LMFDB - Embedded newform 25.34.a.b.1.4

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1372039866x^{3} - 648067657640x^{2} + 285631173782445856x - 33409741805340964224 $ x^5 - 2x^4 - 1372039866x^3 - 648067657640x^2 + 285631173782445856x - 33409741805340964224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$15553.7$ 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)

$f(q)$	$=$	$q+56118.7 q^{2} -5.48591e7 q^{3} -5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13 q^{7} -7.87377e14 q^{8} -2.54954e15 q^{9} +O(q^{10})$	\(q+56118.7 q^{2} -5.48591e7 q^{3} -5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13 q^{7} -7.87377e14 q^{8} -2.54954e15 q^{9} +3.54535e16 q^{11} +2.98468e17 q^{12} +1.27272e18 q^{13} -4.14468e18 q^{14} +2.54805e18 q^{16} -1.95420e20 q^{17} -1.43077e20 q^{18} +9.67568e20 q^{19} +4.05165e21 q^{21} +1.98961e21 q^{22} +3.06053e22 q^{23} +4.31948e22 q^{24} +7.14231e22 q^{26} +4.44830e23 q^{27} +4.01821e23 q^{28} -1.16201e23 q^{29} -3.89265e23 q^{31} +6.90651e24 q^{32} -1.94495e24 q^{33} -1.09667e25 q^{34} +1.38711e25 q^{36} +2.73400e25 q^{37} +5.42987e25 q^{38} -6.98200e25 q^{39} -7.27564e26 q^{41} +2.27373e26 q^{42} +1.74161e27 q^{43} -1.92889e26 q^{44} +1.71753e27 q^{46} -2.14063e26 q^{47} -1.39784e26 q^{48} -2.27634e27 q^{49} +1.07206e28 q^{51} -6.92437e27 q^{52} +1.96400e28 q^{53} +2.49633e28 q^{54} +5.81522e28 q^{56} -5.30799e28 q^{57} -6.52106e27 q^{58} +2.54315e29 q^{59} -2.81524e29 q^{61} -2.18451e28 q^{62} +1.88298e29 q^{63} +3.65697e29 q^{64} -1.09148e29 q^{66} +8.18392e29 q^{67} +1.06321e30 q^{68} -1.67898e30 q^{69} -3.59524e30 q^{71} +2.00745e30 q^{72} +2.19852e30 q^{73} +1.53429e30 q^{74} -5.26418e30 q^{76} -2.61844e30 q^{77} -3.91821e30 q^{78} +3.90404e31 q^{79} -1.02299e31 q^{81} -4.08299e31 q^{82} -4.98882e30 q^{83} -2.20435e31 q^{84} +9.77368e31 q^{86} +6.37469e30 q^{87} -2.79153e31 q^{88} -1.23819e32 q^{89} -9.39972e31 q^{91} -1.66512e32 q^{92} +2.13547e31 q^{93} -1.20129e31 q^{94} -3.78885e32 q^{96} -1.97176e32 q^{97} -1.27745e32 q^{98} -9.03903e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) $ 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9	$ 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9 - 287801801877976640 * q^11 + 405379955363513088 * q^12 - 2397201150889907466 * q^13 + 11676449916272482320 * q^14 - 89180089543245957120 * q^16 + 308725634324001653918 * q^17 - 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 10535115771712805413140 * q^21 + 13757888128329419319296 * q^22 - 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 - 424902360762721464761840 * q^26 - 679342131249712739644500 * q^27 + 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1336046479411821372201940 * q^31 + 813043271605502937899008 * q^32 + 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 - 180374200000978588488558720 * q^36 + 142836045294254023962738038 * q^37 + 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 1325620030754525933329256290 * q^41 + 2645870671030939362357320736 * q^42 + 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2874649720834424257835685840 * q^46 + 7724956189479550762134222398 * q^47 + 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 7346719218915268753088875260 * q^51 - 48963787841701555176191049472 * q^52 - 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 144880509244845944794630156800 * q^56 - 208512654554635835530896805800 * q^57 - 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 742889693167672203496619446410 * q^61 - 532537079706659761431026425824 * q^62 + 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 3327517517031282146197646561280 * q^66 + 3757683664783078488809531637718 * q^67 - 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 5502085339682331744817794354940 * q^71 + 15971664273931445780329968326400 * q^72 + 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 + 7186339982587317558706196185600 * q^76 - 47237885671577674597763242652544 * q^77 - 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 78583804836302041006582647314505 * q^81 - 27306575776891610455800103348784 * q^82 - 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 65486114707827974097903540464560 * q^86 - 137286065258860195168416991536900 * q^87 - 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 268937084803738847432203207735340 * q^91 + 697440932909638690403668496563968 * q^92 + 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 344518603172836645970889894051840 * q^96 + 867959773515074594808067717684598 * q^97 + 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * 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 $

$2$	56118.7	0.605498	0.302749	−	0.953070i	$-0.402096\pi$
$2$	56118.7	0.605498	0.302749	+	0.953070i	$0.402096\pi$
$3$	−5.48591e7	−0.735780	−0.367890	−	0.929869i	$-0.619920\pi$
$3$	−5.48591e7	−0.735780	−0.367890	+	0.929869i	$0.619920\pi$
$4$	−5.44063e9	−0.633372
$5$	0	0
$5$	0	0
$6$	−3.07862e12	−0.445513
$7$	−7.38557e13	−0.839975	−0.419987	−	0.907530i	$-0.637965\pi$
$7$	−7.38557e13	−0.839975	−0.419987	+	0.907530i	$0.637965\pi$
$8$	−7.87377e14	−0.989004
$9$	−2.54954e15	−0.458628
$10$	0	0
$11$	3.54535e16	0.232638	0.116319	−	0.993212i	$-0.462891\pi$
$11$	3.54535e16	0.232638	0.116319	+	0.993212i	$0.462891\pi$
$12$	2.98468e17	0.466022
$13$	1.27272e18	0.530476	0.265238	−	0.964183i	$-0.414549\pi$
$13$	1.27272e18	0.530476	0.265238	+	0.964183i	$0.414549\pi$
$14$	−4.14468e18	−0.508603
$15$	0	0
$16$	2.54805e18	0.0345325
$17$	−1.95420e20	−0.974006	−0.487003	−	0.873400i	$-0.661910\pi$
$17$	−1.95420e20	−0.974006	−0.487003	+	0.873400i	$0.661910\pi$
$18$	−1.43077e20	−0.277699
$19$	9.67568e20	0.769568	0.384784	−	0.923007i	$-0.374276\pi$
$19$	9.67568e20	0.769568	0.384784	+	0.923007i	$0.374276\pi$
$20$	0	0
$21$	4.05165e21	0.618036
$22$	1.98961e21	0.140862
$23$	3.06053e22	1.04061	0.520305	−	0.853981i	$-0.325818\pi$
$23$	3.06053e22	1.04061	0.520305	+	0.853981i	$0.325818\pi$
$24$	4.31948e22	0.727689
$25$	0	0
$26$	7.14231e22	0.321202
$27$	4.44830e23	1.07323
$28$	4.01821e23	0.532017
$29$	−1.16201e23	−0.0862271	−0.0431135	−	0.999070i	$-0.513728\pi$
$29$	−1.16201e23	−0.0862271	−0.0431135	+	0.999070i	$0.513728\pi$
$30$	0	0
$31$	−3.89265e23	−0.0961121	−0.0480560	−	0.998845i	$-0.515303\pi$
$31$	−3.89265e23	−0.0961121	−0.0480560	+	0.998845i	$0.515303\pi$
$32$	6.90651e24	1.00991
$33$	−1.94495e24	−0.171170
$34$	−1.09667e25	−0.589759
$35$	0	0
$36$	1.38711e25	0.290482
$37$	2.73400e25	0.364310	0.182155	−	0.983270i	$-0.441693\pi$
$37$	2.73400e25	0.364310	0.182155	+	0.983270i	$0.441693\pi$
$38$	5.42987e25	0.465972
$39$	−6.98200e25	−0.390314
$40$	0	0
$41$	−7.27564e26	−1.78212	−0.891061	−	0.453883i	$-0.850038\pi$
$41$	−7.27564e26	−1.78212	−0.891061	+	0.453883i	$0.850038\pi$
$42$	2.27373e26	0.374220
$43$	1.74161e27	1.94411	0.972055	−	0.234754i	$-0.0754284\pi$
$43$	1.74161e27	1.94411	0.972055	+	0.234754i	$0.0754284\pi$
$44$	−1.92889e26	−0.147346
$45$	0	0
$46$	1.71753e27	0.630087
$47$	−2.14063e26	−0.0550714	−0.0275357	−	0.999621i	$-0.508766\pi$
$47$	−2.14063e26	−0.0550714	−0.0275357	+	0.999621i	$0.508766\pi$
$48$	−1.39784e26	−0.0254083
$49$	−2.27634e27	−0.294443
$50$	0	0
$51$	1.07206e28	0.716654
$52$	−6.92437e27	−0.335989
$53$	1.96400e28	0.695970	0.347985	−	0.937500i	$-0.386866\pi$
$53$	1.96400e28	0.695970	0.347985	+	0.937500i	$0.386866\pi$
$54$	2.49633e28	0.649838
$55$	0	0
$56$	5.81522e28	0.830738
$57$	−5.30799e28	−0.566233
$58$	−6.52106e27	−0.0522103
$59$	2.54315e29	1.53573	0.767864	−	0.640612i	$-0.221319\pi$
$59$	2.54315e29	1.53573	0.767864	+	0.640612i	$0.221319\pi$
$60$	0	0
$61$	−2.81524e29	−0.980785	−0.490392	−	0.871502i	$-0.663147\pi$
$61$	−2.81524e29	−0.980785	−0.490392	+	0.871502i	$0.663147\pi$
$62$	−2.18451e28	−0.0581957
$63$	1.88298e29	0.385236
$64$	3.65697e29	0.576968
$65$	0	0
$66$	−1.09148e29	−0.103643
$67$	8.18392e29	0.606355	0.303178	−	0.952934i	$-0.401952\pi$
$67$	8.18392e29	0.606355	0.303178	+	0.952934i	$0.401952\pi$
$68$	1.06321e30	0.616908
$69$	−1.67898e30	−0.765660
$70$	0	0
$71$	−3.59524e30	−1.02321	−0.511606	−	0.859220i	$-0.670949\pi$
$71$	−3.59524e30	−1.02321	−0.511606	+	0.859220i	$0.670949\pi$
$72$	2.00745e30	0.453585
$73$	2.19852e30	0.395642	0.197821	−	0.980238i	$-0.436613\pi$
$73$	2.19852e30	0.395642	0.197821	+	0.980238i	$0.436613\pi$
$74$	1.53429e30	0.220589
$75$	0	0
$76$	−5.26418e30	−0.487423
$77$	−2.61844e30	−0.195410
$78$	−3.91821e30	−0.236334
$79$	3.90404e31	1.90839	0.954194	−	0.299188i	$-0.0967156\pi$
$79$	3.90404e31	1.90839	0.954194	+	0.299188i	$0.0967156\pi$
$80$	0	0
$81$	−1.02299e31	−0.331032
$82$	−4.08299e31	−1.07907
$83$	−4.98882e30	−0.107947	−0.0539734	−	0.998542i	$-0.517189\pi$
$83$	−4.98882e30	−0.107947	−0.0539734	+	0.998542i	$0.517189\pi$
$84$	−2.20435e31	−0.391447
$85$	0	0
$86$	9.77368e31	1.17715
$87$	6.37469e30	0.0634441
$88$	−2.79153e31	−0.230080
$89$	−1.23819e32	−0.846937	−0.423469	−	0.905911i	$-0.639188\pi$
$89$	−1.23819e32	−0.846937	−0.423469	+	0.905911i	$0.639188\pi$
$90$	0	0
$91$	−9.39972e31	−0.445587
$92$	−1.66512e32	−0.659093
$93$	2.13547e31	0.0707173
$94$	−1.20129e31	−0.0333456
$95$	0	0
$96$	−3.78885e32	−0.743073
$97$	−1.97176e32	−0.325926	−0.162963	−	0.986632i	$-0.552105\pi$
$97$	−1.97176e32	−0.325926	−0.162963	+	0.986632i	$0.552105\pi$
$98$	−1.27745e32	−0.178285
$99$	−9.03903e31	−0.106694
$100$	0	0
$101$	−1.97472e33	−1.67573	−0.837865	−	0.545878i	$-0.816196\pi$
$101$	−1.97472e33	−1.67573	−0.837865	+	0.545878i	$0.816196\pi$
$102$	6.01624e32	0.433932
$103$	−5.57056e32	−0.342046	−0.171023	−	0.985267i	$-0.554707\pi$
$103$	−5.57056e32	−0.342046	−0.171023	+	0.985267i	$0.554707\pi$
$104$	−1.00211e33	−0.524643
$105$	0	0
$106$	1.10217e33	0.421409
$107$	−3.76704e33	−1.23358	−0.616791	−	0.787127i	$-0.711568\pi$
$107$	−3.76704e33	−1.23358	−0.616791	+	0.787127i	$0.711568\pi$
$108$	−2.42016e33	−0.679753
$109$	7.25238e33	1.74962	0.874810	−	0.484467i	$-0.160986\pi$
$109$	7.25238e33	1.74962	0.874810	+	0.484467i	$0.160986\pi$
$110$	0	0
$111$	−1.49985e33	−0.268051
$112$	−1.88188e32	−0.0290064
$113$	3.76366e32	0.0500976	0.0250488	−	0.999686i	$-0.492026\pi$
$113$	3.76366e32	0.0500976	0.0250488	+	0.999686i	$0.492026\pi$
$114$	−2.97878e33	−0.342853
$115$	0	0
$116$	6.32207e32	0.0546138
$117$	−3.24484e33	−0.243291
$118$	1.42719e34	0.929881
$119$	1.44329e34	0.818140
$120$	0	0
$121$	−2.19682e34	−0.945880
$122$	−1.57988e34	−0.593863
$123$	3.99135e34	1.31125
$124$	2.11785e33	0.0608747
$125$	0	0
$126$	1.05671e34	0.233260
$127$	4.97180e34	0.963279	0.481640	−	0.876369i	$-0.340041\pi$
$127$	4.97180e34	0.963279	0.481640	+	0.876369i	$0.340041\pi$
$128$	−3.88040e34	−0.660560
$129$	−9.55430e34	−1.43044
$130$	0	0
$131$	3.26112e34	0.378782	0.189391	−	0.981902i	$-0.439349\pi$
$131$	3.26112e34	0.378782	0.189391	+	0.981902i	$0.439349\pi$
$132$	1.05817e34	0.108414
$133$	−7.14604e34	−0.646418
$134$	4.59271e34	0.367147
$135$	0	0
$136$	1.53869e35	0.963296
$137$	4.83496e34	0.268228	0.134114	−	0.990966i	$-0.457181\pi$
$137$	4.83496e34	0.268228	0.134114	+	0.990966i	$0.457181\pi$
$138$	−9.42222e34	−0.463605
$139$	−1.61945e35	−0.707334	−0.353667	−	0.935371i	$-0.615065\pi$
$139$	−1.61945e35	−0.707334	−0.353667	+	0.935371i	$0.615065\pi$
$140$	0	0
$141$	1.17433e34	0.0405204
$142$	−2.01760e35	−0.619552
$143$	4.51223e34	0.123409
$144$	−6.49637e33	−0.0158376
$145$	0	0
$146$	1.23378e35	0.239561
$147$	1.24878e35	0.216645
$148$	−1.48747e35	−0.230744
$149$	−4.97369e35	−0.690407	−0.345204	−	0.938528i	$-0.612190\pi$
$149$	−4.97369e35	−0.690407	−0.345204	+	0.938528i	$0.612190\pi$
$150$	0	0
$151$	1.20125e35	0.133818	0.0669090	−	0.997759i	$-0.478686\pi$
$151$	1.20125e35	0.133818	0.0669090	+	0.997759i	$0.478686\pi$
$152$	−7.61841e35	−0.761106
$153$	4.98232e35	0.446707
$154$	−1.46944e35	−0.118320
$155$	0	0
$156$	3.79864e35	0.247214
$157$	1.58453e36	0.928018	0.464009	−	0.885830i	$-0.346410\pi$
$157$	1.58453e36	0.928018	0.464009	+	0.885830i	$0.346410\pi$
$158$	2.19089e36	1.15553
$159$	−1.07743e36	−0.512081
$160$	0	0
$161$	−2.26038e36	−0.874086
$162$	−5.74090e35	−0.200439
$163$	3.31440e36	1.04546	0.522732	−	0.852497i	$-0.324913\pi$
$163$	3.31440e36	1.04546	0.522732	+	0.852497i	$0.324913\pi$
$164$	3.95840e36	1.12875
$165$	0	0
$166$	−2.79966e35	−0.0653615
$167$	−7.73877e36	−1.63625	−0.818126	−	0.575039i	$-0.804987\pi$
$167$	−7.73877e36	−1.63625	−0.818126	+	0.575039i	$0.804987\pi$
$168$	−3.19018e36	−0.611240
$169$	−4.13633e36	−0.718595
$170$	0	0
$171$	−2.46686e36	−0.352946
$172$	−9.47543e36	−1.23135
$173$	−4.62098e36	−0.545725	−0.272862	−	0.962053i	$-0.587970\pi$
$173$	−4.62098e36	−0.545725	−0.272862	+	0.962053i	$0.587970\pi$
$174$	3.57739e35	0.0384153
$175$	0	0
$176$	9.03374e34	0.00803357
$177$	−1.39515e37	−1.12996
$178$	−6.94855e36	−0.512819
$179$	−1.73851e37	−1.16977	−0.584886	−	0.811115i	$-0.698861\pi$
$179$	−1.73851e37	−1.16977	−0.584886	+	0.811115i	$0.698861\pi$
$180$	0	0
$181$	−2.20579e37	−1.23557	−0.617785	−	0.786347i	$-0.711970\pi$
$181$	−2.20579e37	−1.23557	−0.617785	+	0.786347i	$0.711970\pi$
$182$	−5.27500e36	−0.269802
$183$	1.54442e37	0.721641
$184$	−2.40979e37	−1.02917
$185$	0	0
$186$	1.19840e36	0.0428192
$187$	−6.92833e36	−0.226591
$188$	1.16463e36	0.0348807
$189$	−3.28532e37	−0.901485
$190$	0	0
$191$	3.27319e37	0.754954	0.377477	−	0.926019i	$-0.376792\pi$
$191$	3.27319e37	0.754954	0.377477	+	0.926019i	$0.376792\pi$
$192$	−2.00618e37	−0.424521
$193$	8.15189e37	1.58330	0.791649	−	0.610976i	$-0.209223\pi$
$193$	8.15189e37	1.58330	0.791649	+	0.610976i	$0.209223\pi$
$194$	−1.10652e37	−0.197348
$195$	0	0
$196$	1.23847e37	0.186492
$197$	−1.16510e38	−1.61313	−0.806565	−	0.591145i	$-0.798676\pi$
$197$	−1.16510e38	−1.61313	−0.806565	+	0.591145i	$0.798676\pi$
$198$	−5.07259e36	−0.0646032
$199$	−1.05328e38	−1.23443	−0.617216	−	0.786794i	$-0.711739\pi$
$199$	−1.05328e38	−1.23443	−0.617216	+	0.786794i	$0.711739\pi$
$200$	0	0
$201$	−4.48962e37	−0.446144
$202$	−1.10819e38	−1.01465
$203$	8.58211e36	0.0724285
$204$	−5.83265e37	−0.453909
$205$	0	0
$206$	−3.12613e37	−0.207108
$207$	−7.80296e37	−0.477253
$208$	3.24294e36	0.0183187
$209$	3.43037e37	0.179031
$210$	0	0
$211$	3.80288e38	1.69610	0.848051	−	0.529915i	$-0.177776\pi$
$211$	3.80288e38	1.69610	0.848051	+	0.529915i	$0.177776\pi$
$212$	−1.06854e38	−0.440808
$213$	1.97232e38	0.752858
$214$	−2.11401e38	−0.746931
$215$	0	0
$216$	−3.50249e38	−1.06143
$217$	2.87495e37	0.0807317
$218$	4.06994e38	1.05939
$219$	−1.20609e38	−0.291106
$220$	0	0
$221$	−2.48714e38	−0.516687
$222$	−8.41696e37	−0.162305
$223$	−4.60089e38	−0.823780	−0.411890	−	0.911234i	$-0.635131\pi$
$223$	−4.60089e38	−0.823780	−0.411890	+	0.911234i	$0.635131\pi$
$224$	−5.10085e38	−0.848301
$225$	0	0
$226$	2.11212e37	0.0303340
$227$	−1.13977e39	−1.52192	−0.760958	−	0.648801i	$-0.775271\pi$
$227$	−1.13977e39	−1.52192	−0.760958	+	0.648801i	$0.775271\pi$
$228$	2.88788e38	0.358636
$229$	−1.46028e39	−1.68713	−0.843566	−	0.537025i	$-0.819548\pi$
$229$	−1.46028e39	−1.68713	−0.843566	+	0.537025i	$0.819548\pi$
$230$	0	0
$231$	1.43645e38	0.143779
$232$	9.14941e37	0.0852789
$233$	2.05161e37	0.0178124	0.00890620	−	0.999960i	$-0.497165\pi$
$233$	2.05161e37	0.0178124	0.00890620	+	0.999960i	$0.497165\pi$
$234$	−1.82096e38	−0.147313
$235$	0	0
$236$	−1.38364e39	−0.972688
$237$	−2.14172e39	−1.40415
$238$	8.09954e38	0.495382
$239$	9.20750e38	0.525505	0.262752	−	0.964863i	$-0.415370\pi$
$239$	9.20750e38	0.525505	0.262752	+	0.964863i	$0.415370\pi$
$240$	0	0
$241$	1.79093e39	0.890834	0.445417	−	0.895323i	$-0.353056\pi$
$241$	1.79093e39	0.890834	0.445417	+	0.895323i	$0.353056\pi$
$242$	−1.23283e39	−0.572728
$243$	−1.91164e39	−0.829663
$244$	1.53167e39	0.621202
$245$	0	0
$246$	2.23989e39	0.793959
$247$	1.23144e39	0.408238
$248$	3.06499e38	0.0950552
$249$	2.73682e38	0.0794250
$250$	0	0
$251$	−4.16615e39	−1.05954	−0.529772	−	0.848140i	$-0.677723\pi$
$251$	−4.16615e39	−1.05954	−0.529772	+	0.848140i	$0.677723\pi$
$252$	−1.02446e39	−0.243998
$253$	1.08507e39	0.242085
$254$	2.79011e39	0.583264
$255$	0	0
$256$	−5.31894e39	−0.976936
$257$	1.03274e40	1.77867	0.889336	−	0.457254i	$-0.151167\pi$
$257$	1.03274e40	1.77867	0.889336	+	0.457254i	$0.151167\pi$
$258$	−5.36175e39	−0.866126
$259$	−2.01922e39	−0.306011
$260$	0	0
$261$	2.96260e38	0.0395462
$262$	1.83010e39	0.229352
$263$	7.85107e39	0.923972	0.461986	−	0.886887i	$-0.347137\pi$
$263$	7.85107e39	0.923972	0.461986	+	0.886887i	$0.347137\pi$
$264$	1.53141e39	0.169288
$265$	0	0
$266$	−4.01027e39	−0.391405
$267$	6.79258e39	0.623159
$268$	−4.45257e39	−0.384049
$269$	1.76099e40	1.42838	0.714189	−	0.699953i	$-0.246796\pi$
$269$	1.76099e40	1.42838	0.714189	+	0.699953i	$0.246796\pi$
$270$	0	0
$271$	1.63883e40	1.17636	0.588179	−	0.808730i	$-0.299845\pi$
$271$	1.63883e40	1.17636	0.588179	+	0.808730i	$0.299845\pi$
$272$	−4.97940e38	−0.0336349
$273$	5.15660e39	0.327853
$274$	2.71332e39	0.162411
$275$	0	0
$276$	9.13470e39	0.484947
$277$	3.39112e40	1.69601	0.848003	−	0.529991i	$-0.177805\pi$
$277$	3.39112e40	1.69601	0.848003	+	0.529991i	$0.177805\pi$
$278$	−9.08817e39	−0.428289
$279$	9.92449e38	0.0440797
$280$	0	0
$281$	3.38855e40	1.33770	0.668851	−	0.743396i	$-0.266786\pi$
$281$	3.38855e40	1.33770	0.668851	+	0.743396i	$0.266786\pi$
$282$	6.59017e38	0.0245350
$283$	−2.32437e40	−0.816263	−0.408131	−	0.912923i	$-0.633819\pi$
$283$	−2.32437e40	−0.816263	−0.408131	+	0.912923i	$0.633819\pi$
$284$	1.95604e40	0.648074
$285$	0	0
$286$	2.53220e39	0.0747238
$287$	5.37347e40	1.49694
$288$	−1.76084e40	−0.463175
$289$	−2.06553e39	−0.0513118
$290$	0	0
$291$	1.08169e40	0.239810
$292$	−1.19613e40	−0.250589
$293$	−3.19376e40	−0.632393	−0.316197	−	0.948694i	$-0.602406\pi$
$293$	−3.19376e40	−0.632393	−0.316197	+	0.948694i	$0.602406\pi$
$294$	7.00797e39	0.131178
$295$	0	0
$296$	−2.15269e40	−0.360303
$297$	1.57708e40	0.249674
$298$	−2.79117e40	−0.418040
$299$	3.89519e40	0.552019
$300$	0	0
$301$	−1.28628e41	−1.63300
$302$	6.74127e39	0.0810265
$303$	1.08332e41	1.23297
$304$	2.46541e39	0.0265751
$305$	0	0
$306$	2.79601e40	0.270480
$307$	9.23782e40	0.846810	0.423405	−	0.905940i	$-0.360835\pi$
$307$	9.23782e40	0.846810	0.423405	+	0.905940i	$0.360835\pi$
$308$	1.42460e40	0.123767
$309$	3.05596e40	0.251670
$310$	0	0
$311$	2.21387e40	0.163910	0.0819550	−	0.996636i	$-0.473884\pi$
$311$	2.21387e40	0.163910	0.0819550	+	0.996636i	$0.473884\pi$
$312$	5.49746e40	0.386022
$313$	−2.73315e40	−0.182046	−0.0910231	−	0.995849i	$-0.529014\pi$
$313$	−2.73315e40	−0.182046	−0.0910231	+	0.995849i	$0.529014\pi$
$314$	8.89219e40	0.561913
$315$	0	0
$316$	−2.12404e41	−1.20872
$317$	−2.26706e41	−1.22457	−0.612286	−	0.790636i	$-0.709750\pi$
$317$	−2.26706e41	−1.22457	−0.612286	+	0.790636i	$0.709750\pi$
$318$	−6.04642e40	−0.310064
$319$	−4.11974e39	−0.0200597
$320$	0	0
$321$	2.06656e41	0.907644
$322$	−1.26849e41	−0.529257
$323$	−1.89082e41	−0.749565
$324$	5.56572e40	0.209666
$325$	0	0
$326$	1.86000e41	0.633027
$327$	−3.97859e41	−1.28733
$328$	5.72867e41	1.76253
$329$	1.58097e40	0.0462586
$330$	0	0
$331$	−2.06805e41	−0.547520	−0.273760	−	0.961798i	$-0.588267\pi$
$331$	−2.06805e41	−0.547520	−0.273760	+	0.961798i	$0.588267\pi$
$332$	2.71423e40	0.0683705
$333$	−6.97046e40	−0.167083
$334$	−4.34290e41	−0.990747
$335$	0	0
$336$	1.03238e40	0.0213423
$337$	−5.63835e40	−0.110984	−0.0554918	−	0.998459i	$-0.517673\pi$
$337$	−5.63835e40	−0.110984	−0.0554918	+	0.998459i	$0.517673\pi$
$338$	−2.32125e41	−0.435108
$339$	−2.06471e40	−0.0368608
$340$	0	0
$341$	−1.38008e40	−0.0223593
$342$	−1.38437e41	−0.213708
$343$	7.39098e41	1.08730
$344$	−1.37130e42	−1.92273
$345$	0	0
$346$	−2.59323e41	−0.330435
$347$	−2.54567e41	−0.309289	−0.154645	−	0.987970i	$-0.549423\pi$
$347$	−2.54567e41	−0.309289	−0.154645	+	0.987970i	$0.549423\pi$
$348$	−3.46823e40	−0.0401837
$349$	−1.42434e42	−1.57397	−0.786983	−	0.616974i	$-0.788358\pi$
$349$	−1.42434e42	−1.57397	−0.786983	+	0.616974i	$0.788358\pi$
$350$	0	0
$351$	5.66143e41	0.569323
$352$	2.44860e41	0.234944
$353$	−4.58433e41	−0.419752	−0.209876	−	0.977728i	$-0.567306\pi$
$353$	−4.58433e41	−0.419752	−0.209876	+	0.977728i	$0.567306\pi$
$354$	−7.82941e41	−0.684187
$355$	0	0
$356$	6.73651e41	0.536427
$357$	−7.91774e41	−0.601971
$358$	−9.75628e41	−0.708295
$359$	1.13078e42	0.784004	0.392002	−	0.919964i	$-0.371783\pi$
$359$	1.13078e42	0.784004	0.392002	+	0.919964i	$0.371783\pi$
$360$	0	0
$361$	−6.44582e41	−0.407764
$362$	−1.23786e42	−0.748135
$363$	1.20516e42	0.695959
$364$	5.11404e41	0.282222
$365$	0	0
$366$	8.66707e41	0.436952
$367$	−1.40753e42	−0.678369	−0.339185	−	0.940720i	$-0.610151\pi$
$367$	−1.40753e42	−0.678369	−0.339185	+	0.940720i	$0.610151\pi$
$368$	7.79840e40	0.0359349
$369$	1.85496e42	0.817332
$370$	0	0
$371$	−1.45053e42	−0.584597
$372$	−1.16183e41	−0.0447904
$373$	4.43848e42	1.63696	0.818480	−	0.574535i	$-0.194817\pi$
$373$	4.43848e42	1.63696	0.818480	+	0.574535i	$0.194817\pi$
$374$	−3.88809e41	−0.137200
$375$	0	0
$376$	1.68548e41	0.0544658
$377$	−1.47891e41	−0.0457414
$378$	−1.84368e42	−0.545847
$379$	−1.41996e42	−0.402466	−0.201233	−	0.979543i	$-0.564495\pi$
$379$	−1.41996e42	−0.402466	−0.201233	+	0.979543i	$0.564495\pi$
$380$	0	0
$381$	−2.72748e42	−0.708761
$382$	1.83687e42	0.457123
$383$	−1.04448e40	−0.00248955	−0.00124478	−	0.999999i	$-0.500396\pi$
$383$	−1.04448e40	−0.00248955	−0.00124478	+	0.999999i	$0.500396\pi$
$384$	2.12875e42	0.486027
$385$	0	0
$386$	4.57473e42	0.958684
$387$	−4.44030e42	−0.891624
$388$	1.07276e42	0.206433
$389$	3.78074e41	0.0697282	0.0348641	−	0.999392i	$-0.488900\pi$
$389$	3.78074e41	0.0697282	0.0348641	+	0.999392i	$0.488900\pi$
$390$	0	0
$391$	−5.98090e42	−1.01356
$392$	1.79233e42	0.291205
$393$	−1.78902e42	−0.278700
$394$	−6.53838e42	−0.976747
$395$	0	0
$396$	4.91780e41	0.0675772
$397$	1.40626e43	1.85363	0.926815	−	0.375519i	$-0.122536\pi$
$397$	1.40626e43	1.85363	0.926815	+	0.375519i	$0.122536\pi$
$398$	−5.91086e42	−0.747446
$399$	3.92025e42	0.475621
$400$	0	0
$401$	−3.90184e42	−0.435900	−0.217950	−	0.975960i	$-0.569937\pi$
$401$	−3.90184e42	−0.435900	−0.217950	+	0.975960i	$0.569937\pi$
$402$	−2.51952e42	−0.270139
$403$	−4.95424e41	−0.0509852
$404$	1.07437e43	1.06136
$405$	0	0
$406$	4.81617e41	0.0438553
$407$	9.69301e41	0.0847522
$408$	−8.44112e42	−0.708773
$409$	1.05489e43	0.850694	0.425347	−	0.905030i	$-0.360152\pi$
$409$	1.05489e43	0.850694	0.425347	+	0.905030i	$0.360152\pi$
$410$	0	0
$411$	−2.65242e42	−0.197357
$412$	3.03073e42	0.216642
$413$	−1.87826e43	−1.28997
$414$	−4.37892e42	−0.288976
$415$	0	0
$416$	8.79002e42	0.535735
$417$	8.88418e42	0.520442
$418$	1.92508e42	0.108403
$419$	2.64714e43	1.43300	0.716498	−	0.697589i	$-0.245744\pi$
$419$	2.64714e43	1.43300	0.716498	+	0.697589i	$0.245744\pi$
$420$	0	0
$421$	2.92799e43	1.46526	0.732630	−	0.680627i	$-0.238293\pi$
$421$	2.92799e43	1.46526	0.732630	+	0.680627i	$0.238293\pi$
$422$	2.13413e43	1.02699
$423$	5.45762e41	0.0252573
$424$	−1.54641e43	−0.688317
$425$	0	0
$426$	1.10684e43	0.455854
$427$	2.07922e43	0.823834
$428$	2.04951e43	0.781316
$429$	−2.47537e42	−0.0908017
$430$	0	0
$431$	7.41005e42	0.251736	0.125868	−	0.992047i	$-0.459828\pi$
$431$	7.41005e42	0.251736	0.125868	+	0.992047i	$0.459828\pi$
$432$	1.13345e42	0.0370613
$433$	2.63001e43	0.827766	0.413883	−	0.910330i	$-0.364172\pi$
$433$	2.63001e43	0.827766	0.413883	+	0.910330i	$0.364172\pi$
$434$	1.61338e42	0.0488829
$435$	0	0
$436$	−3.94575e43	−1.10816
$437$	2.96128e43	0.800821
$438$	−6.76840e42	−0.176264
$439$	1.79135e43	0.449278	0.224639	−	0.974442i	$-0.427880\pi$
$439$	1.79135e43	0.449278	0.224639	+	0.974442i	$0.427880\pi$
$440$	0	0
$441$	5.80362e42	0.135040
$442$	−1.39575e43	−0.312853
$443$	3.40634e43	0.735575	0.367788	−	0.929910i	$-0.380115\pi$
$443$	3.40634e43	0.735575	0.367788	+	0.929910i	$0.380115\pi$
$444$	8.16011e42	0.169776
$445$	0	0
$446$	−2.58196e43	−0.498797
$447$	2.72852e43	0.507988
$448$	−2.70088e43	−0.484638
$449$	8.25218e43	1.42726	0.713632	−	0.700521i	$-0.247049\pi$
$449$	8.25218e43	1.42726	0.713632	+	0.700521i	$0.247049\pi$
$450$	0	0
$451$	−2.57947e43	−0.414589
$452$	−2.04767e42	−0.0317304
$453$	−6.58996e42	−0.0984605
$454$	−6.39625e43	−0.921517
$455$	0	0
$456$	4.17939e43	0.560006
$457$	−1.09927e44	−1.42065	−0.710323	−	0.703876i	$-0.751451\pi$
$457$	−1.09927e44	−1.42065	−0.710323	+	0.703876i	$0.751451\pi$
$458$	−8.19488e43	−1.02156
$459$	−8.69288e43	−1.04533
$460$	0	0
$461$	5.08918e43	0.569616	0.284808	−	0.958585i	$-0.408070\pi$
$461$	5.08918e43	0.569616	0.284808	+	0.958585i	$0.408070\pi$
$462$	8.06120e42	0.0870576
$463$	−5.67339e43	−0.591229	−0.295615	−	0.955307i	$-0.595524\pi$
$463$	−5.67339e43	−0.591229	−0.295615	+	0.955307i	$0.595524\pi$
$464$	−2.96086e41	−0.00297764
$465$	0	0
$466$	1.15134e42	0.0107854
$467$	−8.56548e43	−0.774503	−0.387251	−	0.921974i	$-0.626575\pi$
$467$	−8.56548e43	−0.774503	−0.387251	+	0.921974i	$0.626575\pi$
$468$	1.76540e43	0.154094
$469$	−6.04429e43	−0.509323
$470$	0	0
$471$	−8.69259e43	−0.682817
$472$	−2.00242e44	−1.51884
$473$	6.17462e43	0.452273
$474$	−1.20190e44	−0.850212
$475$	0	0
$476$	−7.85239e43	−0.518187
$477$	−5.00732e43	−0.319192
$478$	5.16713e43	0.318192
$479$	−1.29441e44	−0.770079	−0.385040	−	0.922900i	$-0.625812\pi$
$479$	−1.29441e44	−0.770079	−0.385040	+	0.922900i	$0.625812\pi$
$480$	0	0
$481$	3.47961e43	0.193258
$482$	1.00504e44	0.539398
$483$	1.24002e44	0.643134
$484$	1.19521e44	0.599094
$485$	0	0
$486$	−1.07279e44	−0.502359
$487$	−2.61068e44	−1.18175	−0.590876	−	0.806762i	$-0.701218\pi$
$487$	−2.61068e44	−1.18175	−0.590876	+	0.806762i	$0.701218\pi$
$488$	2.21666e44	0.970000
$489$	−1.81825e44	−0.769231
$490$	0	0
$491$	−1.66397e44	−0.658114	−0.329057	−	0.944310i	$-0.606731\pi$
$491$	−1.66397e44	−0.658114	−0.329057	+	0.944310i	$0.606731\pi$
$492$	−2.17154e44	−0.830509
$493$	2.27080e43	0.0839857
$494$	6.91068e43	0.247187
$495$	0	0
$496$	−9.91868e41	−0.00331899
$497$	2.65529e44	0.859472
$498$	1.53587e43	0.0480917
$499$	6.52589e43	0.197688	0.0988441	−	0.995103i	$-0.468485\pi$
$499$	6.52589e43	0.197688	0.0988441	+	0.995103i	$0.468485\pi$
$500$	0	0
$501$	4.24542e44	1.20392
$502$	−2.33799e44	−0.641552
$503$	1.10537e43	0.0293519	0.0146759	−	0.999892i	$-0.495328\pi$
$503$	1.10537e43	0.0293519	0.0146759	+	0.999892i	$0.495328\pi$
$504$	−1.48262e44	−0.381000
$505$	0	0
$506$	6.08926e43	0.146582
$507$	2.26915e44	0.528727
$508$	−2.70497e44	−0.610114
$509$	−4.80472e44	−1.04912	−0.524559	−	0.851374i	$-0.675770\pi$
$509$	−4.80472e44	−1.04912	−0.524559	+	0.851374i	$0.675770\pi$
$510$	0	0
$511$	−1.62373e44	−0.332329
$512$	3.48319e43	0.0690276
$513$	4.30404e44	0.825923
$514$	5.79562e44	1.07698
$515$	0	0
$516$	5.19814e44	0.905999
$517$	−7.58928e42	−0.0128117
$518$	−1.13316e44	−0.185289
$519$	2.53503e44	0.401533
$520$	0	0
$521$	−2.39684e44	−0.356301	−0.178150	−	0.984003i	$-0.557011\pi$
$521$	−2.39684e44	−0.356301	−0.178150	+	0.984003i	$0.557011\pi$
$522$	1.66257e43	0.0239451
$523$	−7.19573e44	−1.00415	−0.502073	−	0.864825i	$-0.667429\pi$
$523$	−7.19573e44	−1.00415	−0.502073	+	0.864825i	$0.667429\pi$
$524$	−1.77425e44	−0.239910
$525$	0	0
$526$	4.40592e44	0.559463
$527$	7.60702e43	0.0936138
$528$	−4.95583e42	−0.00591094
$529$	7.16821e43	0.0828690
$530$	0	0
$531$	−6.48388e44	−0.704329
$532$	3.88789e44	0.409423
$533$	−9.25982e44	−0.945374
$534$	3.81191e44	0.377322
$535$	0	0
$536$	−6.44383e44	−0.599688
$537$	9.53729e44	0.860695
$538$	9.88243e44	0.864880
$539$	−8.07041e43	−0.0684985
$540$	0	0
$541$	8.82482e44	0.704613	0.352307	−	0.935885i	$-0.385397\pi$
$541$	8.82482e44	0.704613	0.352307	+	0.935885i	$0.385397\pi$
$542$	9.19689e44	0.712283
$543$	1.21007e45	0.909107
$544$	−1.34967e45	−0.983662
$545$	0	0
$546$	2.89382e44	0.198515
$547$	5.81429e44	0.386996	0.193498	−	0.981101i	$-0.438017\pi$
$547$	5.81429e44	0.386996	0.193498	+	0.981101i	$0.438017\pi$
$548$	−2.63052e44	−0.169888
$549$	7.17759e44	0.449816
$550$	0	0
$551$	−1.12433e44	−0.0663576
$552$	1.32199e45	0.757240
$553$	−2.88335e45	−1.60300
$554$	1.90306e45	1.02693
$555$	0	0
$556$	8.81085e44	0.448006
$557$	−2.61541e45	−1.29101	−0.645504	−	0.763757i	$-0.723353\pi$
$557$	−2.61541e45	−1.29101	−0.645504	+	0.763757i	$0.723353\pi$
$558$	5.56950e43	0.0266902
$559$	2.21657e45	1.03130
$560$	0	0
$561$	3.80082e44	0.166721
$562$	1.90161e45	0.809976
$563$	−1.43034e45	−0.591632	−0.295816	−	0.955245i	$-0.595592\pi$
$563$	−1.43034e45	−0.591632	−0.295816	+	0.955245i	$0.595592\pi$
$564$	−6.38908e43	−0.0256645
$565$	0	0
$566$	−1.30441e45	−0.494245
$567$	7.55537e44	0.278058
$568$	2.83081e45	1.01196
$569$	5.30235e45	1.84127	0.920633	−	0.390430i	$-0.127674\pi$
$569$	5.30235e45	1.84127	0.920633	+	0.390430i	$0.127674\pi$
$570$	0	0
$571$	−3.41063e45	−1.11774	−0.558868	−	0.829257i	$-0.688764\pi$
$571$	−3.41063e45	−1.11774	−0.558868	+	0.829257i	$0.688764\pi$
$572$	−2.45493e44	−0.0781637
$573$	−1.79564e45	−0.555480
$574$	3.01552e45	0.906393
$575$	0	0
$576$	−9.32360e44	−0.264614
$577$	−2.80984e45	−0.774962	−0.387481	−	0.921878i	$-0.626655\pi$
$577$	−2.80984e45	−0.774962	−0.387481	+	0.921878i	$0.626655\pi$
$578$	−1.15915e44	−0.0310692
$579$	−4.47205e45	−1.16496
$580$	0	0
$581$	3.68453e44	0.0906725
$582$	6.07028e44	0.145204
$583$	6.96309e44	0.161909
$584$	−1.73106e45	−0.391292
$585$	0	0
$586$	−1.79230e45	−0.382913
$587$	5.96514e45	1.23906	0.619529	−	0.784973i	$-0.287323\pi$
$587$	5.96514e45	1.23906	0.619529	+	0.784973i	$0.287323\pi$
$588$	−6.79412e44	−0.137217
$589$	−3.76641e44	−0.0739648
$590$	0	0
$591$	6.39162e45	1.18691
$592$	6.96638e43	0.0125805
$593$	1.29305e45	0.227099	0.113549	−	0.993532i	$-0.463778\pi$
$593$	1.29305e45	0.227099	0.113549	+	0.993532i	$0.463778\pi$
$594$	8.85038e44	0.151177
$595$	0	0
$596$	2.70600e45	0.437285
$597$	5.77818e45	0.908270
$598$	2.18593e45	0.334246
$599$	−1.23551e46	−1.83782	−0.918910	−	0.394467i	$-0.870929\pi$
$599$	−1.23551e46	−1.83782	−0.918910	+	0.394467i	$0.870929\pi$
$600$	0	0
$601$	−4.92073e45	−0.692788	−0.346394	−	0.938089i	$-0.612594\pi$
$601$	−4.92073e45	−0.692788	−0.346394	+	0.938089i	$0.612594\pi$
$602$	−7.21841e45	−0.988780
$603$	−2.08653e45	−0.278092
$604$	−6.53556e44	−0.0847566
$605$	0	0
$606$	6.07943e45	0.746559
$607$	−2.23242e45	−0.266786	−0.133393	−	0.991063i	$-0.542587\pi$
$607$	−2.23242e45	−0.266786	−0.133393	+	0.991063i	$0.542587\pi$
$608$	6.68252e45	0.777197
$609$	−4.70807e44	−0.0532914
$610$	0	0
$611$	−2.72441e44	−0.0292141
$612$	−2.71069e45	−0.282932
$613$	−1.28306e45	−0.130362	−0.0651808	−	0.997873i	$-0.520762\pi$
$613$	−1.28306e45	−0.130362	−0.0651808	+	0.997873i	$0.520762\pi$
$614$	5.18414e45	0.512742
$615$	0	0
$616$	2.06170e45	0.193261
$617$	−1.81527e46	−1.65667	−0.828333	−	0.560235i	$-0.810711\pi$
$617$	−1.81527e46	−1.65667	−0.828333	+	0.560235i	$0.810711\pi$
$618$	1.71496e45	0.152386
$619$	−1.88787e46	−1.63334	−0.816670	−	0.577104i	$-0.804183\pi$
$619$	−1.88787e46	−1.63334	−0.816670	+	0.577104i	$0.804183\pi$
$620$	0	0
$621$	1.36142e46	1.11681
$622$	1.24239e45	0.0992472
$623$	9.14471e45	0.711406
$624$	−1.77905e44	−0.0134785
$625$	0	0
$626$	−1.53381e45	−0.110229
$627$	−1.88187e45	−0.131727
$628$	−8.62084e45	−0.587781
$629$	−5.34279e45	−0.354840
$630$	0	0
$631$	−1.84920e46	−1.16547	−0.582733	−	0.812664i	$-0.698017\pi$
$631$	−1.84920e46	−1.16547	−0.582733	+	0.812664i	$0.698017\pi$
$632$	−3.07395e46	−1.88740
$633$	−2.08622e46	−1.24796
$634$	−1.27224e46	−0.741476
$635$	0	0
$636$	5.86192e45	0.324338
$637$	−2.89713e45	−0.156195
$638$	−2.31195e44	−0.0121461
$639$	9.16623e45	0.469274
$640$	0	0
$641$	−2.03686e46	−0.990382	−0.495191	−	0.868784i	$-0.664902\pi$
$641$	−2.03686e46	−0.990382	−0.495191	+	0.868784i	$0.664902\pi$
$642$	1.15973e46	0.549577
$643$	3.33285e46	1.53934	0.769671	−	0.638440i	$-0.220420\pi$
$643$	3.33285e46	1.53934	0.769671	+	0.638440i	$0.220420\pi$
$644$	1.22979e46	0.553622
$645$	0	0
$646$	−1.06110e46	−0.453860
$647$	2.86276e46	1.19361	0.596807	−	0.802385i	$-0.296436\pi$
$647$	2.86276e46	1.19361	0.596807	+	0.802385i	$0.296436\pi$
$648$	8.05480e45	0.327391
$649$	9.01638e45	0.357269
$650$	0	0
$651$	−1.57717e45	−0.0594007
$652$	−1.80324e46	−0.662168
$653$	4.94384e43	0.00177010	0.000885048	−	1.00000i	$-0.499718\pi$
$653$	4.94384e43	0.00177010	0.000885048		1.00000i	$0.499718\pi$
$654$	−2.23273e46	−0.779478
$655$	0	0
$656$	−1.85387e45	−0.0615412
$657$	−5.60522e45	−0.181453
$658$	8.87222e44	0.0280095
$659$	3.69093e45	0.113639	0.0568194	−	0.998384i	$-0.481904\pi$
$659$	3.69093e45	0.113639	0.0568194	+	0.998384i	$0.481904\pi$
$660$	0	0
$661$	−1.92860e46	−0.564830	−0.282415	−	0.959292i	$-0.591136\pi$
$661$	−1.92860e46	−0.564830	−0.282415	+	0.959292i	$0.591136\pi$
$662$	−1.16056e46	−0.331522
$663$	1.36442e46	0.380168
$664$	3.92808e45	0.106760
$665$	0	0
$666$	−3.91173e45	−0.101168
$667$	−3.55638e45	−0.0897287
$668$	4.21037e46	1.03636
$669$	2.52400e46	0.606120
$670$	0	0
$671$	−9.98104e45	−0.228168
$672$	2.79828e46	0.624163
$673$	−6.71207e46	−1.46086	−0.730428	−	0.682989i	$-0.760680\pi$
$673$	−6.71207e46	−1.46086	−0.730428	+	0.682989i	$0.760680\pi$
$674$	−3.16417e45	−0.0672003
$675$	0	0
$676$	2.25042e46	0.455138
$677$	−6.40029e46	−1.26324	−0.631621	−	0.775278i	$-0.717610\pi$
$677$	−6.40029e46	−1.26324	−0.631621	+	0.775278i	$0.717610\pi$
$678$	−1.15869e45	−0.0223191
$679$	1.45625e46	0.273770
$680$	0	0
$681$	6.25268e46	1.11980
$682$	−7.74485e44	−0.0135385
$683$	−8.73990e46	−1.49130	−0.745650	−	0.666338i	$-0.767861\pi$
$683$	−8.73990e46	−1.49130	−0.745650	+	0.666338i	$0.767861\pi$
$684$	1.34212e46	0.223546
$685$	0	0
$686$	4.14772e46	0.658357
$687$	8.01093e46	1.24136
$688$	4.43770e45	0.0671350
$689$	2.49962e46	0.369196
$690$	0	0
$691$	4.89363e46	0.689039	0.344519	−	0.938779i	$-0.388042\pi$
$691$	4.89363e46	0.689039	0.344519	+	0.938779i	$0.388042\pi$
$692$	2.51410e46	0.345647
$693$	6.67584e45	0.0896205
$694$	−1.42859e46	−0.187274
$695$	0	0
$696$	−5.01928e45	−0.0627464
$697$	1.42181e47	1.73580
$698$	−7.99324e46	−0.953034
$699$	−1.12550e45	−0.0131060
$700$	0	0
$701$	−3.51093e46	−0.390009	−0.195004	−	0.980802i	$-0.562472\pi$
$701$	−3.51093e46	−0.390009	−0.195004	+	0.980802i	$0.562472\pi$
$702$	3.17712e46	0.344724
$703$	2.64533e46	0.280361
$704$	1.29652e46	0.134225
$705$	0	0
$706$	−2.57267e46	−0.254159
$707$	1.45845e47	1.40757
$708$	7.59049e46	0.715684
$709$	9.47916e46	0.873187	0.436593	−	0.899659i	$-0.356185\pi$
$709$	9.47916e46	0.873187	0.436593	+	0.899659i	$0.356185\pi$
$710$	0	0
$711$	−9.95351e46	−0.875241
$712$	9.74920e46	0.837624
$713$	−1.19136e46	−0.100015
$714$	−4.44333e46	−0.364492
$715$	0	0
$716$	9.45857e46	0.740901
$717$	−5.05115e46	−0.386656
$718$	6.34577e46	0.474713
$719$	−1.57057e46	−0.114823	−0.0574116	−	0.998351i	$-0.518285\pi$
$719$	−1.57057e46	−0.114823	−0.0574116	+	0.998351i	$0.518285\pi$
$720$	0	0
$721$	4.11417e46	0.287310
$722$	−3.61731e46	−0.246900
$723$	−9.82486e46	−0.655457
$724$	1.20009e47	0.782576
$725$	0	0
$726$	6.76317e46	0.421402
$727$	−5.94494e46	−0.362101	−0.181051	−	0.983474i	$-0.557950\pi$
$727$	−5.94494e46	−0.362101	−0.181051	+	0.983474i	$0.557950\pi$
$728$	7.40112e46	0.440687
$729$	1.61739e47	0.941480
$730$	0	0
$731$	−3.40345e47	−1.89358
$732$	−8.40259e46	−0.457068
$733$	−2.58199e47	−1.37322	−0.686608	−	0.727028i	$-0.740901\pi$
$733$	−2.58199e47	−1.37322	−0.686608	+	0.727028i	$0.740901\pi$
$734$	−7.89885e46	−0.410751
$735$	0	0
$736$	2.11376e47	1.05093
$737$	2.90149e46	0.141061
$738$	1.04098e47	0.494893
$739$	−1.03631e47	−0.481790	−0.240895	−	0.970551i	$-0.577441\pi$
$739$	−1.03631e47	−0.481790	−0.240895	+	0.970551i	$0.577441\pi$
$740$	0	0
$741$	−6.75556e46	−0.300373
$742$	−8.14018e46	−0.353973
$743$	2.33354e47	0.992428	0.496214	−	0.868200i	$-0.334723\pi$
$743$	2.33354e47	0.992428	0.496214	+	0.868200i	$0.334723\pi$
$744$	−1.68142e46	−0.0699397
$745$	0	0
$746$	2.49081e47	0.991176
$747$	1.27192e46	0.0495075
$748$	3.76945e46	0.143516
$749$	2.78217e47	1.03618
$750$	0	0
$751$	−1.20809e47	−0.430568	−0.215284	−	0.976552i	$-0.569068\pi$
$751$	−1.20809e47	−0.430568	−0.215284	+	0.976552i	$0.569068\pi$
$752$	−5.45442e44	−0.00190175
$753$	2.28551e47	0.779591
$754$	−8.29945e45	−0.0276963
$755$	0	0
$756$	1.78742e47	0.570976
$757$	−5.96569e47	−1.86457	−0.932285	−	0.361724i	$-0.882188\pi$
$757$	−5.96569e47	−1.86457	−0.932285	+	0.361724i	$0.882188\pi$
$758$	−7.96864e46	−0.243693
$759$	−5.95258e46	−0.178121
$760$	0	0
$761$	−3.41953e47	−0.979760	−0.489880	−	0.871790i	$-0.662959\pi$
$761$	−3.41953e47	−0.979760	−0.489880	+	0.871790i	$0.662959\pi$
$762$	−1.53063e47	−0.429153
$763$	−5.35630e47	−1.46964
$764$	−1.78082e47	−0.478167
$765$	0	0
$766$	−5.86149e44	−0.00150742
$767$	3.23671e47	0.814668
$768$	2.91792e47	0.718809
$769$	−7.47483e47	−1.80226	−0.901129	−	0.433551i	$-0.857260\pi$
$769$	−7.47483e47	−1.80226	−0.901129	+	0.433551i	$0.857260\pi$
$770$	0	0
$771$	−5.66554e47	−1.30871
$772$	−4.43514e47	−1.00282
$773$	−1.39866e47	−0.309565	−0.154782	−	0.987949i	$-0.549468\pi$
$773$	−1.39866e47	−0.309565	−0.154782	+	0.987949i	$0.549468\pi$
$774$	−2.49184e47	−0.539877
$775$	0	0
$776$	1.55251e47	0.322342
$777$	1.10772e47	0.225156
$778$	2.12170e46	0.0422203
$779$	−7.03968e47	−1.37147
$780$	0	0
$781$	−1.27464e47	−0.238038
$782$	−3.35640e47	−0.613709
$783$	−5.16898e46	−0.0925414
$784$	−5.80022e45	−0.0101679
$785$	0	0
$786$	−1.00397e47	−0.168753
$787$	−6.12282e47	−1.00779	−0.503893	−	0.863766i	$-0.668099\pi$
$787$	−6.12282e47	−1.00779	−0.503893	+	0.863766i	$0.668099\pi$
$788$	6.33886e47	1.02171
$789$	−4.30702e47	−0.679840
$790$	0	0
$791$	−2.77968e46	−0.0420807
$792$	7.11713e46	0.105521
$793$	−3.58300e47	−0.520283
$794$	7.89176e47	1.12237
$795$	0	0
$796$	5.73049e47	0.781855
$797$	7.29365e47	0.974726	0.487363	−	0.873199i	$-0.337959\pi$
$797$	7.29365e47	0.974726	0.487363	+	0.873199i	$0.337959\pi$
$798$	2.19999e47	0.287988
$799$	4.18321e46	0.0536399
$800$	0	0
$801$	3.15681e47	0.388430
$802$	−2.18966e47	−0.263937
$803$	7.79452e46	0.0920414
$804$	2.44264e47	0.282575
$805$	0	0
$806$	−2.78026e46	−0.0308714
$807$	−9.66061e47	−1.05097
$808$	1.55485e48	1.65730
$809$	4.30397e47	0.449489	0.224744	−	0.974418i	$-0.427845\pi$
$809$	4.30397e47	0.449489	0.224744	+	0.974418i	$0.427845\pi$
$810$	0	0
$811$	1.20340e48	1.20660	0.603302	−	0.797513i	$-0.293851\pi$
$811$	1.20340e48	1.20660	0.603302	+	0.797513i	$0.293851\pi$
$812$	−4.66921e46	−0.0458742
$813$	−8.99045e47	−0.865541
$814$	5.43959e46	0.0513173
$815$	0	0
$816$	2.73165e46	0.0247479
$817$	1.68512e48	1.49613
$818$	5.91992e47	0.515094
$819$	2.39650e47	0.204359
$820$	0	0
$821$	1.31428e48	1.07653	0.538264	−	0.842776i	$-0.319080\pi$
$821$	1.31428e48	1.07653	0.538264	+	0.842776i	$0.319080\pi$
$822$	−1.48850e47	−0.119499
$823$	−1.85531e48	−1.45989	−0.729945	−	0.683506i	$-0.760454\pi$
$823$	−1.85531e48	−1.45989	−0.729945	+	0.683506i	$0.760454\pi$
$824$	4.38613e47	0.338285
$825$	0	0
$826$	−1.05406e48	−0.781076
$827$	−3.05619e47	−0.221993	−0.110997	−	0.993821i	$-0.535404\pi$
$827$	−3.05619e47	−0.221993	−0.110997	+	0.993821i	$0.535404\pi$
$828$	4.24530e47	0.302279
$829$	−1.49161e48	−1.04113	−0.520567	−	0.853821i	$-0.674279\pi$
$829$	−1.49161e48	−1.04113	−0.520567	+	0.853821i	$0.674279\pi$
$830$	0	0
$831$	−1.86034e48	−1.24789
$832$	4.65428e47	0.306068
$833$	4.44841e47	0.286789
$834$	4.98569e47	0.315127
$835$	0	0
$836$	−1.86634e47	−0.113393
$837$	−1.73157e47	−0.103150
$838$	1.48554e48	0.867676
$839$	1.58547e48	0.907999	0.454000	−	0.891002i	$-0.349997\pi$
$839$	1.58547e48	0.907999	0.454000	+	0.891002i	$0.349997\pi$
$840$	0	0
$841$	−1.80257e48	−0.992565
$842$	1.64315e48	0.887212
$843$	−1.85893e48	−0.984254
$844$	−2.06900e48	−1.07426
$845$	0	0
$846$	3.06274e46	0.0152933
$847$	1.62248e48	0.794515
$848$	5.00438e46	0.0240336
$849$	1.27513e48	0.600589
$850$	0	0
$851$	8.36751e47	0.379104
$852$	−1.07306e48	−0.476839
$853$	−1.56569e48	−0.682414	−0.341207	−	0.939988i	$-0.610836\pi$
$853$	−1.56569e48	−0.682414	−0.341207	+	0.939988i	$0.610836\pi$
$854$	1.16683e48	0.498830
$855$	0	0
$856$	2.96608e48	1.22002
$857$	3.16984e48	1.27895	0.639476	−	0.768811i	$-0.279151\pi$
$857$	3.16984e48	1.27895	0.639476	+	0.768811i	$0.279151\pi$
$858$	−1.38914e47	−0.0549802
$859$	−8.88897e47	−0.345115	−0.172558	−	0.984999i	$-0.555203\pi$
$859$	−8.88897e47	−0.345115	−0.172558	+	0.984999i	$0.555203\pi$
$860$	0	0
$861$	−2.94784e48	−1.10142
$862$	4.15842e47	0.152426
$863$	−4.50727e48	−1.62082	−0.810411	−	0.585862i	$-0.800756\pi$
$863$	−4.50727e48	−1.62082	−0.810411	+	0.585862i	$0.800756\pi$
$864$	3.07223e48	1.08387
$865$	0	0
$866$	1.47593e48	0.501211
$867$	1.13313e47	0.0377542
$868$	−1.56415e47	−0.0511332
$869$	1.38412e48	0.443963
$870$	0	0
$871$	1.04158e48	0.321657
$872$	−5.71036e48	−1.73038
$873$	5.02708e47	0.149479
$874$	1.66183e48	0.484895
$875$	0	0
$876$	6.56186e47	0.184378
$877$	3.88746e48	1.07195	0.535973	−	0.844235i	$-0.319945\pi$
$877$	3.88746e48	1.07195	0.535973	+	0.844235i	$0.319945\pi$
$878$	1.00528e48	0.272037
$879$	1.75207e48	0.465302
$880$	0	0
$881$	−4.23545e48	−1.08342	−0.541711	−	0.840565i	$-0.682223\pi$
$881$	−4.23545e48	−1.08342	−0.541711	+	0.840565i	$0.682223\pi$
$882$	3.25691e47	0.0817663
$883$	−2.06647e48	−0.509188	−0.254594	−	0.967048i	$-0.581942\pi$
$883$	−2.06647e48	−0.509188	−0.254594	+	0.967048i	$0.581942\pi$
$884$	1.35316e48	0.327255
$885$	0	0
$886$	1.91160e48	0.445389
$887$	1.92447e48	0.440121	0.220060	−	0.975486i	$-0.429375\pi$
$887$	1.92447e48	0.440121	0.220060	+	0.975486i	$0.429375\pi$
$888$	1.18095e48	0.265104
$889$	−3.67195e48	−0.809130
$890$	0	0
$891$	−3.62687e47	−0.0770105
$892$	2.50317e48	0.521759
$893$	−2.07120e47	−0.0423812
$894$	1.53121e48	0.307585
$895$	0	0
$896$	2.86590e48	0.554854
$897$	−2.13686e48	−0.406164
$898$	4.63102e48	0.864205
$899$	4.52331e46	0.00828746
$900$	0	0
$901$	−3.83806e48	−0.677879
$902$	−1.44757e48	−0.251033
$903$	7.05639e48	1.20153
$904$	−2.96342e47	−0.0495467
$905$	0	0
$906$	−3.69820e47	−0.0596177
$907$	2.02864e48	0.321133	0.160567	−	0.987025i	$-0.448668\pi$
$907$	2.02864e48	0.321133	0.160567	+	0.987025i	$0.448668\pi$
$908$	6.20107e48	0.963940
$909$	5.03465e48	0.768537
$910$	0	0
$911$	3.08415e48	0.454028	0.227014	−	0.973891i	$-0.427104\pi$
$911$	3.08415e48	0.454028	0.227014	+	0.973891i	$0.427104\pi$
$912$	−1.35250e47	−0.0195534
$913$	−1.76871e47	−0.0251125
$914$	−6.16894e48	−0.860198
$915$	0	0
$916$	7.94481e48	1.06858
$917$	−2.40852e48	−0.318168
$918$	−4.87833e48	−0.632946
$919$	−7.76805e48	−0.989933	−0.494967	−	0.868912i	$-0.664820\pi$
$919$	−7.76805e48	−0.989933	−0.494967	+	0.868912i	$0.664820\pi$
$920$	0	0
$921$	−5.06778e48	−0.623066
$922$	2.85598e48	0.344902
$923$	−4.57572e48	−0.542789
$924$	−7.81521e47	−0.0910653
$925$	0	0
$926$	−3.18383e48	−0.357988
$927$	1.42024e48	0.156872
$928$	−8.02544e47	−0.0870818
$929$	−1.29507e49	−1.38049	−0.690244	−	0.723576i	$-0.742497\pi$
$929$	−1.29507e49	−1.38049	−0.690244	+	0.723576i	$0.742497\pi$
$930$	0	0
$931$	−2.20251e48	−0.226594
$932$	−1.11621e47	−0.0112819
$933$	−1.21451e48	−0.120602
$934$	−4.80683e48	−0.468960
$935$	0	0
$936$	2.55491e48	0.240616
$937$	−1.36587e49	−1.26388	−0.631940	−	0.775017i	$-0.717741\pi$
$937$	−1.36587e49	−1.26388	−0.631940	+	0.775017i	$0.717741\pi$
$938$	−3.39198e48	−0.308394
$939$	1.49938e48	0.133946
$940$	0	0
$941$	−1.17124e45	−0.000101022 0	−5.05109e−5	−	1.00000i	$-0.500016\pi$
$941$	−1.17124e45	−0.000101022 0	−5.05109e−5		1.00000i	$0.500016\pi$
$942$	−4.87817e48	−0.413444
$943$	−2.22673e49	−1.85449
$944$	6.48009e47	0.0530326
$945$	0	0
$946$	3.46511e48	0.273851
$947$	−1.87235e49	−1.45416	−0.727081	−	0.686551i	$-0.759124\pi$
$947$	−1.87235e49	−1.45416	−0.727081	+	0.686551i	$0.759124\pi$
$948$	1.16523e49	0.889352
$949$	2.79809e48	0.209879
$950$	0	0
$951$	1.24369e49	0.901015
$952$	−1.13641e49	−0.809144
$953$	2.01399e49	1.40937	0.704685	−	0.709521i	$-0.251088\pi$
$953$	2.01399e49	1.40937	0.704685	+	0.709521i	$0.251088\pi$
$954$	−2.81004e48	−0.193270
$955$	0	0
$956$	−5.00946e48	−0.332840
$957$	2.26005e47	0.0147595
$958$	−7.26405e48	−0.466282
$959$	−3.57089e48	−0.225305
$960$	0	0
$961$	−1.62519e49	−0.990762
$962$	1.95271e48	0.117017
$963$	9.60423e48	0.565756
$964$	−9.74376e48	−0.564229
$965$	0	0
$966$	6.95884e48	0.389417
$967$	−1.68504e49	−0.926985	−0.463493	−	0.886101i	$-0.653404\pi$
$967$	−1.68504e49	−0.926985	−0.463493	+	0.886101i	$0.653404\pi$
$968$	1.72973e49	0.935478
$969$	1.03729e49	0.551514
$970$	0	0
$971$	−1.57857e49	−0.811234	−0.405617	−	0.914043i	$-0.632943\pi$
$971$	−1.57857e49	−0.811234	−0.405617	+	0.914043i	$0.632943\pi$
$972$	1.04005e49	0.525485
$973$	1.19606e49	0.594143
$974$	−1.46508e49	−0.715549
$975$	0	0
$976$	−7.17338e47	−0.0338690
$977$	1.78305e49	0.827759	0.413880	−	0.910332i	$-0.364173\pi$
$977$	1.78305e49	0.827759	0.413880	+	0.910332i	$0.364173\pi$
$978$	−1.02038e49	−0.465768
$979$	−4.38981e48	−0.197030
$980$	0	0
$981$	−1.84903e49	−0.802425
$982$	−9.33798e48	−0.398486
$983$	−1.52674e48	−0.0640667	−0.0320333	−	0.999487i	$-0.510198\pi$
$983$	−1.52674e48	−0.0640667	−0.0320333	+	0.999487i	$0.510198\pi$
$984$	−3.14269e49	−1.29683
$985$	0	0
$986$	1.27435e48	0.0508532
$987$	−8.67307e47	−0.0340361
$988$	−6.69980e48	−0.258566
$989$	5.33025e49	2.02306
$990$	0	0
$991$	1.40402e49	0.515416	0.257708	−	0.966223i	$-0.417033\pi$
$991$	1.40402e49	0.515416	0.257708	+	0.966223i	$0.417033\pi$
$992$	−2.68847e48	−0.0970648
$993$	1.13451e49	0.402854
$994$	1.49011e49	0.520408
$995$	0	0
$996$	−1.48900e48	−0.0503056
$997$	7.92661e48	0.263401	0.131701	−	0.991290i	$-0.457956\pi$
$997$	7.92661e48	0.263401	0.131701	+	0.991290i	$0.457956\pi$
$998$	3.66225e48	0.119700
$999$	1.21617e49	0.390988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.b.1.4		5
5.2	odd	4		25.34.b.b.24.7		10
5.3	odd	4		25.34.b.b.24.4		10
5.4	even	2		5.34.a.a.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.2	✓	5	5.4	even	2
25.34.a.b.1.4		5	1.1	even	1	trivial
25.34.b.b.24.4		10	5.3	odd	4
25.34.b.b.24.7		10	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+56118.7 q^{2} -5.48591e7 q^{3} -5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13 q^{7} -7.87377e14 q^{8} -2.54954e15 q^{9} +O(q^{10})\)	\(q+56118.7 q^{2} -5.48591e7 q^{3} -5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13 q^{7} -7.87377e14 q^{8} -2.54954e15 q^{9} +3.54535e16 q^{11} +2.98468e17 q^{12} +1.27272e18 q^{13} -4.14468e18 q^{14} +2.54805e18 q^{16} -1.95420e20 q^{17} -1.43077e20 q^{18} +9.67568e20 q^{19} +4.05165e21 q^{21} +1.98961e21 q^{22} +3.06053e22 q^{23} +4.31948e22 q^{24} +7.14231e22 q^{26} +4.44830e23 q^{27} +4.01821e23 q^{28} -1.16201e23 q^{29} -3.89265e23 q^{31} +6.90651e24 q^{32} -1.94495e24 q^{33} -1.09667e25 q^{34} +1.38711e25 q^{36} +2.73400e25 q^{37} +5.42987e25 q^{38} -6.98200e25 q^{39} -7.27564e26 q^{41} +2.27373e26 q^{42} +1.74161e27 q^{43} -1.92889e26 q^{44} +1.71753e27 q^{46} -2.14063e26 q^{47} -1.39784e26 q^{48} -2.27634e27 q^{49} +1.07206e28 q^{51} -6.92437e27 q^{52} +1.96400e28 q^{53} +2.49633e28 q^{54} +5.81522e28 q^{56} -5.30799e28 q^{57} -6.52106e27 q^{58} +2.54315e29 q^{59} -2.81524e29 q^{61} -2.18451e28 q^{62} +1.88298e29 q^{63} +3.65697e29 q^{64} -1.09148e29 q^{66} +8.18392e29 q^{67} +1.06321e30 q^{68} -1.67898e30 q^{69} -3.59524e30 q^{71} +2.00745e30 q^{72} +2.19852e30 q^{73} +1.53429e30 q^{74} -5.26418e30 q^{76} -2.61844e30 q^{77} -3.91821e30 q^{78} +3.90404e31 q^{79} -1.02299e31 q^{81} -4.08299e31 q^{82} -4.98882e30 q^{83} -2.20435e31 q^{84} +9.77368e31 q^{86} +6.37469e30 q^{87} -2.79153e31 q^{88} -1.23819e32 q^{89} -9.39972e31 q^{91} -1.66512e32 q^{92} +2.13547e31 q^{93} -1.20129e31 q^{94} -3.78885e32 q^{96} -1.97176e32 q^{97} -1.27745e32 q^{98} -9.03903e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) \) 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9	\( 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9 - 287801801877976640 * q^11 + 405379955363513088 * q^12 - 2397201150889907466 * q^13 + 11676449916272482320 * q^14 - 89180089543245957120 * q^16 + 308725634324001653918 * q^17 - 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 10535115771712805413140 * q^21 + 13757888128329419319296 * q^22 - 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 - 424902360762721464761840 * q^26 - 679342131249712739644500 * q^27 + 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1336046479411821372201940 * q^31 + 813043271605502937899008 * q^32 + 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 - 180374200000978588488558720 * q^36 + 142836045294254023962738038 * q^37 + 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 1325620030754525933329256290 * q^41 + 2645870671030939362357320736 * q^42 + 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2874649720834424257835685840 * q^46 + 7724956189479550762134222398 * q^47 + 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 7346719218915268753088875260 * q^51 - 48963787841701555176191049472 * q^52 - 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 144880509244845944794630156800 * q^56 - 208512654554635835530896805800 * q^57 - 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 742889693167672203496619446410 * q^61 - 532537079706659761431026425824 * q^62 + 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 3327517517031282146197646561280 * q^66 + 3757683664783078488809531637718 * q^67 - 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 5502085339682331744817794354940 * q^71 + 15971664273931445780329968326400 * q^72 + 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 + 7186339982587317558706196185600 * q^76 - 47237885671577674597763242652544 * q^77 - 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 78583804836302041006582647314505 * q^81 - 27306575776891610455800103348784 * q^82 - 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 65486114707827974097903540464560 * q^86 - 137286065258860195168416991536900 * q^87 - 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 268937084803738847432203207735340 * q^91 + 697440932909638690403668496563968 * q^92 + 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 344518603172836645970889894051840 * q^96 + 867959773515074594808067717684598 * q^97 + 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * q^99

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