.20289e41	−0.814146
$454$	−1.98409e41	−1.29776
$455$	0	0
$456$	−2.02030e41	−1.23441
$457$	−1.73624e41	−1.02544	−0.512719	−	0.858556i	$-0.671362\pi$
$457$	−1.73624e41	−1.02544	−0.512719	+	0.858556i	$0.671362\pi$
$458$	−8.56530e39	−0.0489021
$459$	−3.47416e39	−0.0191758
$460$	0	0
$461$	−1.69460e41	−0.874384	−0.437192	−	0.899368i	$-0.644027\pi$
$461$	−1.69460e41	−0.874384	−0.437192	+	0.899368i	$0.644027\pi$
$462$	3.38865e41	1.69074
$463$	1.59616e41	0.770141	0.385070	−	0.922887i	$-0.374177\pi$
$463$	1.59616e41	0.770141	0.385070	+	0.922887i	$0.374177\pi$
$464$	2.78110e41	1.29774
$465$	0	0
$466$	3.81620e41	1.66590
$467$	−3.56199e41	−1.50411	−0.752057	−	0.659098i	$-0.770938\pi$
$467$	−3.56199e41	−1.50411	−0.752057	+	0.659098i	$0.770938\pi$
$468$	−4.06992e40	−0.166255
$469$	1.82661e41	0.721883
$470$	0	0
$471$	−3.98228e40	−0.147336
$472$	−4.40355e41	−1.57653
$473$	5.52228e41	1.91325
$474$	−3.19693e41	−1.07194
$475$	0	0
$476$	−1.51244e40	−0.0475083
$477$	2.31047e41	0.702532
$478$	4.65403e41	1.36992
$479$	−2.77088e41	−0.789619	−0.394809	−	0.918763i	$-0.629189\pi$
$479$	−2.77088e41	−0.789619	−0.394809	+	0.918763i	$0.629189\pi$
$480$	0	0
$481$	−1.07904e41	−0.288262
$482$	2.40032e41	0.620927
$483$	3.90168e41	0.977398
$484$	1.87033e41	0.453748
$485$	0	0
$486$	−6.81319e41	−1.55056
$487$	−8.87356e41	−1.95614	−0.978068	−	0.208285i	$-0.933212\pi$
$487$	−8.87356e41	−1.95614	−0.978068	+	0.208285i	$0.933212\pi$
$488$	−6.86169e41	−1.46529
$489$	6.37830e41	1.31953
$490$	0	0
$491$	1.02124e41	0.198319	0.0991596	−	0.995072i	$-0.468385\pi$
$491$	1.02124e41	0.198319	0.0991596	+	0.995072i	$0.468385\pi$
$492$	9.43841e40	0.177599
$493$	−2.68660e41	−0.489864
$494$	5.21988e41	0.922343
$495$	0	0
$496$	−1.47193e41	−0.244299
$497$	−6.31558e41	−1.01599
$498$	−1.56154e42	−2.43499
$499$	1.15532e42	1.74640	0.873202	−	0.487359i	$-0.162040\pi$
$499$	1.15532e42	1.74640	0.873202	+	0.487359i	$0.162040\pi$
$500$	0	0
$501$	−6.20166e41	−0.881096
$502$	3.21802e41	0.443282
$503$	−8.98250e41	−1.19976	−0.599878	−	0.800091i	$-0.704784\pi$
$503$	−8.98250e41	−1.19976	−0.599878	+	0.800091i	$0.704784\pi$
$504$	−4.14510e41	−0.536861
$505$	0	0
$506$	1.93565e42	2.35773
$507$	3.00162e41	0.354595
$508$	−3.14527e41	−0.360388
$509$	−2.04179e41	−0.226927	−0.113463	−	0.993542i	$-0.536194\pi$
$509$	−2.04179e41	−0.226927	−0.113463	+	0.993542i	$0.536194\pi$
$510$	0	0
$511$	−5.90153e41	−0.617221
$512$	5.88815e41	0.597440
$513$	−4.37932e40	−0.0431110
$514$	5.49385e41	0.524745
$515$	0	0
$516$	3.04199e41	0.273582
$517$	−4.51462e41	−0.394020
$518$	2.51221e41	0.212787
$519$	−1.00045e42	−0.822436
$520$	0	0
$521$	−4.50719e41	−0.349077	−0.174538	−	0.984650i	$-0.555843\pi$
$521$	−4.50719e41	−0.349077	−0.174538	+	0.984650i	$0.555843\pi$
$522$	1.68319e42	1.26543
$523$	3.50199e41	0.255587	0.127794	−	0.991801i	$-0.459210\pi$
$523$	3.50199e41	0.255587	0.127794	+	0.991801i	$0.459210\pi$
$524$	1.98349e41	0.140538
$525$	0	0
$526$	−3.45387e41	−0.230689
$527$	1.42192e41	0.0922168
$528$	−4.83186e42	−3.04291
$529$	5.93533e41	0.362979
$530$	0	0
$531$	−3.17880e42	−1.83357
$532$	−1.90649e41	−0.106808
$533$	1.06677e42	0.580498
$534$	−4.53631e42	−2.39780
$535$	0	0
$536$	−2.18368e42	−1.08927
$537$	5.79712e41	0.280938
$538$	1.92511e42	0.906422
$539$	2.65456e42	1.21441
$540$	0	0
$541$	1.03013e42	0.444974	0.222487	−	0.974936i	$-0.428583\pi$
$541$	1.03013e42	0.444974	0.222487	+	0.974936i	$0.428583\pi$
$542$	−4.62574e42	−1.94175
$543$	−1.61443e41	−0.0658601
$544$	4.02951e41	0.159760
$545$	0	0
$546$	2.10979e42	0.790230
$547$	2.42722e42	0.883701	0.441851	−	0.897089i	$-0.354322\pi$
$547$	2.42722e42	0.883701	0.441851	+	0.897089i	$0.354322\pi$
$548$	5.15366e41	0.182397
$549$	−4.95327e42	−1.70420
$550$	0	0
$551$	−3.38657e42	−1.10131
$552$	−4.66439e42	−1.47482
$553$	1.31972e42	0.405734
$554$	2.83972e42	0.848934
$555$	0	0
$556$	−4.69225e41	−0.132654
$557$	8.00704e41	0.220149	0.110074	−	0.993923i	$-0.464891\pi$
$557$	8.00704e41	0.220149	0.110074	+	0.993923i	$0.464891\pi$
$558$	−8.90849e41	−0.238218
$559$	3.43820e42	0.894228
$560$	0	0
$561$	4.66768e42	1.14862
$562$	2.14787e42	0.514155
$563$	5.81315e42	1.35373	0.676864	−	0.736108i	$-0.263339\pi$
$563$	5.81315e42	1.35373	0.676864	+	0.736108i	$0.263339\pi$
$564$	−2.48691e41	−0.0563423
$565$	0	0
$566$	6.11724e42	1.31190
$567$	2.72538e42	0.568708
$568$	7.55016e42	1.53305
$569$	3.55543e42	0.702510	0.351255	−	0.936280i	$-0.385755\pi$
$569$	3.55543e42	0.702510	0.351255	+	0.936280i	$0.385755\pi$
$570$	0	0
$571$	−1.36185e42	−0.254840	−0.127420	−	0.991849i	$-0.540670\pi$
$571$	−1.36185e42	−0.254840	−0.127420	+	0.991849i	$0.540670\pi$
$572$	1.64198e42	0.299040
$573$	6.55049e42	1.16112
$574$	−2.48366e42	−0.428507
$575$	0	0
$576$	4.73707e42	0.774392
$577$	−3.39833e42	−0.540805	−0.270403	−	0.962747i	$-0.587157\pi$
$577$	−3.39833e42	−0.540805	−0.270403	+	0.962747i	$0.587157\pi$
$578$	5.70168e42	0.883327
$579$	−1.06869e43	−1.61188
$580$	0	0
$581$	6.44614e42	0.921658
$582$	5.05160e42	0.703271
$583$	−9.32144e42	−1.26363
$584$	7.05518e42	0.931342
$585$	0	0
$586$	1.23017e43	1.54011
$587$	6.84778e42	0.834948	0.417474	−	0.908689i	$-0.362916\pi$
$587$	6.84778e42	0.834948	0.417474	+	0.908689i	$0.362916\pi$
$588$	1.46228e42	0.173653
$589$	1.79239e42	0.207322
$590$	0	0
$591$	1.33106e43	1.46080
$592$	−3.58215e42	−0.382964
$593$	−5.19197e42	−0.540735	−0.270367	−	0.962757i	$-0.587145\pi$
$593$	−5.19197e42	−0.540735	−0.270367	+	0.962757i	$0.587145\pi$
$594$	−8.78135e41	−0.0890987
$595$	0	0
$596$	−2.52402e42	−0.243094
$597$	1.04695e43	0.982477
$598$	1.20515e43	1.10197
$599$	3.82744e42	0.341030	0.170515	−	0.985355i	$-0.445457\pi$
$599$	3.82744e42	0.341030	0.170515	+	0.985355i	$0.445457\pi$
$600$	0	0
$601$	−2.00425e43	−1.69589	−0.847944	−	0.530086i	$-0.822159\pi$
$601$	−2.00425e43	−1.69589	−0.847944	+	0.530086i	$0.822159\pi$
$602$	−8.00482e42	−0.660094
$603$	−1.57634e43	−1.26687
$604$	1.35702e42	0.106295
$605$	0	0
$606$	−3.06096e43	−2.27789
$607$	−5.42746e42	−0.393706	−0.196853	−	0.980433i	$-0.563072\pi$
$607$	−5.42746e42	−0.393706	−0.196853	+	0.980433i	$0.563072\pi$
$608$	5.07936e42	0.359173
$609$	−1.36880e43	−0.943564
$610$	0	0
$611$	−2.81083e42	−0.184160
$612$	1.30521e42	0.0833746
$613$	9.70689e42	0.604565	0.302282	−	0.953218i	$-0.402251\pi$
$613$	9.70689e42	0.604565	0.302282	+	0.953218i	$0.402251\pi$
$614$	−1.16181e43	−0.705545
$615$	0	0
$616$	1.67231e43	0.965642
$617$	2.73058e42	0.153757	0.0768786	−	0.997040i	$-0.475505\pi$
$617$	2.73058e42	0.153757	0.0768786	+	0.997040i	$0.475505\pi$
$618$	−2.82717e42	−0.155250
$619$	−2.73719e43	−1.46588	−0.732942	−	0.680291i	$-0.761853\pi$
$619$	−2.73719e43	−1.46588	−0.732942	+	0.680291i	$0.761853\pi$
$620$	0	0
$621$	−1.01108e42	−0.0515070
$622$	−3.25789e43	−1.61877
$623$	1.87262e43	0.907580
$624$	−3.00834e43	−1.42222
$625$	0	0
$626$	−1.14058e43	−0.513123
$627$	5.88381e43	2.58233
$628$	4.49256e41	0.0192362
$629$	3.46044e42	0.144559
$630$	0	0
$631$	−2.09278e43	−0.832280	−0.416140	−	0.909301i	$-0.636617\pi$
$631$	−2.09278e43	−0.832280	−0.416140	+	0.909301i	$0.636617\pi$
$632$	−1.57770e43	−0.612222
$633$	−3.11727e43	−1.18037
$634$	1.68285e43	0.621817
$635$	0	0
$636$	−5.13479e42	−0.180691
$637$	1.65274e43	0.567601
$638$	−6.79070e43	−2.27611
$639$	5.45026e43	1.78301
$640$	0	0
$641$	−8.79186e41	−0.0274019	−0.0137010	−	0.999906i	$-0.504361\pi$
$641$	−8.79186e41	−0.0274019	−0.0137010	+	0.999906i	$0.504361\pi$
$642$	−8.94098e43	−2.72015
$643$	−4.86507e42	−0.144484	−0.0722418	−	0.997387i	$-0.523015\pi$
$643$	−4.86507e42	−0.144484	−0.0722418	+	0.997387i	$0.523015\pi$
$644$	−4.40163e42	−0.127609
$645$	0	0
$646$	−1.67400e43	−0.462542
$647$	3.20540e43	0.864701	0.432351	−	0.901706i	$-0.357684\pi$
$647$	3.20540e43	0.864701	0.432351	+	0.901706i	$0.357684\pi$
$648$	−3.25814e43	−0.858138
$649$	1.28247e44	3.29802
$650$	0	0
$651$	7.24454e42	0.177626
$652$	−7.19560e42	−0.172278
$653$	−2.55276e43	−0.596838	−0.298419	−	0.954435i	$-0.596459\pi$
$653$	−2.55276e43	−0.596838	−0.298419	+	0.954435i	$0.596459\pi$
$654$	−8.98439e42	−0.205132
$655$	0	0
$656$	3.54144e43	0.771206
$657$	5.09294e43	1.08319
$658$	6.54417e42	0.135942
$659$	4.03603e43	0.818900	0.409450	−	0.912333i	$-0.365721\pi$
$659$	4.03603e43	0.818900	0.409450	+	0.912333i	$0.365721\pi$
$660$	0	0
$661$	−2.96661e43	−0.574299	−0.287149	−	0.957886i	$-0.592708\pi$
$661$	−2.96661e43	−0.574299	−0.287149	+	0.957886i	$0.592708\pi$
$662$	−2.62968e43	−0.497283
$663$	2.90612e43	0.536852
$664$	−7.70625e43	−1.39071
$665$	0	0
$666$	−2.16800e43	−0.373430
$667$	−7.81879e43	−1.31580
$668$	6.99632e42	0.115036
$669$	6.53940e43	1.05059
$670$	0	0
$671$	1.99836e44	3.06531
$672$	2.05300e43	0.307726
$673$	9.75824e42	0.142935	0.0714674	−	0.997443i	$-0.477232\pi$
$673$	9.75824e42	0.142935	0.0714674	+	0.997443i	$0.477232\pi$
$674$	5.43202e43	0.777558
$675$	0	0
$676$	−3.38624e42	−0.0462960
$677$	−5.75918e43	−0.769549	−0.384775	−	0.923011i	$-0.625721\pi$
$677$	−5.75918e43	−0.769549	−0.384775	+	0.923011i	$0.625721\pi$
$678$	−7.80956e43	−1.01992
$679$	−2.08534e43	−0.266192
$680$	0	0
$681$	−1.39243e44	−1.69821
$682$	3.59407e43	0.428478
$683$	−1.28137e42	−0.0149332	−0.00746659	−	0.999972i	$-0.502377\pi$
$683$	−1.28137e42	−0.0149332	−0.00746659	+	0.999972i	$0.502377\pi$
$684$	1.64527e43	0.187443
$685$	0	0
$686$	−9.72354e43	−1.05877
$687$	−6.01110e42	−0.0639918
$688$	1.14140e44	1.18801
$689$	−5.80357e43	−0.590606
$690$	0	0
$691$	−1.04701e44	−1.01869	−0.509344	−	0.860563i	$-0.670112\pi$
$691$	−1.04701e44	−1.01869	−0.509344	+	0.860563i	$0.670112\pi$
$692$	1.12865e43	0.107377
$693$	1.20720e44	1.12308
$694$	−2.27371e44	−2.06853
$695$	0	0
$696$	1.63637e44	1.42377
$697$	−3.42111e43	−0.291111
$698$	−5.06966e43	−0.421910
$699$	2.67820e44	2.17995
$700$	0	0
$701$	−2.97574e43	−0.231721	−0.115861	−	0.993265i	$-0.536963\pi$
$701$	−2.97574e43	−0.231721	−0.115861	+	0.993265i	$0.536963\pi$
$702$	−5.46731e42	−0.0416436
$703$	4.36202e43	0.324998
$704$	−1.91114e44	−1.39289
$705$	0	0
$706$	−1.17224e44	−0.817603
$707$	1.26359e44	0.862193
$708$	7.06456e43	0.471596
$709$	−1.24196e44	−0.811132	−0.405566	−	0.914066i	$-0.632926\pi$
$709$	−1.24196e44	−0.811132	−0.405566	+	0.914066i	$0.632926\pi$
$710$	0	0
$711$	−1.13890e44	−0.712042
$712$	−2.23868e44	−1.36947
$713$	4.13820e43	0.247699
$714$	−6.76604e43	−0.396289
$715$	0	0
$716$	−6.53994e42	−0.0366794
$717$	3.26618e44	1.79264
$718$	−3.59712e44	−1.93209
$719$	−2.70426e44	−1.42151	−0.710755	−	0.703439i	$-0.751647\pi$
$719$	−2.70426e44	−1.42151	−0.710755	+	0.703439i	$0.751647\pi$
$720$	0	0
$721$	1.16708e43	0.0587629
$722$	9.97956e42	0.0491796
$723$	1.68454e44	0.812526
$724$	1.82130e42	0.00859872
$725$	0	0
$726$	8.36711e44	3.78493
$727$	2.23994e44	0.991867	0.495934	−	0.868360i	$-0.334826\pi$
$727$	2.23994e44	0.991867	0.495934	+	0.868360i	$0.334826\pi$
$728$	1.04119e44	0.451329
$729$	−2.50013e44	−1.06093
$730$	0	0
$731$	−1.10262e44	−0.448443
$732$	1.10081e44	0.438320
$733$	3.60937e44	1.40708	0.703541	−	0.710655i	$-0.251601\pi$
$733$	3.60937e44	1.40708	0.703541	+	0.710655i	$0.251601\pi$
$734$	2.62735e44	1.00283
$735$	0	0
$736$	1.17270e44	0.429124
$737$	6.35963e44	2.27869
$738$	2.14337e44	0.752008
$739$	−1.34591e44	−0.462409	−0.231205	−	0.972905i	$-0.574267\pi$
$739$	−1.34591e44	−0.462409	−0.231205	+	0.972905i	$0.574267\pi$
$740$	0	0
$741$	3.66329e44	1.20695
$742$	1.35119e44	0.435969
$743$	−2.29970e44	−0.726682	−0.363341	−	0.931656i	$-0.618364\pi$
$743$	−2.29970e44	−0.726682	−0.363341	+	0.931656i	$0.618364\pi$
$744$	−8.66073e43	−0.268024
$745$	0	0
$746$	4.10803e44	1.21950
$747$	−5.56293e44	−1.61746
$748$	−5.26578e43	−0.149964
$749$	3.69090e44	1.02959
$750$	0	0
$751$	−6.82476e44	−1.82671	−0.913353	−	0.407169i	$-0.866516\pi$
$751$	−6.82476e44	−1.82671	−0.913353	+	0.407169i	$0.866516\pi$
$752$	−9.33130e43	−0.244661
$753$	2.25839e44	0.580065
$754$	−4.22792e44	−1.06383
$755$	0	0
$756$	1.99686e42	0.00482236
$757$	−5.83963e44	−1.38165	−0.690827	−	0.723020i	$-0.742753\pi$
$757$	−5.83963e44	−1.38165	−0.690827	+	0.723020i	$0.742753\pi$
$758$	3.01429e43	0.0698736
$759$	1.35843e45	3.08525
$760$	0	0
$761$	−4.47927e44	−0.976664	−0.488332	−	0.872658i	$-0.662394\pi$
$761$	−4.47927e44	−0.976664	−0.488332	+	0.872658i	$0.662394\pi$
$762$	−1.40707e45	−3.00617
$763$	3.70882e43	0.0776435
$764$	−7.38985e43	−0.151596
$765$	0	0
$766$	−1.10856e44	−0.218380
$767$	7.98469e44	1.54145
$768$	−4.06814e44	−0.769656
$769$	−5.08233e44	−0.942334	−0.471167	−	0.882044i	$-0.656167\pi$
$769$	−5.08233e44	−0.942334	−0.471167	+	0.882044i	$0.656167\pi$
$770$	0	0
$771$	3.85556e44	0.686665
$772$	1.20563e44	0.210448
$773$	2.24846e44	0.384682	0.192341	−	0.981328i	$-0.438392\pi$
$773$	2.24846e44	0.384682	0.192341	+	0.981328i	$0.438392\pi$
$774$	6.90805e44	1.15843
$775$	0	0
$776$	2.49298e44	0.401664
$777$	1.76306e44	0.278446
$778$	3.79828e44	0.588036
$779$	−4.31245e44	−0.654476
$780$	0	0
$781$	−2.19887e45	−3.20707
$782$	−3.86487e44	−0.552624
$783$	3.54710e43	0.0497240
$784$	5.48672e44	0.754074
$785$	0	0
$786$	8.87332e44	1.17229
$787$	1.36341e45	1.76612	0.883059	−	0.469263i	$-0.155480\pi$
$787$	1.36341e45	1.76612	0.883059	+	0.469263i	$0.155480\pi$
$788$	−1.50161e44	−0.190722
$789$	−2.42391e44	−0.301872
$790$	0	0
$791$	3.22384e44	0.386045
$792$	−1.44318e45	−1.69465
$793$	1.24419e45	1.43269
$794$	−4.64849e44	−0.524921
$795$	0	0
$796$	−1.18110e44	−0.128272
$797$	−9.47512e44	−1.00921	−0.504604	−	0.863351i	$-0.668362\pi$
$797$	−9.47512e44	−1.00921	−0.504604	+	0.863351i	$0.668362\pi$
$798$	−8.52887e44	−0.890936
$799$	9.01423e43	0.0923536
$800$	0	0
$801$	−1.61604e45	−1.59276
$802$	−1.93113e44	−0.186685
$803$	−2.05471e45	−1.94832
$804$	3.50325e44	0.325839
$805$	0	0
$806$	2.23768e44	0.200265
$807$	1.35104e45	1.18612
$808$	−1.51060e45	−1.30099
$809$	5.00741e44	0.423069	0.211535	−	0.977371i	$-0.432154\pi$
$809$	5.00741e44	0.423069	0.211535	+	0.977371i	$0.432154\pi$
$810$	0	0
$811$	−4.64497e44	−0.377711	−0.188856	−	0.982005i	$-0.560478\pi$
$811$	−4.64497e44	−0.377711	−0.188856	+	0.982005i	$0.560478\pi$
$812$	1.54419e44	0.123192
$813$	−3.24633e45	−2.54091
$814$	8.74666e44	0.671682
$815$	0	0
$816$	9.64766e44	0.713222
$817$	−1.38990e45	−1.00819
$818$	−1.83466e45	−1.30581
$819$	7.51606e44	0.524916
$820$	0	0
$821$	8.53797e44	0.574164	0.287082	−	0.957906i	$-0.407315\pi$
$821$	8.53797e44	0.574164	0.287082	+	0.957906i	$0.407315\pi$
$822$	2.30554e45	1.52146
$823$	1.45427e45	0.941779	0.470890	−	0.882192i	$-0.343933\pi$
$823$	1.45427e45	0.941779	0.470890	+	0.882192i	$0.343933\pi$
$824$	−1.39522e44	−0.0886688
$825$	0	0
$826$	−1.85900e45	−1.13786
$827$	2.09313e45	1.25736	0.628681	−	0.777663i	$-0.283595\pi$
$827$	2.09313e45	1.25736	0.628681	+	0.777663i	$0.283595\pi$
$828$	3.79855e44	0.223948
$829$	−2.58269e45	−1.49444	−0.747219	−	0.664578i	$-0.768611\pi$
$829$	−2.58269e45	−1.49444	−0.747219	+	0.664578i	$0.768611\pi$
$830$	0	0
$831$	1.99290e45	1.11089
$832$	−1.18988e45	−0.651017
$833$	−5.30029e44	−0.284644
$834$	−2.09913e45	−1.10653
$835$	0	0
$836$	−6.63774e44	−0.337150
$837$	−1.87735e43	−0.00936054
$838$	−4.94497e43	−0.0242037
$839$	1.29282e45	0.621192	0.310596	−	0.950542i	$-0.399471\pi$
$839$	1.29282e45	0.621192	0.310596	+	0.950542i	$0.399471\pi$
$840$	0	0
$841$	5.83585e44	0.270250
$842$	2.92679e45	1.33062
$843$	1.50736e45	0.672807
$844$	3.51670e44	0.154109
$845$	0	0
$846$	−5.64752e44	−0.238571
$847$	−3.45400e45	−1.43262
$848$	−1.92665e45	−0.784635
$849$	4.29306e45	1.71671
$850$	0	0
$851$	1.00709e45	0.388293
$852$	−1.21126e45	−0.458590
$853$	4.80470e45	1.78631	0.893154	−	0.449752i	$-0.148488\pi$
$853$	4.80470e45	1.78631	0.893154	+	0.449752i	$0.148488\pi$
$854$	−2.89672e45	−1.05757
$855$	0	0
$856$	−4.41241e45	−1.55357
$857$	−4.21760e44	−0.145835	−0.0729176	−	0.997338i	$-0.523231\pi$
$857$	−4.21760e44	−0.145835	−0.0729176	+	0.997338i	$0.523231\pi$
$858$	7.34557e45	2.49444
$859$	−4.58182e45	−1.52807	−0.764037	−	0.645172i	$-0.776786\pi$
$859$	−4.58182e45	−1.52807	−0.764037	+	0.645172i	$0.776786\pi$
$860$	0	0
$861$	−1.74302e45	−0.560731
$862$	−6.21550e45	−1.96387
$863$	1.31315e45	0.407518	0.203759	−	0.979021i	$-0.434684\pi$
$863$	1.31315e45	0.407518	0.203759	+	0.979021i	$0.434684\pi$
$864$	−5.32013e43	−0.0162166
$865$	0	0
$866$	5.48345e45	1.61260
$867$	4.00142e45	1.15589
$868$	−8.17283e43	−0.0231909
$869$	4.59480e45	1.28074
$870$	0	0
$871$	3.95954e45	1.06503
$872$	−4.43383e44	−0.117158
$873$	1.79962e45	0.467153
$874$	−4.87183e45	−1.24241
$875$	0	0
$876$	−1.13185e45	−0.278597
$877$	−2.11951e45	−0.512557	−0.256279	−	0.966603i	$-0.582496\pi$
$877$	−2.11951e45	−0.512557	−0.256279	+	0.966603i	$0.582496\pi$
$878$	6.63415e45	1.57623
$879$	8.63329e45	2.01534
$880$	0	0
$881$	−2.35738e45	−0.531255	−0.265627	−	0.964076i	$-0.585579\pi$
$881$	−2.35738e45	−0.531255	−0.265627	+	0.964076i	$0.585579\pi$
$882$	3.32069e45	0.735302
$883$	−3.51964e45	−0.765786	−0.382893	−	0.923793i	$-0.625072\pi$
$883$	−3.51964e45	−0.765786	−0.382893	+	0.923793i	$0.625072\pi$
$884$	−3.27850e44	−0.0700915
$885$	0	0
$886$	−3.70641e45	−0.765123
$887$	1.81896e45	0.368983	0.184492	−	0.982834i	$-0.440936\pi$
$887$	1.81896e45	0.368983	0.184492	+	0.982834i	$0.440936\pi$
$888$	−2.10771e45	−0.420155
$889$	5.80848e45	1.13785
$890$	0	0
$891$	9.48883e45	1.79518
$892$	−7.37734e44	−0.137165
$893$	1.13628e45	0.207629
$894$	−1.12914e46	−2.02777
$895$	0	0
$896$	4.01505e45	0.696493
$897$	8.45767e45	1.44201
$898$	−4.48298e44	−0.0751249
$899$	−1.45177e45	−0.239124
$900$	0	0
$901$	1.86119e45	0.296180
$902$	−8.64726e45	−1.35262
$903$	−5.61775e45	−0.863778
$904$	−3.85405e45	−0.582514
$905$	0	0
$906$	6.07076e45	0.886658
$907$	3.55045e45	0.509765	0.254883	−	0.966972i	$-0.417963\pi$
$907$	3.55045e45	0.509765	0.254883	+	0.966972i	$0.417963\pi$
$908$	1.57085e45	0.221719
$909$	−1.09046e46	−1.51310
$910$	0	0
$911$	1.17856e46	1.58059	0.790293	−	0.612729i	$-0.209928\pi$
$911$	1.17856e46	1.58059	0.790293	+	0.612729i	$0.209928\pi$
$912$	1.21613e46	1.60346
$913$	2.24433e46	2.90930
$914$	8.76254e45	1.11677
$915$	0	0
$916$	6.78134e43	0.00835479
$917$	−3.66297e45	−0.443720
$918$	1.75335e44	0.0208837
$919$	−3.13788e45	−0.367491	−0.183745	−	0.982974i	$-0.558822\pi$
$919$	−3.13788e45	−0.367491	−0.183745	+	0.982974i	$0.558822\pi$
$920$	0	0
$921$	−8.15353e45	−0.923255
$922$	8.55235e45	0.952261
$923$	−1.36903e46	−1.49894
$924$	−2.68287e45	−0.288858
$925$	0	0
$926$	−8.05554e45	−0.838734
$927$	−1.00717e45	−0.103126
$928$	−4.11411e45	−0.414269
$929$	−1.03965e46	−1.02954	−0.514772	−	0.857327i	$-0.672123\pi$
$929$	−1.03965e46	−1.02954	−0.514772	+	0.857327i	$0.672123\pi$
$930$	0	0
$931$	−6.68124e45	−0.639936
$932$	−3.02137e45	−0.284615
$933$	−2.28637e46	−2.11827
$934$	1.79768e46	1.63808
$935$	0	0
$936$	−8.98532e45	−0.792060
$937$	−1.31609e45	−0.114110	−0.0570550	−	0.998371i	$-0.518171\pi$
$937$	−1.31609e45	−0.114110	−0.0570550	+	0.998371i	$0.518171\pi$
$938$	−9.21859e45	−0.786178
$939$	−8.00451e45	−0.671457
$940$	0	0
$941$	−4.70374e45	−0.381772	−0.190886	−	0.981612i	$-0.561136\pi$
$941$	−4.70374e45	−0.381772	−0.190886	+	0.981612i	$0.561136\pi$
$942$	2.00979e45	0.160458
$943$	−9.95643e45	−0.781938
$944$	2.65074e46	2.04786
$945$	0	0
$946$	−2.78700e46	−2.08365
$947$	7.16058e43	0.00526652	0.00263326	−	0.999997i	$-0.499162\pi$
$947$	7.16058e43	0.00526652	0.00263326	+	0.999997i	$0.499162\pi$
$948$	2.53108e45	0.183137
$949$	−1.27927e46	−0.910620
$950$	0	0
$951$	1.18102e46	0.813691
$952$	−3.33906e45	−0.226335
$953$	1.01545e46	0.677202	0.338601	−	0.940930i	$-0.390046\pi$
$953$	1.01545e46	0.677202	0.338601	+	0.940930i	$0.390046\pi$
$954$	−1.16606e46	−0.765103
$955$	0	0
$956$	−3.68470e45	−0.234048
$957$	−4.76569e46	−2.97845
$958$	1.39842e46	0.859946
$959$	−9.51744e45	−0.575879
$960$	0	0
$961$	−1.63008e46	−0.954985
$962$	5.44571e45	0.313936
$963$	−3.18520e46	−1.80688
$964$	−1.90039e45	−0.106084
$965$	0	0
$966$	−1.96911e46	−1.06445
$967$	−1.15264e46	−0.613172	−0.306586	−	0.951843i	$-0.599187\pi$
$967$	−1.15264e46	−0.613172	−0.306586	+	0.951843i	$0.599187\pi$
$968$	4.12920e46	2.16171
$969$	−1.17481e46	−0.605268
$970$	0	0
$971$	9.72203e45	0.485131	0.242565	−	0.970135i	$-0.422011\pi$
$971$	9.72203e45	0.485131	0.242565	+	0.970135i	$0.422011\pi$
$972$	5.39415e45	0.264908
$973$	8.66534e45	0.418829
$974$	4.47834e46	2.13036
$975$	0	0
$976$	4.13042e46	1.90337
$977$	1.50140e46	0.680973	0.340486	−	0.940249i	$-0.389408\pi$
$977$	1.50140e46	0.680973	0.340486	+	0.940249i	$0.389408\pi$
$978$	−3.21902e46	−1.43705
$979$	6.51982e46	2.86486
$980$	0	0
$981$	−3.20066e45	−0.136260
$982$	−5.15403e45	−0.215983
$983$	2.48076e45	0.102331	0.0511653	−	0.998690i	$-0.483706\pi$
$983$	2.48076e45	0.102331	0.0511653	+	0.998690i	$0.483706\pi$
$984$	2.08376e46	0.846102
$985$	0	0
$986$	1.35588e46	0.533494
$987$	4.59267e45	0.177889
$988$	−4.13269e45	−0.157580
$989$	−3.20895e46	−1.20454
$990$	0	0
$991$	−2.22619e45	−0.0809879	−0.0404939	−	0.999180i	$-0.512893\pi$
$991$	−2.22619e45	−0.0809879	−0.0404939	+	0.999180i	$0.512893\pi$
$992$	2.17745e45	0.0779860
$993$	−1.84550e46	−0.650728
$994$	3.18737e46	1.10648
$995$	0	0
$996$	1.23630e46	0.416012
$997$	−4.15949e46	−1.37805	−0.689025	−	0.724738i	$-0.741961\pi$
$997$	−4.15949e46	−1.37805	−0.689025	+	0.724738i	$0.741961\pi$
$998$	−5.83072e46	−1.90195
$999$	−4.56879e44	−0.0146736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.32.a.e.1.3	yes	10
5.2	odd	4		25.32.b.d.24.5		20
5.3	odd	4		25.32.b.d.24.16		20
5.4	even	2		25.32.a.d.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.32.a.d.1.8	✓	10	5.4	even	2
25.32.a.e.1.3	yes	10	1.1	even	1	trivial
25.32.b.d.24.5		20	5.2	odd	4
25.32.b.d.24.16		20	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:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-50468.3 q^{2} -3.54185e7 q^{3} +3.99569e8 q^{4} +1.78751e12 q^{6} -7.37897e12 q^{7} +8.82143e13 q^{8} +6.36795e14 q^{9} +O(q^{10})\)	\(q-50468.3 q^{2} -3.54185e7 q^{3} +3.99569e8 q^{4} +1.78751e12 q^{6} -7.37897e12 q^{7} +8.82143e13 q^{8} +6.36795e14 q^{9} -2.56911e16 q^{11} -1.41521e16 q^{12} -1.59954e17 q^{13} +3.72404e17 q^{14} -5.31010e18 q^{16} +5.12967e18 q^{17} -3.21380e19 q^{18} +6.46616e19 q^{19} +2.61352e20 q^{21} +1.29658e21 q^{22} +1.49288e21 q^{23} -3.12442e21 q^{24} +8.07260e21 q^{26} -6.77267e20 q^{27} -2.94841e21 q^{28} -5.23737e22 q^{29} +2.77195e22 q^{31} +7.85529e22 q^{32} +9.09938e23 q^{33} -2.58886e23 q^{34} +2.54443e23 q^{36} +6.74592e23 q^{37} -3.26336e24 q^{38} +5.66532e24 q^{39} -6.66926e24 q^{41} -1.31900e25 q^{42} -2.14950e25 q^{43} -1.02653e25 q^{44} -7.53434e25 q^{46} +1.75727e25 q^{47} +1.88076e26 q^{48} -1.03326e26 q^{49} -1.81685e26 q^{51} -6.39125e25 q^{52} +3.62828e26 q^{53} +3.41806e25 q^{54} -6.50931e26 q^{56} -2.29022e27 q^{57} +2.64322e27 q^{58} -4.99188e27 q^{59} -7.77843e27 q^{61} -1.39896e27 q^{62} -4.69890e27 q^{63} +7.43891e27 q^{64} -4.59231e28 q^{66} -2.47542e28 q^{67} +2.04966e27 q^{68} -5.28757e28 q^{69} +8.55888e28 q^{71} +5.61745e28 q^{72} +7.99777e28 q^{73} -3.40455e28 q^{74} +2.58368e28 q^{76} +1.89574e29 q^{77} -2.85919e29 q^{78} -1.78848e29 q^{79} -3.69344e29 q^{81} +3.36586e29 q^{82} -8.73583e29 q^{83} +1.04428e29 q^{84} +1.08481e30 q^{86} +1.85500e30 q^{87} -2.26632e30 q^{88} -2.53778e30 q^{89} +1.18029e30 q^{91} +5.96510e29 q^{92} -9.81782e29 q^{93} -8.86867e29 q^{94} -2.78223e30 q^{96} +2.82605e30 q^{97} +5.21470e30 q^{98} -1.63599e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 25575 q^{2} - 2760800 q^{3} + 10269794805 q^{4} + 343311916045 q^{6} + 9887556005000 q^{7} - 3578006280975 q^{8} + 18\!\cdots\!20 q^{9}+O(q^{10}) \) 10 * q + 25575 * q^2 - 2760800 * q^3 + 10269794805 * q^4 + 343311916045 * q^6 + 9887556005000 * q^7 - 3578006280975 * q^8 + 1815779931749020 * q^9	\( 10 q + 25575 q^{2} - 2760800 q^{3} + 10269794805 q^{4} + 343311916045 q^{6} + 9887556005000 q^{7} - 3578006280975 q^{8} + 18\!\cdots\!20 q^{9}+ \cdots + 62\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q + 25575 * q^2 - 2760800 * q^3 + 10269794805 * q^4 + 343311916045 * q^6 + 9887556005000 * q^7 - 3578006280975 * q^8 + 1815779931749020 * q^9 + 7349131705193520 * q^11 + 125108909447979275 * q^12 + 297674226399950400 * q^13 + 1792715492267723010 * q^14 + 1334353718260535985 * q^16 + 9523258650276952350 * q^17 + 38495078920359601450 * q^18 + 46352372872867236000 * q^19 - 716978115331506024180 * q^21 + 1690458204465597900775 * q^22 + 631835006725227807600 * q^23 + 3814887329433293073975 * q^24 + 16428044934100377635820 * q^26 - 44922657529601683294400 * q^27 + 16025331740330522453150 * q^28 - 43862751388004829593400 * q^29 - 111398499239730790616480 * q^31 + 624015821508918585234825 * q^32 + 126250963868713519223150 * q^33 + 962162010656367444278285 * q^34 - 2512527250607526541928290 * q^36 + 5644924721128363757179300 * q^37 + 4826095859564212441518975 * q^38 + 7725309347826090604730840 * q^39 - 23954965467751578822345630 * q^41 + 52362312080978950024873350 * q^42 + 14566521950591051962026000 * q^43 + 72655345451170446851237985 * q^44 - 126418292060169078516582330 * q^46 + 324148178060325313916201400 * q^47 + 300309923927800698275303975 * q^48 + 623138091199598015722452130 * q^49 - 924948963841877288638346480 * q^51 + 1416823162531342539559652500 * q^52 + 238005597268840584357269700 * q^53 - 1295576658888572188253302625 * q^54 + 2899658525974131770370991350 * q^56 - 6226349620730017694505216050 * q^57 - 4306284916672849063070827600 * q^58 - 3033079573561674003346257600 * q^59 + 4231817029130863702119286620 * q^61 - 16098304855452311820307766850 * q^62 + 7361575042495709162746930800 * q^63 - 4758679453351220179885580495 * q^64 + 20941748361811791347567292965 * q^66 - 27305019543952980426556158400 * q^67 - 64404565186219577130468886425 * q^68 - 70710746528072109261961650660 * q^69 + 59422726898031051667669065720 * q^71 - 87856614695319178573207323450 * q^72 + 167783929989442631280479528850 * q^73 + 233886472625162831037933838410 * q^74 - 431165109277408954165767525175 * q^76 + 820800484268840888889286594500 * q^77 + 127124231267016797985074322500 * q^78 + 419830654198707399953568495400 * q^79 - 23178478329365819834057302790 * q^81 + 789038645466992754053523018275 * q^82 + 843536130899785235460491302800 * q^83 + 1533731687188227156859469497410 * q^84 - 880018109049133595082445679580 * q^86 - 2019500060946434885638438686200 * q^87 - 298284716872697736218771826075 * q^88 - 1486086045181702570536871131450 * q^89 + 7311774579005982050993260573520 * q^91 - 8592235976506062778549400808150 * q^92 - 4438442492661044963203969196100 * q^93 - 10230327657788093663700166076740 * q^94 + 6355286745483948239059480165295 * q^96 - 6882714708207174103260839260100 * q^97 + 4375208329490354177415738128475 * q^98 + 6243638896172887002986280271040 * q^99

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