LMFDB - Embedded newform 25.8.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,8,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, 8, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
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:	$7.80962563710$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{649}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 162 $ x^2 - x - 162
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-12.2377$ 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)

$f(q)$	$=$	$q+5.23774 q^{2} +5.47548 q^{3} -100.566 q^{4} +28.6791 q^{6} -769.970 q^{7} -1197.17 q^{8} -2157.02 q^{9} +O(q^{10})$	\(q+5.23774 q^{2} +5.47548 q^{3} -100.566 q^{4} +28.6791 q^{6} -769.970 q^{7} -1197.17 q^{8} -2157.02 q^{9} +5356.43 q^{11} -550.647 q^{12} -14037.0 q^{13} -4032.90 q^{14} +6602.00 q^{16} -12402.4 q^{17} -11297.9 q^{18} -5038.89 q^{19} -4215.95 q^{21} +28055.6 q^{22} +75190.5 q^{23} -6555.08 q^{24} -73522.1 q^{26} -23785.6 q^{27} +77432.9 q^{28} +195529. q^{29} -93568.2 q^{31} +187817. q^{32} +29329.0 q^{33} -64960.4 q^{34} +216923. q^{36} -161554. q^{37} -26392.4 q^{38} -76859.3 q^{39} -28767.5 q^{41} -22082.1 q^{42} -739076. q^{43} -538676. q^{44} +393828. q^{46} -1.06799e6 q^{47} +36149.1 q^{48} -230689. q^{49} -67908.9 q^{51} +1.41165e6 q^{52} -626442. q^{53} -124583. q^{54} +921785. q^{56} -27590.3 q^{57} +1.02413e6 q^{58} +2.14861e6 q^{59} -2.57497e6 q^{61} -490086. q^{62} +1.66084e6 q^{63} +138682. q^{64} +153618. q^{66} +807676. q^{67} +1.24726e6 q^{68} +411704. q^{69} -1.72722e6 q^{71} +2.58232e6 q^{72} +1.74519e6 q^{73} -846178. q^{74} +506742. q^{76} -4.12429e6 q^{77} -402569. q^{78} -2.46887e6 q^{79} +4.58716e6 q^{81} -150677. q^{82} -6.90850e6 q^{83} +423982. q^{84} -3.87109e6 q^{86} +1.07061e6 q^{87} -6.41256e6 q^{88} +2.63567e6 q^{89} +1.08081e7 q^{91} -7.56161e6 q^{92} -512331. q^{93} -5.59385e6 q^{94} +1.02839e6 q^{96} +1.01234e7 q^{97} -1.20829e6 q^{98} -1.15539e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 15 q^{2} - 40 q^{3} + 181 q^{4} + 949 q^{6} + 600 q^{7} - 4305 q^{8} - 2276 q^{9}+O(q^{10}) $ 2 * q - 15 * q^2 - 40 * q^3 + 181 * q^4 + 949 * q^6 + 600 * q^7 - 4305 * q^8 - 2276 * q^9	\( 2 q - 15 q^{2} - 40 q^{3} + 181 q^{4} + 949 q^{6} + 600 q^{7} - 4305 q^{8} - 2276 q^{9} + 4344 q^{11} - 13355 q^{12} - 17680 q^{13} - 31758 q^{14} + 33457 q^{16} - 6870 q^{17} - 8890 q^{18} + 18200 q^{19} - 66516 q^{21} + 48545 q^{22} - 21120 q^{23} + 134775 q^{24} + 204 q^{26} + 81080 q^{27} + 463170 q^{28} + 55800 q^{29} - 301776 q^{31} + 42135 q^{32} + 75370 q^{33} - 176923 q^{34} + 183422 q^{36} - 609860 q^{37} - 496695 q^{38} + 88808 q^{39} - 108486 q^{41} + 1238730 q^{42} - 966400 q^{43} - 823743 q^{44} + 2342934 q^{46} - 1787880 q^{47} - 1185095 q^{48} + 822586 q^{49} - 319496 q^{51} + 385900 q^{52} - 130740 q^{53} - 2246825 q^{54} - 3335850 q^{56} - 1084390 q^{57} + 3851920 q^{58} + 2067600 q^{59} + 582044 q^{61} + 3723570 q^{62} + 1497840 q^{63} - 350479 q^{64} - 778147 q^{66} - 255720 q^{67} + 2804985 q^{68} + 4791468 q^{69} - 4728216 q^{71} + 2952090 q^{72} + 1339430 q^{73} + 8226522 q^{74} + 7050025 q^{76} - 5511300 q^{77} - 3755300 q^{78} - 7186200 q^{79} + 78562 q^{81} + 1462645 q^{82} - 12049560 q^{83} - 17117598 q^{84} + 729444 q^{86} + 7424840 q^{87} - 3266085 q^{88} - 5990850 q^{89} + 5817264 q^{91} - 34679370 q^{92} + 8956020 q^{93} + 8975132 q^{94} + 7653359 q^{96} + 17120020 q^{97} - 22524195 q^{98} - 11433472 q^{99}+O(q^{100}) \) 2 * q - 15 * q^2 - 40 * q^3 + 181 * q^4 + 949 * q^6 + 600 * q^7 - 4305 * q^8 - 2276 * q^9 + 4344 * q^11 - 13355 * q^12 - 17680 * q^13 - 31758 * q^14 + 33457 * q^16 - 6870 * q^17 - 8890 * q^18 + 18200 * q^19 - 66516 * q^21 + 48545 * q^22 - 21120 * q^23 + 134775 * q^24 + 204 * q^26 + 81080 * q^27 + 463170 * q^28 + 55800 * q^29 - 301776 * q^31 + 42135 * q^32 + 75370 * q^33 - 176923 * q^34 + 183422 * q^36 - 609860 * q^37 - 496695 * q^38 + 88808 * q^39 - 108486 * q^41 + 1238730 * q^42 - 966400 * q^43 - 823743 * q^44 + 2342934 * q^46 - 1787880 * q^47 - 1185095 * q^48 + 822586 * q^49 - 319496 * q^51 + 385900 * q^52 - 130740 * q^53 - 2246825 * q^54 - 3335850 * q^56 - 1084390 * q^57 + 3851920 * q^58 + 2067600 * q^59 + 582044 * q^61 + 3723570 * q^62 + 1497840 * q^63 - 350479 * q^64 - 778147 * q^66 - 255720 * q^67 + 2804985 * q^68 + 4791468 * q^69 - 4728216 * q^71 + 2952090 * q^72 + 1339430 * q^73 + 8226522 * q^74 + 7050025 * q^76 - 5511300 * q^77 - 3755300 * q^78 - 7186200 * q^79 + 78562 * q^81 + 1462645 * q^82 - 12049560 * q^83 - 17117598 * q^84 + 729444 * q^86 + 7424840 * q^87 - 3266085 * q^88 - 5990850 * q^89 + 5817264 * q^91 - 34679370 * q^92 + 8956020 * q^93 + 8975132 * q^94 + 7653359 * q^96 + 17120020 * q^97 - 22524195 * q^98 - 11433472 * 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 $

$2$	5.23774	0.462955	0.231478	−	0.972840i	$-0.425644\pi$
$2$	5.23774	0.462955	0.231478	+	0.972840i	$0.425644\pi$
$3$	5.47548	0.117084	0.0585420	−	0.998285i	$-0.481355\pi$
$3$	5.47548	0.117084	0.0585420	+	0.998285i	$0.481355\pi$
$4$	−100.566	−0.785673
$5$	0	0
$5$	0	0
$6$	28.6791	0.0542047
$7$	−769.970	−0.848459	−0.424229	−	0.905555i	$-0.639455\pi$
$7$	−769.970	−0.848459	−0.424229	+	0.905555i	$0.639455\pi$
$8$	−1197.17	−0.826686
$9$	−2157.02	−0.986291
$10$	0	0
$11$	5356.43	1.21339	0.606696	−	0.794934i	$-0.292494\pi$
$11$	5356.43	1.21339	0.606696	+	0.794934i	$0.292494\pi$
$12$	−550.647	−0.0919897
$13$	−14037.0	−1.77204	−0.886018	−	0.463651i	$-0.846539\pi$
$13$	−14037.0	−1.77204	−0.886018	+	0.463651i	$0.846539\pi$
$14$	−4032.90	−0.392798
$15$	0	0
$16$	6602.00	0.402954
$17$	−12402.4	−0.612256	−0.306128	−	0.951990i	$-0.599034\pi$
$17$	−12402.4	−0.612256	−0.306128	+	0.951990i	$0.599034\pi$
$18$	−11297.9	−0.456609
$19$	−5038.89	−0.168538	−0.0842689	−	0.996443i	$-0.526855\pi$
$19$	−5038.89	−0.168538	−0.0842689	+	0.996443i	$0.526855\pi$
$20$	0	0
$21$	−4215.95	−0.0993410
$22$	28055.6	0.561746
$23$	75190.5	1.28859	0.644296	−	0.764776i	$-0.277151\pi$
$23$	75190.5	1.28859	0.644296	+	0.764776i	$0.277151\pi$
$24$	−6555.08	−0.0967918
$25$	0	0
$26$	−73522.1	−0.820373
$27$	−23785.6	−0.232563
$28$	77432.9	0.666611
$29$	195529.	1.48874	0.744368	−	0.667770i	$-0.232751\pi$
$29$	195529.	1.48874	0.744368	+	0.667770i	$0.232751\pi$
$30$	0	0
$31$	−93568.2	−0.564108	−0.282054	−	0.959399i	$-0.591016\pi$
$31$	−93568.2	−0.564108	−0.282054	+	0.959399i	$0.591016\pi$
$32$	187817.	1.01324
$33$	29329.0	0.142069
$34$	−64960.4	−0.283447
$35$	0	0
$36$	216923.	0.774902
$37$	−161554.	−0.524338	−0.262169	−	0.965022i	$-0.584438\pi$
$37$	−161554.	−0.524338	−0.262169	+	0.965022i	$0.584438\pi$
$38$	−26392.4	−0.0780254
$39$	−76859.3	−0.207477
$40$	0	0
$41$	−28767.5	−0.0651867	−0.0325933	−	0.999469i	$-0.510377\pi$
$41$	−28767.5	−0.0651867	−0.0325933	+	0.999469i	$0.510377\pi$
$42$	−22082.1	−0.0459904
$43$	−739076.	−1.41759	−0.708793	−	0.705417i	$-0.750760\pi$
$43$	−739076.	−1.41759	−0.708793	+	0.705417i	$0.750760\pi$
$44$	−538676.	−0.953329
$45$	0	0
$46$	393828.	0.596560
$47$	−1.06799e6	−1.50046	−0.750229	−	0.661178i	$-0.770057\pi$
$47$	−1.06799e6	−1.50046	−0.750229	+	0.661178i	$0.770057\pi$
$48$	36149.1	0.0471795
$49$	−230689.	−0.280118
$50$	0	0
$51$	−67908.9	−0.0716855
$52$	1.41165e6	1.39224
$53$	−626442.	−0.577983	−0.288992	−	0.957332i	$-0.593320\pi$
$53$	−626442.	−0.577983	−0.288992	+	0.957332i	$0.593320\pi$
$54$	−124583.	−0.107666
$55$	0	0
$56$	921785.	0.701409
$57$	−27590.3	−0.0197331
$58$	1.02413e6	0.689217
$59$	2.14861e6	1.36199	0.680997	−	0.732287i	$-0.261547\pi$
$59$	2.14861e6	1.36199	0.680997	+	0.732287i	$0.261547\pi$
$60$	0	0
$61$	−2.57497e6	−1.45251	−0.726253	−	0.687428i	$-0.758740\pi$
$61$	−2.57497e6	−1.45251	−0.726253	+	0.687428i	$0.758740\pi$
$62$	−490086.	−0.261157
$63$	1.66084e6	0.836827
$64$	138682.	0.0661288
$65$	0	0
$66$	153618.	0.0657715
$67$	807676.	0.328077	0.164038	−	0.986454i	$-0.447548\pi$
$67$	807676.	0.328077	0.164038	+	0.986454i	$0.447548\pi$
$68$	1.24726e6	0.481033
$69$	411704.	0.150874
$70$	0	0
$71$	−1.72722e6	−0.572722	−0.286361	−	0.958122i	$-0.592446\pi$
$71$	−1.72722e6	−0.572722	−0.286361	+	0.958122i	$0.592446\pi$
$72$	2.58232e6	0.815353
$73$	1.74519e6	0.525064	0.262532	−	0.964923i	$-0.415442\pi$
$73$	1.74519e6	0.525064	0.262532	+	0.964923i	$0.415442\pi$
$74$	−846178.	−0.242745
$75$	0	0
$76$	506742.	0.132416
$77$	−4.12429e6	−1.02951
$78$	−402569.	−0.0960526
$79$	−2.46887e6	−0.563382	−0.281691	−	0.959505i	$-0.590895\pi$
$79$	−2.46887e6	−0.563382	−0.281691	+	0.959505i	$0.590895\pi$
$80$	0	0
$81$	4.58716e6	0.959062
$82$	−150677.	−0.0301785
$83$	−6.90850e6	−1.32620	−0.663102	−	0.748529i	$-0.730760\pi$
$83$	−6.90850e6	−1.32620	−0.663102	+	0.748529i	$0.730760\pi$
$84$	423982.	0.0780495
$85$	0	0
$86$	−3.87109e6	−0.656279
$87$	1.07061e6	0.174307
$88$	−6.41256e6	−1.00310
$89$	2.63567e6	0.396302	0.198151	−	0.980171i	$-0.436506\pi$
$89$	2.63567e6	0.396302	0.198151	+	0.980171i	$0.436506\pi$
$90$	0	0
$91$	1.08081e7	1.50350
$92$	−7.56161e6	−1.01241
$93$	−512331.	−0.0660480
$94$	−5.59385e6	−0.694645
$95$	0	0
$96$	1.02839e6	0.118634
$97$	1.01234e7	1.12622	0.563112	−	0.826381i	$-0.309604\pi$
$97$	1.01234e7	1.12622	0.563112	+	0.826381i	$0.309604\pi$
$98$	−1.20829e6	−0.129682
$99$	−1.15539e7	−1.19676
$100$	0	0
$101$	−8.33196e6	−0.804679	−0.402339	−	0.915491i	$-0.631803\pi$
$101$	−8.33196e6	−0.804679	−0.402339	+	0.915491i	$0.631803\pi$
$102$	−355689.	−0.0331872
$103$	7.75782e6	0.699535	0.349767	−	0.936837i	$-0.386261\pi$
$103$	7.75782e6	0.699535	0.349767	+	0.936837i	$0.386261\pi$
$104$	1.68047e7	1.46492
$105$	0	0
$106$	−3.28114e6	−0.267580
$107$	−8.86598e6	−0.699654	−0.349827	−	0.936814i	$-0.613760\pi$
$107$	−8.86598e6	−0.699654	−0.349827	+	0.936814i	$0.613760\pi$
$108$	2.39202e6	0.182718
$109$	1.55125e6	0.114734	0.0573668	−	0.998353i	$-0.481730\pi$
$109$	1.55125e6	0.114734	0.0573668	+	0.998353i	$0.481730\pi$
$110$	0	0
$111$	−884585.	−0.0613917
$112$	−5.08334e6	−0.341890
$113$	1.80311e7	1.17557	0.587783	−	0.809019i	$-0.300001\pi$
$113$	1.80311e7	1.17557	0.587783	+	0.809019i	$0.300001\pi$
$114$	−144511.	−0.00913553
$115$	0	0
$116$	−1.96636e7	−1.16966
$117$	3.02781e7	1.74774
$118$	1.12538e7	0.630542
$119$	9.54945e6	0.519474
$120$	0	0
$121$	9.20422e6	0.472322
$122$	−1.34870e7	−0.672445
$123$	−157516.	−0.00763232
$124$	9.40979e6	0.443204
$125$	0	0
$126$	8.69905e6	0.387414
$127$	1.98814e7	0.861258	0.430629	−	0.902529i	$-0.358292\pi$
$127$	1.98814e7	0.861258	0.430629	+	0.902529i	$0.358292\pi$
$128$	−2.33142e7	−0.982621
$129$	−4.04679e6	−0.165977
$130$	0	0
$131$	−5.81990e6	−0.226186	−0.113093	−	0.993584i	$-0.536076\pi$
$131$	−5.81990e6	−0.226186	−0.113093	+	0.993584i	$0.536076\pi$
$132$	−2.94951e6	−0.111620
$133$	3.87979e6	0.142997
$134$	4.23040e6	0.151885
$135$	0	0
$136$	1.48477e7	0.506144
$137$	−3.83328e7	−1.27365	−0.636823	−	0.771010i	$-0.719752\pi$
$137$	−3.83328e7	−1.27365	−0.636823	+	0.771010i	$0.719752\pi$
$138$	2.15640e6	0.0698477
$139$	−3.60826e7	−1.13958	−0.569791	−	0.821789i	$-0.692976\pi$
$139$	−3.60826e7	−1.13958	−0.569791	+	0.821789i	$0.692976\pi$
$140$	0	0
$141$	−5.84775e6	−0.175680
$142$	−9.04673e6	−0.265144
$143$	−7.51883e7	−2.15018
$144$	−1.42406e7	−0.397430
$145$	0	0
$146$	9.14084e6	0.243081
$147$	−1.26313e6	−0.0327973
$148$	1.62469e7	0.411958
$149$	−4.91341e6	−0.121683	−0.0608416	−	0.998147i	$-0.519378\pi$
$149$	−4.91341e6	−0.121683	−0.0608416	+	0.998147i	$0.519378\pi$
$150$	0	0
$151$	4.95186e7	1.17044	0.585220	−	0.810874i	$-0.301008\pi$
$151$	4.95186e7	1.17044	0.585220	+	0.810874i	$0.301008\pi$
$152$	6.03241e6	0.139328
$153$	2.67521e7	0.603863
$154$	−2.16020e7	−0.476619
$155$	0	0
$156$	7.72944e6	0.163009
$157$	5.84517e6	0.120545	0.0602724	−	0.998182i	$-0.480803\pi$
$157$	5.84517e6	0.120545	0.0602724	+	0.998182i	$0.480803\pi$
$158$	−1.29313e7	−0.260821
$159$	−3.43007e6	−0.0676726
$160$	0	0
$161$	−5.78944e7	−1.09332
$162$	2.40264e7	0.444003
$163$	−1.79731e7	−0.325062	−0.162531	−	0.986703i	$-0.551966\pi$
$163$	−1.79731e7	−0.325062	−0.162531	+	0.986703i	$0.551966\pi$
$164$	2.89304e6	0.0512154
$165$	0	0
$166$	−3.61849e7	−0.613973
$167$	−5.72460e7	−0.951124	−0.475562	−	0.879682i	$-0.657755\pi$
$167$	−5.72460e7	−0.951124	−0.475562	+	0.879682i	$0.657755\pi$
$168$	5.04721e6	0.0821238
$169$	1.34289e8	2.14011
$170$	0	0
$171$	1.08690e7	0.166227
$172$	7.43260e7	1.11376
$173$	1.09265e8	1.60442	0.802212	−	0.597039i	$-0.203656\pi$
$173$	1.09265e8	1.60442	0.802212	+	0.597039i	$0.203656\pi$
$174$	5.60759e6	0.0806964
$175$	0	0
$176$	3.53632e7	0.488941
$177$	1.17647e7	0.159468
$178$	1.38050e7	0.183470
$179$	1.98072e7	0.258130	0.129065	−	0.991636i	$-0.458802\pi$
$179$	1.98072e7	0.258130	0.129065	+	0.991636i	$0.458802\pi$
$180$	0	0
$181$	−1.00547e8	−1.26036	−0.630178	−	0.776451i	$-0.717018\pi$
$181$	−1.00547e8	−1.26036	−0.630178	+	0.776451i	$0.717018\pi$
$182$	5.66098e7	0.696053
$183$	−1.40992e7	−0.170065
$184$	−9.00157e7	−1.06526
$185$	0	0
$186$	−2.68345e6	−0.0305773
$187$	−6.64325e7	−0.742908
$188$	1.07403e8	1.17887
$189$	1.83142e7	0.197320
$190$	0	0
$191$	2.28106e7	0.236875	0.118437	−	0.992962i	$-0.462211\pi$
$191$	2.28106e7	0.236875	0.118437	+	0.992962i	$0.462211\pi$
$192$	759351.	0.00774262
$193$	1.92250e6	0.0192493	0.00962465	−	0.999954i	$-0.496936\pi$
$193$	1.92250e6	0.0192493	0.00962465	+	0.999954i	$0.496936\pi$
$194$	5.30237e7	0.521391
$195$	0	0
$196$	2.31995e7	0.220081
$197$	1.98118e7	0.184626	0.0923129	−	0.995730i	$-0.470574\pi$
$197$	1.98118e7	0.184626	0.0923129	+	0.995730i	$0.470574\pi$
$198$	−6.05165e7	−0.554046
$199$	−1.14071e8	−1.02610	−0.513048	−	0.858360i	$-0.671484\pi$
$199$	−1.14071e8	−1.02610	−0.513048	+	0.858360i	$0.671484\pi$
$200$	0	0
$201$	4.42241e6	0.0384125
$202$	−4.36407e7	−0.372530
$203$	−1.50551e8	−1.26313
$204$	6.82933e6	0.0563213
$205$	0	0
$206$	4.06334e7	0.323853
$207$	−1.62187e8	−1.27093
$208$	−9.26722e7	−0.714049
$209$	−2.69905e7	−0.204503
$210$	0	0
$211$	9.50285e6	0.0696410	0.0348205	−	0.999394i	$-0.488914\pi$
$211$	9.50285e6	0.0696410	0.0348205	+	0.999394i	$0.488914\pi$
$212$	6.29988e7	0.454106
$213$	−9.45736e6	−0.0670566
$214$	−4.64377e7	−0.323909
$215$	0	0
$216$	2.84754e7	0.192257
$217$	7.20447e7	0.478622
$218$	8.12507e6	0.0531165
$219$	9.55574e6	0.0614766
$220$	0	0
$221$	1.74092e8	1.08494
$222$	−4.63323e6	−0.0284216
$223$	−1.92299e8	−1.16121	−0.580603	−	0.814187i	$-0.697183\pi$
$223$	−1.92299e8	−1.16121	−0.580603	+	0.814187i	$0.697183\pi$
$224$	−1.44614e8	−0.859689
$225$	0	0
$226$	9.44420e7	0.544234
$227$	1.60189e8	0.908955	0.454478	−	0.890758i	$-0.349826\pi$
$227$	1.60189e8	0.908955	0.454478	+	0.890758i	$0.349826\pi$
$228$	2.77465e6	0.0155037
$229$	1.97660e8	1.08766	0.543832	−	0.839194i	$-0.316973\pi$
$229$	1.97660e8	1.08766	0.543832	+	0.839194i	$0.316973\pi$
$230$	0	0
$231$	−2.25825e7	−0.120540
$232$	−2.34081e8	−1.23072
$233$	1.99180e8	1.03157	0.515786	−	0.856717i	$-0.327500\pi$
$233$	1.99180e8	1.03157	0.515786	+	0.856717i	$0.327500\pi$
$234$	1.58589e8	0.809127
$235$	0	0
$236$	−2.16077e8	−1.07008
$237$	−1.35182e7	−0.0659630
$238$	5.00175e7	0.240493
$239$	−3.31111e8	−1.56885	−0.784424	−	0.620225i	$-0.787041\pi$
$239$	−3.31111e8	−1.56885	−0.784424	+	0.620225i	$0.787041\pi$
$240$	0	0
$241$	−3.68270e8	−1.69475	−0.847377	−	0.530991i	$-0.821820\pi$
$241$	−3.68270e8	−1.69475	−0.847377	+	0.530991i	$0.821820\pi$
$242$	4.82093e7	0.218664
$243$	7.71360e7	0.344854
$244$	2.58955e8	1.14119
$245$	0	0
$246$	−825027.	−0.00353342
$247$	7.07309e7	0.298655
$248$	1.12017e8	0.466340
$249$	−3.78273e7	−0.155277
$250$	0	0
$251$	3.74255e8	1.49386	0.746929	−	0.664903i	$-0.231527\pi$
$251$	3.74255e8	1.49386	0.746929	+	0.664903i	$0.231527\pi$
$252$	−1.67024e8	−0.657472
$253$	4.02753e8	1.56357
$254$	1.04133e8	0.398724
$255$	0	0
$256$	−1.39865e8	−0.521038
$257$	4.57062e8	1.67961	0.839807	−	0.542885i	$-0.182668\pi$
$257$	4.57062e8	1.67961	0.839807	+	0.542885i	$0.182668\pi$
$258$	−2.11960e7	−0.0768397
$259$	1.24392e8	0.444880
$260$	0	0
$261$	−4.21759e8	−1.46833
$262$	−3.04831e7	−0.104714
$263$	−6.77338e7	−0.229594	−0.114797	−	0.993389i	$-0.536622\pi$
$263$	−6.77338e7	−0.229594	−0.114797	+	0.993389i	$0.536622\pi$
$264$	−3.51118e7	−0.117446
$265$	0	0
$266$	2.03214e7	0.0662014
$267$	1.44316e7	0.0464007
$268$	−8.12248e7	−0.257761
$269$	2.21000e7	0.0692244	0.0346122	−	0.999401i	$-0.488980\pi$
$269$	2.21000e7	0.0692244	0.0346122	+	0.999401i	$0.488980\pi$
$270$	0	0
$271$	4.22269e8	1.28883	0.644416	−	0.764675i	$-0.277100\pi$
$271$	4.22269e8	1.28883	0.644416	+	0.764675i	$0.277100\pi$
$272$	−8.18804e7	−0.246711
$273$	5.91793e7	0.176036
$274$	−2.00777e8	−0.589641
$275$	0	0
$276$	−4.14034e7	−0.118537
$277$	−1.98868e8	−0.562195	−0.281097	−	0.959679i	$-0.590698\pi$
$277$	−1.98868e8	−0.562195	−0.281097	+	0.959679i	$0.590698\pi$
$278$	−1.88991e8	−0.527576
$279$	2.01828e8	0.556375
$280$	0	0
$281$	3.88135e8	1.04354	0.521771	−	0.853085i	$-0.325271\pi$
$281$	3.88135e8	1.04354	0.521771	+	0.853085i	$0.325271\pi$
$282$	−3.06290e7	−0.0813318
$283$	−2.98951e8	−0.784056	−0.392028	−	0.919953i	$-0.628226\pi$
$283$	−2.98951e8	−0.784056	−0.392028	+	0.919953i	$0.628226\pi$
$284$	1.73700e8	0.449972
$285$	0	0
$286$	−3.93817e8	−0.995435
$287$	2.21501e7	0.0553082
$288$	−4.05125e8	−0.999346
$289$	−2.56520e8	−0.625142
$290$	0	0
$291$	5.54304e7	0.131863
$292$	−1.75507e8	−0.412528
$293$	−1.77029e8	−0.411158	−0.205579	−	0.978641i	$-0.565908\pi$
$293$	−1.77029e8	−0.411158	−0.205579	+	0.978641i	$0.565908\pi$
$294$	−6.61596e6	−0.0151837
$295$	0	0
$296$	1.93408e8	0.433463
$297$	−1.27406e8	−0.282190
$298$	−2.57351e7	−0.0563339
$299$	−1.05545e9	−2.28343
$300$	0	0
$301$	5.69066e8	1.20276
$302$	2.59366e8	0.541862
$303$	−4.56215e7	−0.0942150
$304$	−3.32667e7	−0.0679130
$305$	0	0
$306$	1.40121e8	0.279562
$307$	−2.25726e8	−0.445243	−0.222622	−	0.974905i	$-0.571461\pi$
$307$	−2.25726e8	−0.445243	−0.222622	+	0.974905i	$0.571461\pi$
$308$	4.14764e8	0.808861
$309$	4.24778e7	0.0819044
$310$	0	0
$311$	−8.14288e8	−1.53503	−0.767515	−	0.641031i	$-0.778507\pi$
$311$	−8.14288e8	−1.53503	−0.767515	+	0.641031i	$0.778507\pi$
$312$	9.20136e7	0.171518
$313$	−6.60615e7	−0.121771	−0.0608854	−	0.998145i	$-0.519392\pi$
$313$	−6.60615e7	−0.121771	−0.0608854	+	0.998145i	$0.519392\pi$
$314$	3.06155e7	0.0558068
$315$	0	0
$316$	2.48284e8	0.442634
$317$	−6.63770e7	−0.117033	−0.0585167	−	0.998286i	$-0.518637\pi$
$317$	−6.63770e7	−0.117033	−0.0585167	+	0.998286i	$0.518637\pi$
$318$	−1.79658e7	−0.0313294
$319$	1.04734e9	1.80642
$320$	0	0
$321$	−4.85455e7	−0.0819184
$322$	−3.03236e8	−0.506157
$323$	6.24942e7	0.103188
$324$	−4.61313e8	−0.753509
$325$	0	0
$326$	−9.41385e7	−0.150489
$327$	8.49386e6	0.0134335
$328$	3.44396e7	0.0538889
$329$	8.22319e8	1.27308
$330$	0	0
$331$	−5.59199e8	−0.847557	−0.423778	−	0.905766i	$-0.639296\pi$
$331$	−5.59199e8	−0.847557	−0.423778	+	0.905766i	$0.639296\pi$
$332$	6.94761e8	1.04196
$333$	3.48475e8	0.517150
$334$	−2.99839e8	−0.440328
$335$	0	0
$336$	−2.78337e7	−0.0400298
$337$	4.77074e8	0.679018	0.339509	−	0.940603i	$-0.389739\pi$
$337$	4.77074e8	0.679018	0.339509	+	0.940603i	$0.389739\pi$
$338$	7.03370e8	0.990775
$339$	9.87287e7	0.137640
$340$	0	0
$341$	−5.01192e8	−0.684485
$342$	5.69289e7	0.0769558
$343$	8.11727e8	1.08613
$344$	8.84799e8	1.17190
$345$	0	0
$346$	5.72301e8	0.742777
$347$	−5.49825e8	−0.706433	−0.353217	−	0.935542i	$-0.614912\pi$
$347$	−5.49825e8	−0.706433	−0.353217	+	0.935542i	$0.614912\pi$
$348$	−1.07667e8	−0.136948
$349$	−2.51578e8	−0.316799	−0.158400	−	0.987375i	$-0.550633\pi$
$349$	−2.51578e8	−0.316799	−0.158400	+	0.987375i	$0.550633\pi$
$350$	0	0
$351$	3.33878e8	0.412110
$352$	1.00603e9	1.22945
$353$	−8.04432e8	−0.973370	−0.486685	−	0.873577i	$-0.661794\pi$
$353$	−8.04432e8	−0.973370	−0.486685	+	0.873577i	$0.661794\pi$
$354$	6.16202e7	0.0738264
$355$	0	0
$356$	−2.65059e8	−0.311364
$357$	5.22878e7	0.0608222
$358$	1.03745e8	0.119503
$359$	1.13834e8	0.129850	0.0649250	−	0.997890i	$-0.479319\pi$
$359$	1.13834e8	0.129850	0.0649250	+	0.997890i	$0.479319\pi$
$360$	0	0
$361$	−8.68481e8	−0.971595
$362$	−5.26638e8	−0.583488
$363$	5.03975e7	0.0553014
$364$	−1.08693e9	−1.18126
$365$	0	0
$366$	−7.38479e7	−0.0787325
$367$	−2.25920e8	−0.238574	−0.119287	−	0.992860i	$-0.538061\pi$
$367$	−2.25920e8	−0.238574	−0.119287	+	0.992860i	$0.538061\pi$
$368$	4.96407e8	0.519243
$369$	6.20521e7	0.0642931
$370$	0	0
$371$	4.82342e8	0.490395
$372$	5.15231e7	0.0518921
$373$	−8.19128e8	−0.817280	−0.408640	−	0.912696i	$-0.633997\pi$
$373$	−8.19128e8	−0.817280	−0.408640	+	0.912696i	$0.633997\pi$
$374$	−3.47956e8	−0.343933
$375$	0	0
$376$	1.27856e9	1.24041
$377$	−2.74464e9	−2.63809
$378$	9.59249e7	0.0913504
$379$	−1.86356e8	−0.175836	−0.0879178	−	0.996128i	$-0.528021\pi$
$379$	−1.86356e8	−0.175836	−0.0879178	+	0.996128i	$0.528021\pi$
$380$	0	0
$381$	1.08860e8	0.100840
$382$	1.19476e8	0.109662
$383$	−1.43839e9	−1.30822	−0.654109	−	0.756400i	$-0.726956\pi$
$383$	−1.43839e9	−1.30822	−0.654109	+	0.756400i	$0.726956\pi$
$384$	−1.27657e8	−0.115049
$385$	0	0
$386$	1.00695e7	0.00891156
$387$	1.59420e9	1.39815
$388$	−1.01807e9	−0.884843
$389$	−1.00373e9	−0.864558	−0.432279	−	0.901740i	$-0.642290\pi$
$389$	−1.00373e9	−0.864558	−0.432279	+	0.901740i	$0.642290\pi$
$390$	0	0
$391$	−9.32540e8	−0.788949
$392$	2.76174e8	0.231570
$393$	−3.18668e7	−0.0264828
$394$	1.03769e8	0.0854735
$395$	0	0
$396$	1.16193e9	0.940261
$397$	9.05187e8	0.726058	0.363029	−	0.931778i	$-0.381743\pi$
$397$	9.05187e8	0.726058	0.363029	+	0.931778i	$0.381743\pi$
$398$	−5.97472e8	−0.475036
$399$	2.12437e7	0.0167427
$400$	0	0
$401$	2.05917e9	1.59473	0.797363	−	0.603500i	$-0.206228\pi$
$401$	2.05917e9	1.59473	0.797363	+	0.603500i	$0.206228\pi$
$402$	2.31634e7	0.0177833
$403$	1.31342e9	0.999619
$404$	8.37913e8	0.632214
$405$	0	0
$406$	−7.88548e8	−0.584773
$407$	−8.65354e8	−0.636229
$408$	8.12985e7	0.0592614
$409$	−6.09853e8	−0.440751	−0.220376	−	0.975415i	$-0.570728\pi$
$409$	−6.09853e8	−0.440751	−0.220376	+	0.975415i	$0.570728\pi$
$410$	0	0
$411$	−2.09891e8	−0.149124
$412$	−7.80173e8	−0.549605
$413$	−1.65436e9	−1.15559
$414$	−8.49495e8	−0.588382
$415$	0	0
$416$	−2.63639e9	−1.79549
$417$	−1.97569e8	−0.133427
$418$	−1.41369e8	−0.0946755
$419$	2.76626e9	1.83715	0.918574	−	0.395248i	$-0.129341\pi$
$419$	2.76626e9	1.83715	0.918574	+	0.395248i	$0.129341\pi$
$420$	0	0
$421$	1.11034e9	0.725219	0.362609	−	0.931941i	$-0.381886\pi$
$421$	1.11034e9	0.725219	0.362609	+	0.931941i	$0.381886\pi$
$422$	4.97734e7	0.0322407
$423$	2.30367e9	1.47989
$424$	7.49957e8	0.477811
$425$	0	0
$426$	−4.95352e7	−0.0310442
$427$	1.98265e9	1.23239
$428$	8.91617e8	0.549699
$429$	−4.11692e8	−0.251751
$430$	0	0
$431$	−1.55134e9	−0.933331	−0.466666	−	0.884434i	$-0.654545\pi$
$431$	−1.55134e9	−0.933331	−0.466666	+	0.884434i	$0.654545\pi$
$432$	−1.57032e8	−0.0937122
$433$	1.19534e9	0.707593	0.353797	−	0.935322i	$-0.384891\pi$
$433$	1.19534e9	0.707593	0.353797	+	0.935322i	$0.384891\pi$
$434$	3.77351e8	0.221581
$435$	0	0
$436$	−1.56004e8	−0.0901430
$437$	−3.78876e8	−0.217176
$438$	5.00505e7	0.0284609
$439$	−2.81223e8	−0.158644	−0.0793221	−	0.996849i	$-0.525276\pi$
$439$	−2.81223e8	−0.158644	−0.0793221	+	0.996849i	$0.525276\pi$
$440$	0	0
$441$	4.97601e8	0.276278
$442$	9.11849e8	0.502279
$443$	2.07780e9	1.13551	0.567756	−	0.823197i	$-0.307812\pi$
$443$	2.07780e9	1.13551	0.567756	+	0.823197i	$0.307812\pi$
$444$	8.89593e7	0.0482337
$445$	0	0
$446$	−1.00721e9	−0.537586
$447$	−2.69033e7	−0.0142472
$448$	−1.06781e8	−0.0561075
$449$	−1.73277e9	−0.903397	−0.451698	−	0.892171i	$-0.649182\pi$
$449$	−1.73277e9	−0.903397	−0.451698	+	0.892171i	$0.649182\pi$
$450$	0	0
$451$	−1.54091e8	−0.0790971
$452$	−1.81331e9	−0.923609
$453$	2.71138e8	0.137040
$454$	8.39029e8	0.420805
$455$	0	0
$456$	3.30303e7	0.0163131
$457$	1.78846e9	0.876541	0.438270	−	0.898843i	$-0.355591\pi$
$457$	1.78846e9	0.876541	0.438270	+	0.898843i	$0.355591\pi$
$458$	1.03529e9	0.503539
$459$	2.94998e8	0.142388
$460$	0	0
$461$	−3.91667e8	−0.186193	−0.0930965	−	0.995657i	$-0.529677\pi$
$461$	−3.91667e8	−0.186193	−0.0930965	+	0.995657i	$0.529677\pi$
$462$	−1.18281e8	−0.0558044
$463$	1.05509e9	0.494034	0.247017	−	0.969011i	$-0.420550\pi$
$463$	1.05509e9	0.494034	0.247017	+	0.969011i	$0.420550\pi$
$464$	1.29088e9	0.599892
$465$	0	0
$466$	1.04325e9	0.477572
$467$	1.73541e9	0.788485	0.394243	−	0.919006i	$-0.371007\pi$
$467$	1.73541e9	0.788485	0.394243	+	0.919006i	$0.371007\pi$
$468$	−3.04495e9	−1.37315
$469$	−6.21886e8	−0.278360
$470$	0	0
$471$	3.20051e7	0.0141139
$472$	−2.57225e9	−1.12594
$473$	−3.95881e9	−1.72009
$474$	−7.08050e7	−0.0305379
$475$	0	0
$476$	−9.60351e8	−0.408137
$477$	1.35125e9	0.570060
$478$	−1.73427e9	−0.726306
$479$	2.46088e8	0.102310	0.0511548	−	0.998691i	$-0.483710\pi$
$479$	2.46088e8	0.102310	0.0511548	+	0.998691i	$0.483710\pi$
$480$	0	0
$481$	2.26773e9	0.929146
$482$	−1.92890e9	−0.784595
$483$	−3.17000e8	−0.128010
$484$	−9.25633e8	−0.371091
$485$	0	0
$486$	4.04018e8	0.159652
$487$	−2.60089e9	−1.02040	−0.510201	−	0.860055i	$-0.670429\pi$
$487$	−2.60089e9	−1.02040	−0.510201	+	0.860055i	$0.670429\pi$
$488$	3.08267e9	1.20077
$489$	−9.84114e7	−0.0380596
$490$	0	0
$491$	3.18729e9	1.21517	0.607584	−	0.794256i	$-0.292139\pi$
$491$	3.18729e9	1.21517	0.607584	+	0.794256i	$0.292139\pi$
$492$	1.58408e7	0.00599651
$493$	−2.42502e9	−0.911488
$494$	3.70470e8	0.138264
$495$	0	0
$496$	−6.17737e8	−0.227310
$497$	1.32991e9	0.485931
$498$	−1.98130e8	−0.0718864
$499$	−3.08098e9	−1.11004	−0.555018	−	0.831838i	$-0.687289\pi$
$499$	−3.08098e9	−1.11004	−0.555018	+	0.831838i	$0.687289\pi$
$500$	0	0
$501$	−3.13449e8	−0.111361
$502$	1.96025e9	0.691590
$503$	−2.17354e9	−0.761517	−0.380759	−	0.924674i	$-0.624337\pi$
$503$	−2.17354e9	−0.761517	−0.380759	+	0.924674i	$0.624337\pi$
$504$	−1.98831e9	−0.691794
$505$	0	0
$506$	2.10951e9	0.723862
$507$	7.35295e8	0.250573
$508$	−1.99939e9	−0.676667
$509$	−1.91522e9	−0.643733	−0.321866	−	0.946785i	$-0.604310\pi$
$509$	−1.91522e9	−0.643733	−0.321866	+	0.946785i	$0.604310\pi$
$510$	0	0
$511$	−1.34374e9	−0.445495
$512$	2.25164e9	0.741404
$513$	1.19853e8	0.0391957
$514$	2.39397e9	0.777586
$515$	0	0
$516$	4.06970e8	0.130403
$517$	−5.72061e9	−1.82065
$518$	6.51532e8	0.205959
$519$	5.98278e8	0.187853
$520$	0	0
$521$	−6.78513e8	−0.210197	−0.105098	−	0.994462i	$-0.533516\pi$
$521$	−6.78513e8	−0.210197	−0.105098	+	0.994462i	$0.533516\pi$
$522$	−2.20906e9	−0.679769
$523$	5.85186e9	1.78870	0.894351	−	0.447366i	$-0.147638\pi$
$523$	5.85186e9	1.78870	0.894351	+	0.447366i	$0.147638\pi$
$524$	5.85285e8	0.177708
$525$	0	0
$526$	−3.54772e8	−0.106292
$527$	1.16047e9	0.345379
$528$	1.93630e8	0.0572472
$529$	2.24878e9	0.660468
$530$	0	0
$531$	−4.63459e9	−1.34332
$532$	−3.90176e8	−0.112349
$533$	4.03810e8	0.115513
$534$	7.55889e7	0.0214814
$535$	0	0
$536$	−9.66925e8	−0.271216
$537$	1.08454e8	0.0302229
$538$	1.15754e8	0.0320478
$539$	−1.23567e9	−0.339893
$540$	0	0
$541$	−7.71811e8	−0.209566	−0.104783	−	0.994495i	$-0.533415\pi$
$541$	−7.71811e8	−0.209566	−0.104783	+	0.994495i	$0.533415\pi$
$542$	2.21173e9	0.596672
$543$	−5.50542e8	−0.147568
$544$	−2.32938e9	−0.620360
$545$	0	0
$546$	3.09966e8	0.0814967
$547$	5.26686e9	1.37593	0.687965	−	0.725744i	$-0.258504\pi$
$547$	5.26686e9	1.37593	0.687965	+	0.725744i	$0.258504\pi$
$548$	3.85498e9	1.00067
$549$	5.55426e9	1.43259
$550$	0	0
$551$	−9.85247e8	−0.250908
$552$	−4.92879e8	−0.124725
$553$	1.90095e9	0.478006
$554$	−1.04162e9	−0.260271
$555$	0	0
$556$	3.62869e9	0.895339
$557$	8.78323e7	0.0215358	0.0107679	−	0.999942i	$-0.496572\pi$
$557$	8.78323e7	0.0215358	0.0107679	+	0.999942i	$0.496572\pi$
$558$	1.05712e9	0.257577
$559$	1.03744e10	2.51201
$560$	0	0
$561$	−3.63750e8	−0.0869826
$562$	2.03295e9	0.483114
$563$	−5.32226e8	−0.125695	−0.0628473	−	0.998023i	$-0.520018\pi$
$563$	−5.32226e8	−0.125695	−0.0628473	+	0.998023i	$0.520018\pi$
$564$	5.88085e8	0.138027
$565$	0	0
$566$	−1.56583e9	−0.362983
$567$	−3.53198e9	−0.813724
$568$	2.06778e9	0.473461
$569$	−7.55216e9	−1.71861	−0.859306	−	0.511461i	$-0.829104\pi$
$569$	−7.55216e9	−1.71861	−0.859306	+	0.511461i	$0.829104\pi$
$570$	0	0
$571$	−2.55147e9	−0.573541	−0.286771	−	0.957999i	$-0.592582\pi$
$571$	−2.55147e9	−0.573541	−0.286771	+	0.957999i	$0.592582\pi$
$572$	7.56139e9	1.68933
$573$	1.24899e8	0.0277343
$574$	1.16017e8	0.0256052
$575$	0	0
$576$	−2.99140e8	−0.0652222
$577$	−5.53852e9	−1.20027	−0.600135	−	0.799899i	$-0.704886\pi$
$577$	−5.53852e9	−1.20027	−0.600135	+	0.799899i	$0.704886\pi$
$578$	−1.34358e9	−0.289413
$579$	1.05266e7	0.00225379
$580$	0	0
$581$	5.31934e9	1.12523
$582$	2.90330e8	0.0610466
$583$	−3.35550e9	−0.701321
$584$	−2.08929e9	−0.434063
$585$	0	0
$586$	−9.27233e8	−0.190348
$587$	−4.73642e9	−0.966533	−0.483266	−	0.875473i	$-0.660550\pi$
$587$	−4.73642e9	−0.966533	−0.483266	+	0.875473i	$0.660550\pi$
$588$	1.27028e8	0.0257680
$589$	4.71480e8	0.0950735
$590$	0	0
$591$	1.08479e8	0.0216167
$592$	−1.06658e9	−0.211284
$593$	−1.44860e9	−0.285272	−0.142636	−	0.989775i	$-0.545558\pi$
$593$	−1.44860e9	−0.285272	−0.142636	+	0.989775i	$0.545558\pi$
$594$	−6.67319e8	−0.130641
$595$	0	0
$596$	4.94122e8	0.0956032
$597$	−6.24591e8	−0.120139
$598$	−5.52816e9	−1.05713
$599$	1.04150e9	0.198001	0.0990005	−	0.995087i	$-0.468435\pi$
$599$	1.04150e9	0.198001	0.0990005	+	0.995087i	$0.468435\pi$
$600$	0	0
$601$	−7.31995e9	−1.37546	−0.687729	−	0.725967i	$-0.741392\pi$
$601$	−7.31995e9	−1.37546	−0.687729	+	0.725967i	$0.741392\pi$
$602$	2.98062e9	0.556825
$603$	−1.74217e9	−0.323579
$604$	−4.97990e9	−0.919583
$605$	0	0
$606$	−2.38953e8	−0.0436173
$607$	−6.16291e9	−1.11847	−0.559237	−	0.829008i	$-0.688906\pi$
$607$	−6.16291e9	−1.11847	−0.559237	+	0.829008i	$0.688906\pi$
$608$	−9.46391e8	−0.170769
$609$	−8.24340e8	−0.147892
$610$	0	0
$611$	1.49914e10	2.65887
$612$	−2.69036e9	−0.474439
$613$	−3.18382e8	−0.0558260	−0.0279130	−	0.999610i	$-0.508886\pi$
$613$	−3.18382e8	−0.0558260	−0.0279130	+	0.999610i	$0.508886\pi$
$614$	−1.18229e9	−0.206128
$615$	0	0
$616$	4.93748e9	0.851085
$617$	7.13555e9	1.22301	0.611505	−	0.791241i	$-0.290565\pi$
$617$	7.13555e9	1.22301	0.611505	+	0.791241i	$0.290565\pi$
$618$	2.22487e8	0.0379180
$619$	−9.96303e9	−1.68840	−0.844198	−	0.536031i	$-0.819923\pi$
$619$	−9.96303e9	−1.68840	−0.844198	+	0.536031i	$0.819923\pi$
$620$	0	0
$621$	−1.78845e9	−0.299679
$622$	−4.26503e9	−0.710650
$623$	−2.02939e9	−0.336246
$624$	−5.07425e8	−0.0836037
$625$	0	0
$626$	−3.46013e8	−0.0563744
$627$	−1.47786e8	−0.0239440
$628$	−5.87826e8	−0.0947087
$629$	2.00365e9	0.321030
$630$	0	0
$631$	−4.94300e9	−0.783227	−0.391614	−	0.920130i	$-0.628083\pi$
$631$	−4.94300e9	−0.783227	−0.391614	+	0.920130i	$0.628083\pi$
$632$	2.95565e9	0.465740
$633$	5.20326e7	0.00815385
$634$	−3.47665e8	−0.0541813
$635$	0	0
$636$	3.44949e8	0.0531685
$637$	3.23818e9	0.496379
$638$	5.48568e9	0.836292
$639$	3.72565e9	0.564871
$640$	0	0
$641$	−2.18024e9	−0.326965	−0.163482	−	0.986546i	$-0.552273\pi$
$641$	−2.18024e9	−0.326965	−0.163482	+	0.986546i	$0.552273\pi$
$642$	−2.54269e8	−0.0379245
$643$	−8.70849e9	−1.29183	−0.645913	−	0.763411i	$-0.723523\pi$
$643$	−8.70849e9	−1.29183	−0.645913	+	0.763411i	$0.723523\pi$
$644$	5.82221e9	0.858989
$645$	0	0
$646$	3.27328e8	0.0477716
$647$	−4.57610e9	−0.664249	−0.332124	−	0.943236i	$-0.607765\pi$
$647$	−4.57610e9	−0.664249	−0.332124	+	0.943236i	$0.607765\pi$
$648$	−5.49161e9	−0.792843
$649$	1.15089e10	1.65263
$650$	0	0
$651$	3.94479e8	0.0560390
$652$	1.80749e9	0.255393
$653$	9.23098e9	1.29733	0.648667	−	0.761072i	$-0.275327\pi$
$653$	9.23098e9	1.29733	0.648667	+	0.761072i	$0.275327\pi$
$654$	4.44886e7	0.00621909
$655$	0	0
$656$	−1.89923e8	−0.0262672
$657$	−3.76440e9	−0.517866
$658$	4.30709e9	0.589378
$659$	−8.30221e9	−1.13004	−0.565021	−	0.825077i	$-0.691132\pi$
$659$	−8.30221e9	−1.13004	−0.565021	+	0.825077i	$0.691132\pi$
$660$	0	0
$661$	2.67892e9	0.360791	0.180395	−	0.983594i	$-0.442262\pi$
$661$	2.67892e9	0.360791	0.180395	+	0.983594i	$0.442262\pi$
$662$	−2.92894e9	−0.392381
$663$	9.53237e8	0.127029
$664$	8.27064e9	1.09635
$665$	0	0
$666$	1.82522e9	0.239417
$667$	1.47019e10	1.91837
$668$	5.75700e9	0.747272
$669$	−1.05293e9	−0.135959
$670$	0	0
$671$	−1.37927e10	−1.76246
$672$	−7.91829e8	−0.100656
$673$	8.63768e9	1.09231	0.546153	−	0.837685i	$-0.316092\pi$
$673$	8.63768e9	1.09231	0.546153	+	0.837685i	$0.316092\pi$
$674$	2.49879e9	0.314355
$675$	0	0
$676$	−1.35049e10	−1.68143
$677$	8.17701e9	1.01282	0.506412	−	0.862291i	$-0.330971\pi$
$677$	8.17701e9	1.01282	0.506412	+	0.862291i	$0.330971\pi$
$678$	5.17115e8	0.0637211
$679$	−7.79471e9	−0.955555
$680$	0	0
$681$	8.77112e8	0.106424
$682$	−2.62511e9	−0.316886
$683$	3.81811e9	0.458539	0.229269	−	0.973363i	$-0.426366\pi$
$683$	3.81811e9	0.458539	0.229269	+	0.973363i	$0.426366\pi$
$684$	−1.09305e9	−0.130600
$685$	0	0
$686$	4.25162e9	0.502828
$687$	1.08228e9	0.127348
$688$	−4.87938e9	−0.571222
$689$	8.79336e9	1.02421
$690$	0	0
$691$	1.38590e10	1.59794	0.798969	−	0.601372i	$-0.205379\pi$
$691$	1.38590e10	1.59794	0.798969	+	0.601372i	$0.205379\pi$
$692$	−1.09883e10	−1.26055
$693$	8.89618e9	1.01540
$694$	−2.87984e9	−0.327047
$695$	0	0
$696$	−1.28171e9	−0.144097
$697$	3.56785e8	0.0399110
$698$	−1.31770e9	−0.146664
$699$	1.09061e9	0.120781
$700$	0	0
$701$	−4.38274e9	−0.480543	−0.240271	−	0.970706i	$-0.577236\pi$
$701$	−4.38274e9	−0.480543	−0.240271	+	0.970706i	$0.577236\pi$
$702$	1.74877e9	0.190788
$703$	8.14053e8	0.0883708
$704$	7.42842e8	0.0802402
$705$	0	0
$706$	−4.21341e9	−0.450627
$707$	6.41536e9	0.682737
$708$	−1.18312e9	−0.125289
$709$	−5.46537e9	−0.575914	−0.287957	−	0.957643i	$-0.592976\pi$
$709$	−5.46537e9	−0.575914	−0.287957	+	0.957643i	$0.592976\pi$
$710$	0	0
$711$	5.32539e9	0.555659
$712$	−3.15535e9	−0.327618
$713$	−7.03543e9	−0.726905
$714$	2.73870e8	0.0281579
$715$	0	0
$716$	−1.99194e9	−0.202806
$717$	−1.81299e9	−0.183687
$718$	5.96233e8	0.0601147
$719$	−7.24738e9	−0.727160	−0.363580	−	0.931563i	$-0.618446\pi$
$719$	−7.24738e9	−0.727160	−0.363580	+	0.931563i	$0.618446\pi$
$720$	0	0
$721$	−5.97329e9	−0.593526
$722$	−4.54888e9	−0.449805
$723$	−2.01646e9	−0.198429
$724$	1.01116e10	0.990227
$725$	0	0
$726$	2.63969e8	0.0256021
$727$	−1.61701e10	−1.56078	−0.780392	−	0.625291i	$-0.784980\pi$
$727$	−1.61701e10	−1.56078	−0.780392	+	0.625291i	$0.784980\pi$
$728$	−1.29391e10	−1.24292
$729$	−9.60977e9	−0.918685
$730$	0	0
$731$	9.16629e9	0.867926
$732$	1.41790e9	0.133616
$733$	−6.59871e9	−0.618864	−0.309432	−	0.950922i	$-0.600139\pi$
$733$	−6.59871e9	−0.618864	−0.309432	+	0.950922i	$0.600139\pi$
$734$	−1.18331e9	−0.110449
$735$	0	0
$736$	1.41221e10	1.30565
$737$	4.32626e9	0.398086
$738$	3.25013e8	0.0297648
$739$	−4.52765e8	−0.0412683	−0.0206342	−	0.999787i	$-0.506569\pi$
$739$	−4.52765e8	−0.0412683	−0.0206342	+	0.999787i	$0.506569\pi$
$740$	0	0
$741$	3.87285e8	0.0349677
$742$	2.52638e9	0.227031
$743$	−2.03152e10	−1.81702	−0.908509	−	0.417864i	$-0.862779\pi$
$743$	−2.03152e10	−1.81702	−0.908509	+	0.417864i	$0.862779\pi$
$744$	6.13346e8	0.0546010
$745$	0	0
$746$	−4.29038e9	−0.378364
$747$	1.49018e10	1.30802
$748$	6.68085e9	0.583682
$749$	6.82654e9	0.593628
$750$	0	0
$751$	1.40167e10	1.20755	0.603776	−	0.797154i	$-0.293662\pi$
$751$	1.40167e10	1.20755	0.603776	+	0.797154i	$0.293662\pi$
$752$	−7.05086e9	−0.604616
$753$	2.04922e9	0.174907
$754$	−1.43757e10	−1.22132
$755$	0	0
$756$	−1.84179e9	−0.155029
$757$	1.74979e10	1.46605	0.733026	−	0.680200i	$-0.238107\pi$
$757$	1.74979e10	1.46605	0.733026	+	0.680200i	$0.238107\pi$
$758$	−9.76086e8	−0.0814040
$759$	2.20526e9	0.183069
$760$	0	0
$761$	7.69298e9	0.632774	0.316387	−	0.948630i	$-0.397530\pi$
$761$	7.69298e9	0.632774	0.316387	+	0.948630i	$0.397530\pi$
$762$	5.70180e8	0.0466842
$763$	−1.19442e9	−0.0973466
$764$	−2.29397e9	−0.186106
$765$	0	0
$766$	−7.53390e9	−0.605646
$767$	−3.01600e10	−2.41350
$768$	−7.65829e8	−0.0610053
$769$	−6.85942e9	−0.543933	−0.271967	−	0.962307i	$-0.587674\pi$
$769$	−6.85942e9	−0.543933	−0.271967	+	0.962307i	$0.587674\pi$
$770$	0	0
$771$	2.50263e9	0.196656
$772$	−1.93338e8	−0.0151236
$773$	8.93170e9	0.695514	0.347757	−	0.937585i	$-0.386943\pi$
$773$	8.93170e9	0.695514	0.347757	+	0.937585i	$0.386943\pi$
$774$	8.35001e9	0.647282
$775$	0	0
$776$	−1.21194e10	−0.931034
$777$	6.81104e8	0.0520883
$778$	−5.25728e9	−0.400251
$779$	1.44956e8	0.0109864
$780$	0	0
$781$	−9.25175e9	−0.694937
$782$	−4.88440e9	−0.365248
$783$	−4.65076e9	−0.346225
$784$	−1.52301e9	−0.112875
$785$	0	0
$786$	−1.66910e8	−0.0122603
$787$	5.20674e9	0.380762	0.190381	−	0.981710i	$-0.439028\pi$
$787$	5.20674e9	0.380762	0.190381	+	0.981710i	$0.439028\pi$
$788$	−1.99240e9	−0.145055
$789$	−3.70875e8	−0.0268818
$790$	0	0
$791$	−1.38834e10	−0.997419
$792$	1.38320e10	0.989344
$793$	3.61448e10	2.57389
$794$	4.74113e9	0.336132
$795$	0	0
$796$	1.14716e10	0.806176
$797$	−1.96111e10	−1.37214	−0.686068	−	0.727538i	$-0.740665\pi$
$797$	−1.96111e10	−1.37214	−0.686068	+	0.727538i	$0.740665\pi$
$798$	1.11269e8	0.00775112
$799$	1.32456e10	0.918666
$800$	0	0
$801$	−5.68520e9	−0.390870
$802$	1.07854e10	0.738287
$803$	9.34798e9	0.637109
$804$	−4.44745e8	−0.0301797
$805$	0	0
$806$	6.87933e9	0.462779
$807$	1.21008e8	0.00810508
$808$	9.97477e9	0.665217
$809$	1.99512e10	1.32479	0.662397	−	0.749153i	$-0.269539\pi$
$809$	1.99512e10	1.32479	0.662397	+	0.749153i	$0.269539\pi$
$810$	0	0
$811$	2.18039e9	0.143536	0.0717679	−	0.997421i	$-0.477136\pi$
$811$	2.18039e9	0.143536	0.0717679	+	0.997421i	$0.477136\pi$
$812$	1.51403e10	0.992407
$813$	2.31212e9	0.150902
$814$	−4.53250e9	−0.294545
$815$	0	0
$816$	−4.48334e8	−0.0288859
$817$	3.72412e9	0.238917
$818$	−3.19425e9	−0.204048
$819$	−2.33132e10	−1.48289
$820$	0	0
$821$	−2.52847e10	−1.59462	−0.797310	−	0.603570i	$-0.793744\pi$
$821$	−2.52847e10	−1.59462	−0.797310	+	0.603570i	$0.793744\pi$
$822$	−1.09935e9	−0.0690375
$823$	−1.86851e10	−1.16841	−0.584205	−	0.811606i	$-0.698594\pi$
$823$	−1.86851e10	−1.16841	−0.584205	+	0.811606i	$0.698594\pi$
$824$	−9.28742e9	−0.578296
$825$	0	0
$826$	−8.66512e9	−0.534989
$827$	7.19901e9	0.442592	0.221296	−	0.975207i	$-0.428971\pi$
$827$	7.19901e9	0.442592	0.221296	+	0.975207i	$0.428971\pi$
$828$	1.63105e10	0.998532
$829$	1.83330e10	1.11762	0.558808	−	0.829297i	$-0.311259\pi$
$829$	1.83330e10	1.11762	0.558808	+	0.829297i	$0.311259\pi$
$830$	0	0
$831$	−1.08890e9	−0.0658240
$832$	−1.94668e9	−0.117183
$833$	2.86109e9	0.171504
$834$	−1.03482e9	−0.0617707
$835$	0	0
$836$	2.71433e9	0.160672
$837$	2.22557e9	0.131191
$838$	1.44890e10	0.850517
$839$	2.42360e10	1.41675	0.708376	−	0.705835i	$-0.249428\pi$
$839$	2.42360e10	1.41675	0.708376	+	0.705835i	$0.249428\pi$
$840$	0	0
$841$	2.09816e10	1.21633
$842$	5.81568e9	0.335744
$843$	2.12522e9	0.122182
$844$	−9.55664e8	−0.0547150
$845$	0	0
$846$	1.20660e10	0.685122
$847$	−7.08698e9	−0.400746
$848$	−4.13577e9	−0.232901
$849$	−1.63690e9	−0.0918004
$850$	0	0
$851$	−1.21473e10	−0.675658
$852$	9.51090e8	0.0526845
$853$	−3.21411e10	−1.77312	−0.886561	−	0.462612i	$-0.846912\pi$
$853$	−3.21411e10	−1.77312	−0.886561	+	0.462612i	$0.846912\pi$
$854$	1.03846e10	0.570541
$855$	0	0
$856$	1.06141e10	0.578395
$857$	−9.48584e9	−0.514805	−0.257403	−	0.966304i	$-0.582867\pi$
$857$	−9.48584e9	−0.514805	−0.257403	+	0.966304i	$0.582867\pi$
$858$	−2.15633e9	−0.116550
$859$	−1.33721e10	−0.719819	−0.359910	−	0.932987i	$-0.617192\pi$
$859$	−1.33721e10	−0.719819	−0.359910	+	0.932987i	$0.617192\pi$
$860$	0	0
$861$	1.21283e8	0.00647571
$862$	−8.12550e9	−0.432091
$863$	−1.13928e10	−0.603381	−0.301690	−	0.953406i	$-0.597551\pi$
$863$	−1.13928e10	−0.603381	−0.301690	+	0.953406i	$0.597551\pi$
$864$	−4.46734e9	−0.235641
$865$	0	0
$866$	6.26088e9	0.327584
$867$	−1.40457e9	−0.0731941
$868$	−7.24525e9	−0.376040
$869$	−1.32243e10	−0.683604
$870$	0	0
$871$	−1.13373e10	−0.581364
$872$	−1.85711e9	−0.0948486
$873$	−2.18363e10	−1.11079
$874$	−1.98446e9	−0.100543
$875$	0	0
$876$	−9.60983e8	−0.0483005
$877$	−1.45509e10	−0.728435	−0.364218	−	0.931314i	$-0.618664\pi$
$877$	−1.45509e10	−0.728435	−0.364218	+	0.931314i	$0.618664\pi$
$878$	−1.47297e9	−0.0734452
$879$	−9.69320e8	−0.0481400
$880$	0	0
$881$	−5.46095e9	−0.269062	−0.134531	−	0.990909i	$-0.542953\pi$
$881$	−5.46095e9	−0.269062	−0.134531	+	0.990909i	$0.542953\pi$
$882$	2.60630e9	0.127904
$883$	1.95772e10	0.956948	0.478474	−	0.878102i	$-0.341190\pi$
$883$	1.95772e10	0.956948	0.478474	+	0.878102i	$0.341190\pi$
$884$	−1.75078e10	−0.852408
$885$	0	0
$886$	1.08830e10	0.525691
$887$	−1.35654e10	−0.652678	−0.326339	−	0.945253i	$-0.605815\pi$
$887$	−1.35654e10	−0.652678	−0.326339	+	0.945253i	$0.605815\pi$
$888$	1.05900e9	0.0507516
$889$	−1.53081e10	−0.730742
$890$	0	0
$891$	2.45708e10	1.16372
$892$	1.93387e10	0.912328
$893$	5.38148e9	0.252884
$894$	−1.40912e8	−0.00659580
$895$	0	0
$896$	1.79513e10	0.833714
$897$	−5.77908e9	−0.267353
$898$	−9.07579e9	−0.418232
$899$	−1.82953e10	−0.839807
$900$	0	0
$901$	7.76936e9	0.353874
$902$	−8.07090e8	−0.0366184
$903$	3.11591e9	0.140824
$904$	−2.15862e10	−0.971824
$905$	0	0
$906$	1.42015e9	0.0634433
$907$	7.63541e9	0.339787	0.169894	−	0.985462i	$-0.445658\pi$
$907$	7.63541e9	0.339787	0.169894	+	0.985462i	$0.445658\pi$
$908$	−1.61096e10	−0.714141
$909$	1.79722e10	0.793648
$910$	0	0
$911$	−2.03069e10	−0.889875	−0.444937	−	0.895562i	$-0.646774\pi$
$911$	−2.03069e10	−0.889875	−0.444937	+	0.895562i	$0.646774\pi$
$912$	−1.82151e8	−0.00795152
$913$	−3.70049e10	−1.60921
$914$	9.36748e9	0.405799
$915$	0	0
$916$	−1.98779e10	−0.854547
$917$	4.48115e9	0.191910
$918$	1.54512e9	0.0659193
$919$	1.93832e10	0.823797	0.411899	−	0.911230i	$-0.364866\pi$
$919$	1.93832e10	0.823797	0.411899	+	0.911230i	$0.364866\pi$
$920$	0	0
$921$	−1.23596e9	−0.0521309
$922$	−2.05145e9	−0.0861990
$923$	2.42450e10	1.01488
$924$	2.27103e9	0.0947047
$925$	0	0
$926$	5.52629e9	0.228715
$927$	−1.67338e10	−0.689945
$928$	3.67237e10	1.50844
$929$	1.17298e10	0.479993	0.239997	−	0.970774i	$-0.422854\pi$
$929$	1.17298e10	0.479993	0.239997	+	0.970774i	$0.422854\pi$
$930$	0	0
$931$	1.16242e9	0.0472104
$932$	−2.00307e10	−0.810478
$933$	−4.45862e9	−0.179727
$934$	9.08964e9	0.365033
$935$	0	0
$936$	−3.62480e10	−1.44484
$937$	1.41104e10	0.560340	0.280170	−	0.959950i	$-0.409609\pi$
$937$	1.41104e10	0.560340	0.280170	+	0.959950i	$0.409609\pi$
$938$	−3.25728e9	−0.128868
$939$	−3.61718e8	−0.0142574
$940$	0	0
$941$	1.98332e10	0.775942	0.387971	−	0.921672i	$-0.373176\pi$
$941$	1.98332e10	0.775942	0.387971	+	0.921672i	$0.373176\pi$
$942$	1.67634e8	0.00653409
$943$	−2.16304e9	−0.0839990
$944$	1.41851e10	0.548821
$945$	0	0
$946$	−2.07352e10	−0.796324
$947$	4.96249e10	1.89878	0.949390	−	0.314098i	$-0.101702\pi$
$947$	4.96249e10	1.89878	0.949390	+	0.314098i	$0.101702\pi$
$948$	1.35948e9	0.0518253
$949$	−2.44972e10	−0.930432
$950$	0	0
$951$	−3.63446e8	−0.0137028
$952$	−1.14323e10	−0.429442
$953$	3.24475e10	1.21438	0.607192	−	0.794555i	$-0.292296\pi$
$953$	3.24475e10	1.21438	0.607192	+	0.794555i	$0.292296\pi$
$954$	7.07748e9	0.263912
$955$	0	0
$956$	3.32985e10	1.23260
$957$	5.73467e9	0.211503
$958$	1.28895e9	0.0473648
$959$	2.95151e10	1.08064
$960$	0	0
$961$	−1.87576e10	−0.681782
$962$	1.18778e10	0.430153
$963$	1.91241e10	0.690063
$964$	3.70355e10	1.33152
$965$	0	0
$966$	−1.66036e9	−0.0592629
$967$	−6.43301e9	−0.228782	−0.114391	−	0.993436i	$-0.536492\pi$
$967$	−6.43301e9	−0.228782	−0.114391	+	0.993436i	$0.536492\pi$
$968$	−1.10190e10	−0.390462
$969$	3.42186e8	0.0120817
$970$	0	0
$971$	7.99885e9	0.280389	0.140194	−	0.990124i	$-0.455227\pi$
$971$	7.99885e9	0.280389	0.140194	+	0.990124i	$0.455227\pi$
$972$	−7.75726e9	−0.270942
$973$	2.77825e10	0.966889
$974$	−1.36228e10	−0.472400
$975$	0	0
$976$	−1.69999e10	−0.585293
$977$	2.43029e10	0.833733	0.416866	−	0.908968i	$-0.363128\pi$
$977$	2.43029e10	0.833733	0.416866	+	0.908968i	$0.363128\pi$
$978$	−5.15453e8	−0.0176199
$979$	1.41178e10	0.480871
$980$	0	0
$981$	−3.34609e9	−0.113161
$982$	1.66942e10	0.562568
$983$	2.05054e10	0.688544	0.344272	−	0.938870i	$-0.388126\pi$
$983$	2.05054e10	0.688544	0.344272	+	0.938870i	$0.388126\pi$
$984$	1.88573e8	0.00630953
$985$	0	0
$986$	−1.27016e10	−0.421978
$987$	4.50259e9	0.149057
$988$	−7.11313e9	−0.234645
$989$	−5.55714e10	−1.82669
$990$	0	0
$991$	−3.93587e10	−1.28464	−0.642322	−	0.766435i	$-0.722029\pi$
$991$	−3.93587e10	−1.28464	−0.642322	+	0.766435i	$0.722029\pi$
$992$	−1.75737e10	−0.571574
$993$	−3.06188e9	−0.0992353
$994$	6.96571e9	0.224964
$995$	0	0
$996$	3.80415e9	0.121997
$997$	−2.18052e10	−0.696831	−0.348416	−	0.937340i	$-0.613280\pi$
$997$	−2.18052e10	−0.696831	−0.348416	+	0.937340i	$0.613280\pi$
$998$	−1.61374e10	−0.513897
$999$	3.84266e9	0.121942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.a.c.1.2	✓	2
3.2	odd	2		225.8.a.v.1.1		2
4.3	odd	2		400.8.a.bd.1.1		2
5.2	odd	4		25.8.b.b.24.3		4
5.3	odd	4		25.8.b.b.24.2		4
5.4	even	2		25.8.a.e.1.1	yes	2
15.2	even	4		225.8.b.l.199.2		4
15.8	even	4		225.8.b.l.199.3		4
15.14	odd	2		225.8.a.k.1.2		2
20.3	even	4		400.8.c.s.49.2		4
20.7	even	4		400.8.c.s.49.3		4
20.19	odd	2		400.8.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.a.c.1.2	✓	2	1.1	even	1	trivial
25.8.a.e.1.1	yes	2	5.4	even	2
25.8.b.b.24.2		4	5.3	odd	4
25.8.b.b.24.3		4	5.2	odd	4
225.8.a.k.1.2		2	15.14	odd	2
225.8.a.v.1.1		2	3.2	odd	2
225.8.b.l.199.2		4	15.2	even	4
225.8.b.l.199.3		4	15.8	even	4
400.8.a.v.1.2		2	20.19	odd	2
400.8.a.bd.1.1		2	4.3	odd	2
400.8.c.s.49.2		4	20.3	even	4
400.8.c.s.49.3		4	20.7	even	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+5.23774 q^{2} +5.47548 q^{3} -100.566 q^{4} +28.6791 q^{6} -769.970 q^{7} -1197.17 q^{8} -2157.02 q^{9} +O(q^{10})\)	\(q+5.23774 q^{2} +5.47548 q^{3} -100.566 q^{4} +28.6791 q^{6} -769.970 q^{7} -1197.17 q^{8} -2157.02 q^{9} +5356.43 q^{11} -550.647 q^{12} -14037.0 q^{13} -4032.90 q^{14} +6602.00 q^{16} -12402.4 q^{17} -11297.9 q^{18} -5038.89 q^{19} -4215.95 q^{21} +28055.6 q^{22} +75190.5 q^{23} -6555.08 q^{24} -73522.1 q^{26} -23785.6 q^{27} +77432.9 q^{28} +195529. q^{29} -93568.2 q^{31} +187817. q^{32} +29329.0 q^{33} -64960.4 q^{34} +216923. q^{36} -161554. q^{37} -26392.4 q^{38} -76859.3 q^{39} -28767.5 q^{41} -22082.1 q^{42} -739076. q^{43} -538676. q^{44} +393828. q^{46} -1.06799e6 q^{47} +36149.1 q^{48} -230689. q^{49} -67908.9 q^{51} +1.41165e6 q^{52} -626442. q^{53} -124583. q^{54} +921785. q^{56} -27590.3 q^{57} +1.02413e6 q^{58} +2.14861e6 q^{59} -2.57497e6 q^{61} -490086. q^{62} +1.66084e6 q^{63} +138682. q^{64} +153618. q^{66} +807676. q^{67} +1.24726e6 q^{68} +411704. q^{69} -1.72722e6 q^{71} +2.58232e6 q^{72} +1.74519e6 q^{73} -846178. q^{74} +506742. q^{76} -4.12429e6 q^{77} -402569. q^{78} -2.46887e6 q^{79} +4.58716e6 q^{81} -150677. q^{82} -6.90850e6 q^{83} +423982. q^{84} -3.87109e6 q^{86} +1.07061e6 q^{87} -6.41256e6 q^{88} +2.63567e6 q^{89} +1.08081e7 q^{91} -7.56161e6 q^{92} -512331. q^{93} -5.59385e6 q^{94} +1.02839e6 q^{96} +1.01234e7 q^{97} -1.20829e6 q^{98} -1.15539e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 15 q^{2} - 40 q^{3} + 181 q^{4} + 949 q^{6} + 600 q^{7} - 4305 q^{8} - 2276 q^{9}+O(q^{10}) \) 2 * q - 15 * q^2 - 40 * q^3 + 181 * q^4 + 949 * q^6 + 600 * q^7 - 4305 * q^8 - 2276 * q^9	\( 2 q - 15 q^{2} - 40 q^{3} + 181 q^{4} + 949 q^{6} + 600 q^{7} - 4305 q^{8} - 2276 q^{9} + 4344 q^{11} - 13355 q^{12} - 17680 q^{13} - 31758 q^{14} + 33457 q^{16} - 6870 q^{17} - 8890 q^{18} + 18200 q^{19} - 66516 q^{21} + 48545 q^{22} - 21120 q^{23} + 134775 q^{24} + 204 q^{26} + 81080 q^{27} + 463170 q^{28} + 55800 q^{29} - 301776 q^{31} + 42135 q^{32} + 75370 q^{33} - 176923 q^{34} + 183422 q^{36} - 609860 q^{37} - 496695 q^{38} + 88808 q^{39} - 108486 q^{41} + 1238730 q^{42} - 966400 q^{43} - 823743 q^{44} + 2342934 q^{46} - 1787880 q^{47} - 1185095 q^{48} + 822586 q^{49} - 319496 q^{51} + 385900 q^{52} - 130740 q^{53} - 2246825 q^{54} - 3335850 q^{56} - 1084390 q^{57} + 3851920 q^{58} + 2067600 q^{59} + 582044 q^{61} + 3723570 q^{62} + 1497840 q^{63} - 350479 q^{64} - 778147 q^{66} - 255720 q^{67} + 2804985 q^{68} + 4791468 q^{69} - 4728216 q^{71} + 2952090 q^{72} + 1339430 q^{73} + 8226522 q^{74} + 7050025 q^{76} - 5511300 q^{77} - 3755300 q^{78} - 7186200 q^{79} + 78562 q^{81} + 1462645 q^{82} - 12049560 q^{83} - 17117598 q^{84} + 729444 q^{86} + 7424840 q^{87} - 3266085 q^{88} - 5990850 q^{89} + 5817264 q^{91} - 34679370 q^{92} + 8956020 q^{93} + 8975132 q^{94} + 7653359 q^{96} + 17120020 q^{97} - 22524195 q^{98} - 11433472 q^{99}+O(q^{100}) \) 2 * q - 15 * q^2 - 40 * q^3 + 181 * q^4 + 949 * q^6 + 600 * q^7 - 4305 * q^8 - 2276 * q^9 + 4344 * q^11 - 13355 * q^12 - 17680 * q^13 - 31758 * q^14 + 33457 * q^16 - 6870 * q^17 - 8890 * q^18 + 18200 * q^19 - 66516 * q^21 + 48545 * q^22 - 21120 * q^23 + 134775 * q^24 + 204 * q^26 + 81080 * q^27 + 463170 * q^28 + 55800 * q^29 - 301776 * q^31 + 42135 * q^32 + 75370 * q^33 - 176923 * q^34 + 183422 * q^36 - 609860 * q^37 - 496695 * q^38 + 88808 * q^39 - 108486 * q^41 + 1238730 * q^42 - 966400 * q^43 - 823743 * q^44 + 2342934 * q^46 - 1787880 * q^47 - 1185095 * q^48 + 822586 * q^49 - 319496 * q^51 + 385900 * q^52 - 130740 * q^53 - 2246825 * q^54 - 3335850 * q^56 - 1084390 * q^57 + 3851920 * q^58 + 2067600 * q^59 + 582044 * q^61 + 3723570 * q^62 + 1497840 * q^63 - 350479 * q^64 - 778147 * q^66 - 255720 * q^67 + 2804985 * q^68 + 4791468 * q^69 - 4728216 * q^71 + 2952090 * q^72 + 1339430 * q^73 + 8226522 * q^74 + 7050025 * q^76 - 5511300 * q^77 - 3755300 * q^78 - 7186200 * q^79 + 78562 * q^81 + 1462645 * q^82 - 12049560 * q^83 - 17117598 * q^84 + 729444 * q^86 + 7424840 * q^87 - 3266085 * q^88 - 5990850 * q^89 + 5817264 * q^91 - 34679370 * q^92 + 8956020 * q^93 + 8975132 * q^94 + 7653359 * q^96 + 17120020 * q^97 - 22524195 * q^98 - 11433472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more