LMFDB - Embedded newform 25.14.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,14,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, 14, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
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:	$26.8077322380$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 17722x^{2} + 125608x + 10385664 $ x^4 - x^3 - 17722x^2 + 125608x + 10385664
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-21.1633$ 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)

$f(q)$	$=$	$q-5.16335 q^{2} +1952.42 q^{3} -8165.34 q^{4} -10081.0 q^{6} -455997. q^{7} +84458.7 q^{8} +2.21763e6 q^{9} +O(q^{10})$	\(q-5.16335 q^{2} +1952.42 q^{3} -8165.34 q^{4} -10081.0 q^{6} -455997. q^{7} +84458.7 q^{8} +2.21763e6 q^{9} +8.01536e6 q^{11} -1.59422e7 q^{12} +2.30242e7 q^{13} +2.35447e6 q^{14} +6.64544e7 q^{16} +1.01602e8 q^{17} -1.14504e7 q^{18} -3.62454e7 q^{19} -8.90299e8 q^{21} -4.13861e7 q^{22} -1.39685e8 q^{23} +1.64899e8 q^{24} -1.18882e8 q^{26} +1.21696e9 q^{27} +3.72337e9 q^{28} +4.32031e9 q^{29} +3.49517e9 q^{31} -1.03501e9 q^{32} +1.56494e10 q^{33} -5.24608e8 q^{34} -1.81077e10 q^{36} +1.48718e10 q^{37} +1.87148e8 q^{38} +4.49530e10 q^{39} -5.64436e10 q^{41} +4.59692e9 q^{42} +2.37173e10 q^{43} -6.54482e10 q^{44} +7.21243e8 q^{46} +7.86799e10 q^{47} +1.29747e11 q^{48} +1.11044e11 q^{49} +1.98370e11 q^{51} -1.88000e11 q^{52} -1.63472e11 q^{53} -6.28359e9 q^{54} -3.85129e10 q^{56} -7.07664e10 q^{57} -2.23073e10 q^{58} -2.32502e11 q^{59} -5.37766e10 q^{61} -1.80468e10 q^{62} -1.01123e12 q^{63} -5.39050e11 q^{64} -8.08032e10 q^{66} +3.74139e11 q^{67} -8.29616e11 q^{68} -2.72724e11 q^{69} +1.60839e12 q^{71} +1.87298e11 q^{72} +1.25178e12 q^{73} -7.67883e10 q^{74} +2.95956e11 q^{76} -3.65498e12 q^{77} -2.32108e11 q^{78} -2.32330e11 q^{79} -1.15960e12 q^{81} +2.91438e11 q^{82} +1.83649e12 q^{83} +7.26959e12 q^{84} -1.22461e11 q^{86} +8.43507e12 q^{87} +6.76967e11 q^{88} -8.13439e12 q^{89} -1.04990e13 q^{91} +1.14058e12 q^{92} +6.82405e12 q^{93} -4.06252e11 q^{94} -2.02078e12 q^{96} +3.00647e9 q^{97} -5.73360e11 q^{98} +1.77751e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9}+O(q^{10}) $ 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9} + 6675428 q^{11} - 520595 q^{12} + 4926920 q^{13} + 37103466 q^{14} - 8440751 q^{16} + 50416220 q^{17} + 22302110 q^{18} + 282648860 q^{19} - 438887472 q^{21} + 969439305 q^{22} + 1208437080 q^{23} + 1415344455 q^{24} - 3267454372 q^{26} + 1714727420 q^{27} + 11782380170 q^{28} + 7630648840 q^{29} - 12716039032 q^{31} + 5288310415 q^{32} + 36748956820 q^{33} + 23123205021 q^{34} - 45497926906 q^{36} + 38137910960 q^{37} + 99584060705 q^{38} + 60691943624 q^{39} - 81254933612 q^{41} + 62466915570 q^{42} + 97224763400 q^{43} + 111616918681 q^{44} - 77938796802 q^{46} + 69940090280 q^{47} + 107001227905 q^{48} + 118071253428 q^{49} + 91953947668 q^{51} - 165428401300 q^{52} - 179518658440 q^{53} - 275242827665 q^{54} + 403963457310 q^{56} - 99736967860 q^{57} - 810275460480 q^{58} - 858015815320 q^{59} + 589205515328 q^{61} - 942802276470 q^{62} - 2020360823760 q^{63} - 1516614058847 q^{64} + 1418821712381 q^{66} - 685669480180 q^{67} - 2270111055215 q^{68} - 1486209750216 q^{69} + 949682379448 q^{71} - 1359611223390 q^{72} - 1688808513820 q^{73} + 1003330480306 q^{74} + 1964117678945 q^{76} + 2180313451200 q^{77} + 171961033900 q^{78} - 355815036160 q^{79} - 1150994540276 q^{81} - 224361325395 q^{82} + 8420327909340 q^{83} + 9279336345306 q^{84} - 11016868246612 q^{86} + 9035391325160 q^{87} + 12729770641515 q^{88} + 2506082642820 q^{89} - 11092233838352 q^{91} + 403195163070 q^{92} + 17882711708520 q^{93} + 15051571815036 q^{94} - 17345568428737 q^{96} + 12121501720280 q^{97} + 19722093248605 q^{98} + 1425639838304 q^{99}+O(q^{100}) \) 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9 + 6675428 * q^11 - 520595 * q^12 + 4926920 * q^13 + 37103466 * q^14 - 8440751 * q^16 + 50416220 * q^17 + 22302110 * q^18 + 282648860 * q^19 - 438887472 * q^21 + 969439305 * q^22 + 1208437080 * q^23 + 1415344455 * q^24 - 3267454372 * q^26 + 1714727420 * q^27 + 11782380170 * q^28 + 7630648840 * q^29 - 12716039032 * q^31 + 5288310415 * q^32 + 36748956820 * q^33 + 23123205021 * q^34 - 45497926906 * q^36 + 38137910960 * q^37 + 99584060705 * q^38 + 60691943624 * q^39 - 81254933612 * q^41 + 62466915570 * q^42 + 97224763400 * q^43 + 111616918681 * q^44 - 77938796802 * q^46 + 69940090280 * q^47 + 107001227905 * q^48 + 118071253428 * q^49 + 91953947668 * q^51 - 165428401300 * q^52 - 179518658440 * q^53 - 275242827665 * q^54 + 403963457310 * q^56 - 99736967860 * q^57 - 810275460480 * q^58 - 858015815320 * q^59 + 589205515328 * q^61 - 942802276470 * q^62 - 2020360823760 * q^63 - 1516614058847 * q^64 + 1418821712381 * q^66 - 685669480180 * q^67 - 2270111055215 * q^68 - 1486209750216 * q^69 + 949682379448 * q^71 - 1359611223390 * q^72 - 1688808513820 * q^73 + 1003330480306 * q^74 + 1964117678945 * q^76 + 2180313451200 * q^77 + 171961033900 * q^78 - 355815036160 * q^79 - 1150994540276 * q^81 - 224361325395 * q^82 + 8420327909340 * q^83 + 9279336345306 * q^84 - 11016868246612 * q^86 + 9035391325160 * q^87 + 12729770641515 * q^88 + 2506082642820 * q^89 - 11092233838352 * q^91 + 403195163070 * q^92 + 17882711708520 * q^93 + 15051571815036 * q^94 - 17345568428737 * q^96 + 12121501720280 * q^97 + 19722093248605 * q^98 + 1425639838304 * 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 $

$2$	−5.16335	−0.0570475	−0.0285237	−	0.999593i	$-0.509081\pi$
$2$	−5.16335	−0.0570475	−0.0285237	+	0.999593i	$0.509081\pi$
$3$	1952.42	1.54627	0.773136	−	0.634241i	$-0.218687\pi$
$3$	1952.42	1.54627	0.773136	+	0.634241i	$0.218687\pi$
$4$	−8165.34	−0.996746
$5$	0	0
$5$	0	0
$6$	−10081.0	−0.0882109
$7$	−455997.	−1.46496	−0.732478	−	0.680790i	$-0.761636\pi$
$7$	−455997.	−1.46496	−0.732478	+	0.680790i	$0.761636\pi$
$8$	84458.7	0.113909
$9$	2.21763e6	1.39095
$10$	0	0
$11$	8.01536e6	1.36418	0.682089	−	0.731270i	$-0.261072\pi$
$11$	8.01536e6	1.36418	0.682089	+	0.731270i	$0.261072\pi$
$12$	−1.59422e7	−1.54124
$13$	2.30242e7	1.32298	0.661489	−	0.749955i	$-0.269925\pi$
$13$	2.30242e7	1.32298	0.661489	+	0.749955i	$0.269925\pi$
$14$	2.35447e6	0.0835721
$15$	0	0
$16$	6.64544e7	0.990247
$17$	1.01602e8	1.02090	0.510452	−	0.859906i	$-0.329478\pi$
$17$	1.01602e8	1.02090	0.510452	+	0.859906i	$0.329478\pi$
$18$	−1.14504e7	−0.0793505
$19$	−3.62454e7	−0.176748	−0.0883740	−	0.996087i	$-0.528167\pi$
$19$	−3.62454e7	−0.176748	−0.0883740	+	0.996087i	$0.528167\pi$
$20$	0	0
$21$	−8.90299e8	−2.26522
$22$	−4.13861e7	−0.0778229
$23$	−1.39685e8	−0.196752	−0.0983760	−	0.995149i	$-0.531365\pi$
$23$	−1.39685e8	−0.196752	−0.0983760	+	0.995149i	$0.531365\pi$
$24$	1.64899e8	0.176135
$25$	0	0
$26$	−1.18882e8	−0.0754726
$27$	1.21696e9	0.604521
$28$	3.72337e9	1.46019
$29$	4.32031e9	1.34874	0.674370	−	0.738394i	$-0.264415\pi$
$29$	4.32031e9	1.34874	0.674370	+	0.738394i	$0.264415\pi$
$30$	0	0
$31$	3.49517e9	0.707322	0.353661	−	0.935374i	$-0.384937\pi$
$31$	3.49517e9	0.707322	0.353661	+	0.935374i	$0.384937\pi$
$32$	−1.03501e9	−0.170400
$33$	1.56494e10	2.10939
$34$	−5.24608e8	−0.0582400
$35$	0	0
$36$	−1.81077e10	−1.38643
$37$	1.48718e10	0.952911	0.476455	−	0.879199i	$-0.341921\pi$
$37$	1.48718e10	0.952911	0.476455	+	0.879199i	$0.341921\pi$
$38$	1.87148e8	0.0100830
$39$	4.49530e10	2.04568
$40$	0	0
$41$	−5.64436e10	−1.85575	−0.927875	−	0.372892i	$-0.878366\pi$
$41$	−5.64436e10	−1.85575	−0.927875	+	0.372892i	$0.878366\pi$
$42$	4.59692e9	0.129225
$43$	2.37173e10	0.572164	0.286082	−	0.958205i	$-0.407647\pi$
$43$	2.37173e10	0.572164	0.286082	+	0.958205i	$0.407647\pi$
$44$	−6.54482e10	−1.35974
$45$	0	0
$46$	7.21243e8	0.0112242
$47$	7.86799e10	1.06470	0.532350	−	0.846524i	$-0.321309\pi$
$47$	7.86799e10	1.06470	0.532350	+	0.846524i	$0.321309\pi$
$48$	1.29747e11	1.53119
$49$	1.11044e11	1.14610
$50$	0	0
$51$	1.98370e11	1.57859
$52$	−1.88000e11	−1.31867
$53$	−1.63472e11	−1.01309	−0.506546	−	0.862213i	$-0.669078\pi$
$53$	−1.63472e11	−1.01309	−0.506546	+	0.862213i	$0.669078\pi$
$54$	−6.28359e9	−0.0344864
$55$	0	0
$56$	−3.85129e10	−0.166872
$57$	−7.07664e10	−0.273300
$58$	−2.23073e10	−0.0769422
$59$	−2.32502e11	−0.717610	−0.358805	−	0.933413i	$-0.616816\pi$
$59$	−2.32502e11	−0.717610	−0.358805	+	0.933413i	$0.616816\pi$
$60$	0	0
$61$	−5.37766e10	−0.133644	−0.0668220	−	0.997765i	$-0.521286\pi$
$61$	−5.37766e10	−0.133644	−0.0668220	+	0.997765i	$0.521286\pi$
$62$	−1.80468e10	−0.0403510
$63$	−1.01123e12	−2.03769
$64$	−5.39050e11	−0.980526
$65$	0	0
$66$	−8.08032e10	−0.120335
$67$	3.74139e11	0.505298	0.252649	−	0.967558i	$-0.418698\pi$
$67$	3.74139e11	0.505298	0.252649	+	0.967558i	$0.418698\pi$
$68$	−8.29616e11	−1.01758
$69$	−2.72724e11	−0.304232
$70$	0	0
$71$	1.60839e12	1.49008	0.745042	−	0.667017i	$-0.232429\pi$
$71$	1.60839e12	1.49008	0.745042	+	0.667017i	$0.232429\pi$
$72$	1.87298e11	0.158443
$73$	1.25178e12	0.968122	0.484061	−	0.875034i	$-0.339161\pi$
$73$	1.25178e12	0.968122	0.484061	+	0.875034i	$0.339161\pi$
$74$	−7.67883e10	−0.0543612
$75$	0	0
$76$	2.95956e11	0.176173
$77$	−3.65498e12	−1.99846
$78$	−2.32108e11	−0.116701
$79$	−2.32330e11	−0.107530	−0.0537650	−	0.998554i	$-0.517122\pi$
$79$	−2.32330e11	−0.107530	−0.0537650	+	0.998554i	$0.517122\pi$
$80$	0	0
$81$	−1.15960e12	−0.456200
$82$	2.91438e11	0.105866
$83$	1.83649e12	0.616569	0.308284	−	0.951294i	$-0.400245\pi$
$83$	1.83649e12	0.616569	0.308284	+	0.951294i	$0.400245\pi$
$84$	7.26959e12	2.25785
$85$	0	0
$86$	−1.22461e11	−0.0326405
$87$	8.43507e12	2.08552
$88$	6.76967e11	0.155393
$89$	−8.13439e12	−1.73496	−0.867481	−	0.497470i	$-0.834262\pi$
$89$	−8.13439e12	−1.73496	−0.867481	+	0.497470i	$0.834262\pi$
$90$	0	0
$91$	−1.04990e13	−1.93811
$92$	1.14058e12	0.196112
$93$	6.82405e12	1.09371
$94$	−4.06252e11	−0.0607385
$95$	0	0
$96$	−2.02078e12	−0.263485
$97$	3.00647e9	0.000366472 0	0.000183236	−	1.00000i	$-0.499942\pi$
$97$	3.00647e9	0.000366472 0	0.000183236		1.00000i	$0.499942\pi$
$98$	−5.73360e11	−0.0653820
$99$	1.77751e13	1.89751
$100$	0	0
$101$	6.91609e12	0.648293	0.324147	−	0.946007i	$-0.394923\pi$
$101$	6.91609e12	0.648293	0.324147	+	0.946007i	$0.394923\pi$
$102$	−1.02426e12	−0.0900549
$103$	1.27267e13	1.05021	0.525103	−	0.851039i	$-0.324027\pi$
$103$	1.27267e13	1.05021	0.525103	+	0.851039i	$0.324027\pi$
$104$	1.94459e12	0.150700
$105$	0	0
$106$	8.44061e11	0.0577944
$107$	−9.16545e12	−0.590418	−0.295209	−	0.955433i	$-0.595389\pi$
$107$	−9.16545e12	−0.590418	−0.295209	+	0.955433i	$0.595389\pi$
$108$	−9.93689e12	−0.602554
$109$	−1.13265e13	−0.646879	−0.323439	−	0.946249i	$-0.604839\pi$
$109$	−1.13265e13	−0.646879	−0.323439	+	0.946249i	$0.604839\pi$
$110$	0	0
$111$	2.90360e13	1.47346
$112$	−3.03030e13	−1.45067
$113$	−7.08078e12	−0.319942	−0.159971	−	0.987122i	$-0.551140\pi$
$113$	−7.08078e12	−0.319942	−0.159971	+	0.987122i	$0.551140\pi$
$114$	3.65391e11	0.0155911
$115$	0	0
$116$	−3.52768e13	−1.34435
$117$	5.10592e13	1.84020
$118$	1.20049e12	0.0409378
$119$	−4.63303e13	−1.49558
$120$	0	0
$121$	2.97234e13	0.860980
$122$	2.77668e11	0.00762406
$123$	−1.10202e14	−2.86949
$124$	−2.85392e13	−0.705020
$125$	0	0
$126$	5.22135e12	0.116245
$127$	1.25999e13	0.266467	0.133233	−	0.991085i	$-0.457464\pi$
$127$	1.25999e13	0.266467	0.133233	+	0.991085i	$0.457464\pi$
$128$	1.12621e13	0.226337
$129$	4.63062e13	0.884721
$130$	0	0
$131$	−2.09615e13	−0.362376	−0.181188	−	0.983448i	$-0.557994\pi$
$131$	−2.09615e13	−0.362376	−0.181188	+	0.983448i	$0.557994\pi$
$132$	−1.27782e14	−2.10252
$133$	1.65278e13	0.258928
$134$	−1.93181e12	−0.0288260
$135$	0	0
$136$	8.58118e12	0.116291
$137$	9.74113e12	0.125871	0.0629355	−	0.998018i	$-0.479954\pi$
$137$	9.74113e12	0.125871	0.0629355	+	0.998018i	$0.479954\pi$
$138$	1.40817e12	0.0173557
$139$	−5.63567e13	−0.662750	−0.331375	−	0.943499i	$-0.607512\pi$
$139$	−5.63567e13	−0.662750	−0.331375	+	0.943499i	$0.607512\pi$
$140$	0	0
$141$	1.53616e14	1.64632
$142$	−8.30466e12	−0.0850056
$143$	1.84547e14	1.80478
$144$	1.47371e14	1.37739
$145$	0	0
$146$	−6.46339e12	−0.0552289
$147$	2.16805e14	1.77218
$148$	−1.21433e14	−0.949810
$149$	3.57326e13	0.267519	0.133759	−	0.991014i	$-0.457295\pi$
$149$	3.57326e13	0.267519	0.133759	+	0.991014i	$0.457295\pi$
$150$	0	0
$151$	−2.04240e14	−1.40214	−0.701068	−	0.713095i	$-0.747293\pi$
$151$	−2.04240e14	−1.40214	−0.701068	+	0.713095i	$0.747293\pi$
$152$	−3.06124e12	−0.0201333
$153$	2.25316e14	1.42003
$154$	1.88720e13	0.114007
$155$	0	0
$156$	−3.67056e14	−2.03903
$157$	−1.14678e13	−0.0611129	−0.0305565	−	0.999533i	$-0.509728\pi$
$157$	−1.14678e13	−0.0611129	−0.0305565	+	0.999533i	$0.509728\pi$
$158$	1.19960e12	0.00613432
$159$	−3.19165e14	−1.56652
$160$	0	0
$161$	6.36960e13	0.288233
$162$	5.98742e12	0.0260251
$163$	2.83088e13	0.118223	0.0591116	−	0.998251i	$-0.481173\pi$
$163$	2.83088e13	0.118223	0.0591116	+	0.998251i	$0.481173\pi$
$164$	4.60881e14	1.84971
$165$	0	0
$166$	−9.48245e12	−0.0351737
$167$	1.84618e14	0.658593	0.329296	−	0.944227i	$-0.393189\pi$
$167$	1.84618e14	0.658593	0.329296	+	0.944227i	$0.393189\pi$
$168$	−7.51934e13	−0.258030
$169$	2.27238e14	0.750271
$170$	0	0
$171$	−8.03789e13	−0.245848
$172$	−1.93660e14	−0.570302
$173$	2.26452e14	0.642210	0.321105	−	0.947044i	$-0.395946\pi$
$173$	2.26452e14	0.642210	0.321105	+	0.947044i	$0.395946\pi$
$174$	−4.35532e13	−0.118974
$175$	0	0
$176$	5.32656e14	1.35087
$177$	−4.53942e14	−1.10962
$178$	4.20007e13	0.0989752
$179$	−5.84334e14	−1.32775	−0.663876	−	0.747843i	$-0.731090\pi$
$179$	−5.84334e14	−1.32775	−0.663876	+	0.747843i	$0.731090\pi$
$180$	0	0
$181$	7.87444e14	1.66460	0.832298	−	0.554328i	$-0.187025\pi$
$181$	7.87444e14	1.66460	0.832298	+	0.554328i	$0.187025\pi$
$182$	5.42098e13	0.110564
$183$	−1.04995e14	−0.206650
$184$	−1.17976e13	−0.0224119
$185$	0	0
$186$	−3.52349e13	−0.0623935
$187$	8.14379e14	1.39269
$188$	−6.42448e14	−1.06124
$189$	−5.54930e14	−0.885598
$190$	0	0
$191$	−4.84275e14	−0.721731	−0.360866	−	0.932618i	$-0.617519\pi$
$191$	−4.84275e14	−0.721731	−0.360866	+	0.932618i	$0.617519\pi$
$192$	−1.05245e15	−1.51616
$193$	−1.05794e15	−1.47346	−0.736728	−	0.676190i	$-0.763630\pi$
$193$	−1.05794e15	−1.47346	−0.736728	+	0.676190i	$0.763630\pi$
$194$	−1.55235e10	−2.09063e−5 0
$195$	0	0
$196$	−9.06714e14	−1.14237
$197$	1.64101e14	0.200024	0.100012	−	0.994986i	$-0.468112\pi$
$197$	1.64101e14	0.200024	0.100012	+	0.994986i	$0.468112\pi$
$198$	−9.17791e13	−0.108248
$199$	9.66561e14	1.10328	0.551638	−	0.834083i	$-0.314003\pi$
$199$	9.66561e14	1.10328	0.551638	+	0.834083i	$0.314003\pi$
$200$	0	0
$201$	7.30478e14	0.781327
$202$	−3.57102e13	−0.0369835
$203$	−1.97005e15	−1.97584
$204$	−1.61976e15	−1.57346
$205$	0	0
$206$	−6.57125e13	−0.0599116
$207$	−3.09770e14	−0.273673
$208$	1.53006e15	1.31008
$209$	−2.90520e14	−0.241116
$210$	0	0
$211$	3.59475e14	0.280435	0.140218	−	0.990121i	$-0.455220\pi$
$211$	3.59475e14	0.280435	0.140218	+	0.990121i	$0.455220\pi$
$212$	1.33480e15	1.00980
$213$	3.14025e15	2.30407
$214$	4.73244e13	0.0336818
$215$	0	0
$216$	1.02783e14	0.0688606
$217$	−1.59379e15	−1.03620
$218$	5.84826e13	0.0369028
$219$	2.44401e15	1.49698
$220$	0	0
$221$	2.33931e15	1.35063
$222$	−1.49923e14	−0.0840571
$223$	−6.89603e14	−0.375507	−0.187753	−	0.982216i	$-0.560121\pi$
$223$	−6.89603e14	−0.375507	−0.187753	+	0.982216i	$0.560121\pi$
$224$	4.71963e14	0.249629
$225$	0	0
$226$	3.65605e13	0.0182519
$227$	2.31395e15	1.12250	0.561249	−	0.827647i	$-0.310321\pi$
$227$	2.31395e15	1.12250	0.561249	+	0.827647i	$0.310321\pi$
$228$	5.77831e14	0.272411
$229$	1.93327e15	0.885853	0.442927	−	0.896558i	$-0.353940\pi$
$229$	1.93327e15	0.885853	0.442927	+	0.896558i	$0.353940\pi$
$230$	0	0
$231$	−7.13607e15	−3.09016
$232$	3.64888e14	0.153634
$233$	4.01520e15	1.64397	0.821984	−	0.569511i	$-0.192867\pi$
$233$	4.01520e15	1.64397	0.821984	+	0.569511i	$0.192867\pi$
$234$	−2.63636e14	−0.104979
$235$	0	0
$236$	1.89846e15	0.715274
$237$	−4.53607e14	−0.166271
$238$	2.39219e14	0.0853191
$239$	−2.64927e15	−0.919476	−0.459738	−	0.888054i	$-0.652057\pi$
$239$	−2.64927e15	−0.919476	−0.459738	+	0.888054i	$0.652057\pi$
$240$	0	0
$241$	−5.31068e15	−1.74598	−0.872990	−	0.487739i	$-0.837822\pi$
$241$	−5.31068e15	−1.74598	−0.872990	+	0.487739i	$0.837822\pi$
$242$	−1.53472e14	−0.0491167
$243$	−4.20426e15	−1.30993
$244$	4.39105e14	0.133209
$245$	0	0
$246$	5.69010e14	0.163697
$247$	−8.34521e14	−0.233834
$248$	2.95197e14	0.0805706
$249$	3.58561e15	0.953383
$250$	0	0
$251$	1.45588e15	0.367490	0.183745	−	0.982974i	$-0.441178\pi$
$251$	1.45588e15	0.367490	0.183745	+	0.982974i	$0.441178\pi$
$252$	8.25706e15	2.03106
$253$	−1.11963e15	−0.268405
$254$	−6.50577e13	−0.0152013
$255$	0	0
$256$	4.35775e15	0.967614
$257$	−4.64051e15	−1.00462	−0.502308	−	0.864689i	$-0.667516\pi$
$257$	−4.64051e15	−1.00462	−0.502308	+	0.864689i	$0.667516\pi$
$258$	−2.39095e14	−0.0504711
$259$	−6.78149e15	−1.39597
$260$	0	0
$261$	9.58086e15	1.87604
$262$	1.08232e14	0.0206727
$263$	8.58684e15	1.60000	0.800002	−	0.599997i	$-0.204832\pi$
$263$	8.58684e15	1.60000	0.800002	+	0.599997i	$0.204832\pi$
$264$	1.32173e15	0.240279
$265$	0	0
$266$	−8.53388e13	−0.0147712
$267$	−1.58818e16	−2.68272
$268$	−3.05498e15	−0.503653
$269$	−3.76914e15	−0.606530	−0.303265	−	0.952906i	$-0.598077\pi$
$269$	−3.76914e15	−0.606530	−0.303265	+	0.952906i	$0.598077\pi$
$270$	0	0
$271$	−9.35477e14	−0.143461	−0.0717303	−	0.997424i	$-0.522852\pi$
$271$	−9.35477e14	−0.143461	−0.0717303	+	0.997424i	$0.522852\pi$
$272$	6.75191e15	1.01095
$273$	−2.04984e16	−2.99684
$274$	−5.02969e13	−0.00718063
$275$	0	0
$276$	2.22689e15	0.303242
$277$	−8.86434e15	−1.17904	−0.589519	−	0.807754i	$-0.700683\pi$
$277$	−8.86434e15	−1.17904	−0.589519	+	0.807754i	$0.700683\pi$
$278$	2.90990e14	0.0378082
$279$	7.75099e15	0.983853
$280$	0	0
$281$	−6.27527e15	−0.760398	−0.380199	−	0.924905i	$-0.624145\pi$
$281$	−6.27527e15	−0.760398	−0.380199	+	0.924905i	$0.624145\pi$
$282$	−7.93175e14	−0.0939182
$283$	1.05807e15	0.122434	0.0612170	−	0.998124i	$-0.480502\pi$
$283$	1.05807e15	0.122434	0.0612170	+	0.998124i	$0.480502\pi$
$284$	−1.31330e16	−1.48524
$285$	0	0
$286$	−9.52882e14	−0.102958
$287$	2.57381e16	2.71859
$288$	−2.29528e15	−0.237019
$289$	4.18426e14	0.0422457
$290$	0	0
$291$	5.86991e12	0.000566666 0
$292$	−1.02212e16	−0.964971
$293$	−5.99802e15	−0.553819	−0.276910	−	0.960896i	$-0.589310\pi$
$293$	−5.99802e15	−0.553819	−0.276910	+	0.960896i	$0.589310\pi$
$294$	−1.11944e15	−0.101098
$295$	0	0
$296$	1.25605e15	0.108545
$297$	9.75437e15	0.824674
$298$	−1.84500e14	−0.0152613
$299$	−3.21614e15	−0.260299
$300$	0	0
$301$	−1.08150e16	−0.838196
$302$	1.05456e15	0.0799883
$303$	1.35031e16	1.00244
$304$	−2.40867e15	−0.175024
$305$	0	0
$306$	−1.16339e15	−0.0810092
$307$	−2.37996e16	−1.62244	−0.811222	−	0.584739i	$-0.801197\pi$
$307$	−2.37996e16	−1.62244	−0.811222	+	0.584739i	$0.801197\pi$
$308$	2.98442e16	1.99196
$309$	2.48479e16	1.62390
$310$	0	0
$311$	1.90749e16	1.19542	0.597710	−	0.801712i	$-0.296077\pi$
$311$	1.90749e16	1.19542	0.597710	+	0.801712i	$0.296077\pi$
$312$	3.79667e15	0.233022
$313$	6.63166e15	0.398643	0.199321	−	0.979934i	$-0.436126\pi$
$313$	6.63166e15	0.398643	0.199321	+	0.979934i	$0.436126\pi$
$314$	5.92123e13	0.00348634
$315$	0	0
$316$	1.89706e15	0.107180
$317$	1.98361e16	1.09792	0.548960	−	0.835848i	$-0.315024\pi$
$317$	1.98361e16	1.09792	0.548960	+	0.835848i	$0.315024\pi$
$318$	1.64796e15	0.0893658
$319$	3.46289e16	1.83992
$320$	0	0
$321$	−1.78948e16	−0.912946
$322$	−3.28885e14	−0.0164430
$323$	−3.68261e15	−0.180443
$324$	9.46853e15	0.454716
$325$	0	0
$326$	−1.46168e14	−0.00674434
$327$	−2.21141e16	−1.00025
$328$	−4.76715e15	−0.211387
$329$	−3.58778e16	−1.55974
$330$	0	0
$331$	−7.07700e15	−0.295779	−0.147890	−	0.989004i	$-0.547248\pi$
$331$	−7.07700e15	−0.295779	−0.147890	+	0.989004i	$0.547248\pi$
$332$	−1.49956e16	−0.614562
$333$	3.29801e16	1.32546
$334$	−9.53247e14	−0.0375711
$335$	0	0
$336$	−5.91642e16	−2.24313
$337$	5.01755e16	1.86594	0.932970	−	0.359955i	$-0.117208\pi$
$337$	5.01755e16	1.86594	0.932970	+	0.359955i	$0.117208\pi$
$338$	−1.17331e15	−0.0428011
$339$	−1.38247e16	−0.494717
$340$	0	0
$341$	2.80151e16	0.964913
$342$	4.15025e14	0.0140250
$343$	−6.45475e15	−0.214026
$344$	2.00313e15	0.0651748
$345$	0	0
$346$	−1.16925e15	−0.0366365
$347$	5.89702e16	1.81339	0.906695	−	0.421788i	$-0.138597\pi$
$347$	5.89702e16	1.81339	0.906695	+	0.421788i	$0.138597\pi$
$348$	−6.88752e16	−2.07873
$349$	−2.75077e16	−0.814871	−0.407435	−	0.913234i	$-0.633577\pi$
$349$	−2.75077e16	−0.814871	−0.407435	+	0.913234i	$0.633577\pi$
$350$	0	0
$351$	2.80195e16	0.799769
$352$	−8.29600e15	−0.232456
$353$	−3.11283e16	−0.856288	−0.428144	−	0.903711i	$-0.640832\pi$
$353$	−3.11283e16	−0.856288	−0.428144	+	0.903711i	$0.640832\pi$
$354$	2.34386e15	0.0633010
$355$	0	0
$356$	6.64201e16	1.72932
$357$	−9.04563e16	−2.31257
$358$	3.01712e15	0.0757449
$359$	5.75500e15	0.141883	0.0709416	−	0.997480i	$-0.477400\pi$
$359$	5.75500e15	0.141883	0.0709416	+	0.997480i	$0.477400\pi$
$360$	0	0
$361$	−4.07393e16	−0.968760
$362$	−4.06585e15	−0.0949611
$363$	5.80325e16	1.33131
$364$	8.57276e16	1.93180
$365$	0	0
$366$	5.42124e14	0.0117889
$367$	−7.60500e16	−1.62469	−0.812344	−	0.583178i	$-0.801809\pi$
$367$	−7.60500e16	−1.62469	−0.812344	+	0.583178i	$0.801809\pi$
$368$	−9.28269e15	−0.194833
$369$	−1.25171e17	−2.58126
$370$	0	0
$371$	7.45425e16	1.48414
$372$	−5.57207e16	−1.09015
$373$	−9.16071e16	−1.76125	−0.880627	−	0.473811i	$-0.842878\pi$
$373$	−9.16071e16	−1.76125	−0.880627	+	0.473811i	$0.842878\pi$
$374$	−4.20492e15	−0.0794497
$375$	0	0
$376$	6.64520e15	0.121279
$377$	9.94717e16	1.78435
$378$	2.86530e15	0.0505211
$379$	1.62258e16	0.281223	0.140612	−	0.990065i	$-0.455093\pi$
$379$	1.62258e16	0.281223	0.140612	+	0.990065i	$0.455093\pi$
$380$	0	0
$381$	2.46003e16	0.412030
$382$	2.50048e15	0.0411729
$383$	2.15358e16	0.348634	0.174317	−	0.984690i	$-0.444228\pi$
$383$	2.15358e16	0.348634	0.174317	+	0.984690i	$0.444228\pi$
$384$	2.19884e16	0.349978
$385$	0	0
$386$	5.46249e15	0.0840569
$387$	5.25963e16	0.795854
$388$	−2.45489e13	−0.000365280 0
$389$	−4.79874e16	−0.702190	−0.351095	−	0.936340i	$-0.614191\pi$
$389$	−4.79874e16	−0.702190	−0.351095	+	0.936340i	$0.614191\pi$
$390$	0	0
$391$	−1.41923e16	−0.200865
$392$	9.37865e15	0.130551
$393$	−4.09258e16	−0.560332
$394$	−8.47313e14	−0.0114109
$395$	0	0
$396$	−1.45140e17	−1.89133
$397$	2.77596e16	0.355857	0.177929	−	0.984043i	$-0.443060\pi$
$397$	2.77596e16	0.355857	0.177929	+	0.984043i	$0.443060\pi$
$398$	−4.99069e15	−0.0629392
$399$	3.22692e16	0.400373
$400$	0	0
$401$	−8.50834e16	−1.02189	−0.510947	−	0.859612i	$-0.670705\pi$
$401$	−8.50834e16	−1.02189	−0.510947	+	0.859612i	$0.670705\pi$
$402$	−3.77172e15	−0.0445728
$403$	8.04735e16	0.935772
$404$	−5.64722e16	−0.646183
$405$	0	0
$406$	1.01721e16	0.112717
$407$	1.19203e17	1.29994
$408$	1.67541e16	0.179817
$409$	8.53238e16	0.901298	0.450649	−	0.892701i	$-0.351193\pi$
$409$	8.53238e16	0.901298	0.450649	+	0.892701i	$0.351193\pi$
$410$	0	0
$411$	1.90188e16	0.194631
$412$	−1.03918e17	−1.04679
$413$	1.06020e17	1.05127
$414$	1.59945e15	0.0156124
$415$	0	0
$416$	−2.38303e16	−0.225436
$417$	−1.10032e17	−1.02479
$418$	1.50006e15	0.0137550
$419$	9.30449e16	0.840043	0.420021	−	0.907514i	$-0.362023\pi$
$419$	9.30449e16	0.840043	0.420021	+	0.907514i	$0.362023\pi$
$420$	0	0
$421$	8.75821e16	0.766623	0.383312	−	0.923619i	$-0.374784\pi$
$421$	8.75821e16	0.766623	0.383312	+	0.923619i	$0.374784\pi$
$422$	−1.85609e15	−0.0159981
$423$	1.74483e17	1.48095
$424$	−1.38066e16	−0.115401
$425$	0	0
$426$	−1.62142e16	−0.131442
$427$	2.45220e16	0.195783
$428$	7.48390e16	0.588496
$429$	3.60314e17	2.79067
$430$	0	0
$431$	−1.02398e17	−0.769466	−0.384733	−	0.923028i	$-0.625707\pi$
$431$	−1.02398e17	−0.769466	−0.384733	+	0.923028i	$0.625707\pi$
$432$	8.08723e16	0.598626
$433$	−1.26034e17	−0.919004	−0.459502	−	0.888177i	$-0.651972\pi$
$433$	−1.26034e17	−0.919004	−0.459502	+	0.888177i	$0.651972\pi$
$434$	8.22928e15	0.0591124
$435$	0	0
$436$	9.24846e16	0.644773
$437$	5.06295e15	0.0347755
$438$	−1.26193e16	−0.0853989
$439$	−2.13985e17	−1.42680	−0.713400	−	0.700757i	$-0.752846\pi$
$439$	−2.13985e17	−1.42680	−0.713400	+	0.700757i	$0.752846\pi$
$440$	0	0
$441$	2.46255e17	1.59417
$442$	−1.20787e16	−0.0770503
$443$	2.47490e16	0.155572	0.0777862	−	0.996970i	$-0.475215\pi$
$443$	2.47490e16	0.155572	0.0777862	+	0.996970i	$0.475215\pi$
$444$	−2.37089e17	−1.46866
$445$	0	0
$446$	3.56066e15	0.0214217
$447$	6.97651e16	0.413656
$448$	2.45805e17	1.43643
$449$	−2.16659e17	−1.24789	−0.623943	−	0.781470i	$-0.714470\pi$
$449$	−2.16659e17	−1.24789	−0.623943	+	0.781470i	$0.714470\pi$
$450$	0	0
$451$	−4.52416e17	−2.53157
$452$	5.78169e16	0.318901
$453$	−3.98762e17	−2.16808
$454$	−1.19477e16	−0.0640357
$455$	0	0
$456$	−5.97683e15	−0.0311315
$457$	1.98785e16	0.102077	0.0510386	−	0.998697i	$-0.483747\pi$
$457$	1.98785e16	0.102077	0.0510386	+	0.998697i	$0.483747\pi$
$458$	−9.98214e15	−0.0505357
$459$	1.23646e17	0.617159
$460$	0	0
$461$	9.61706e16	0.466645	0.233322	−	0.972399i	$-0.425040\pi$
$461$	9.61706e16	0.466645	0.233322	+	0.972399i	$0.425040\pi$
$462$	3.68460e16	0.176286
$463$	−3.62569e17	−1.71046	−0.855232	−	0.518245i	$-0.826586\pi$
$463$	−3.62569e17	−1.71046	−0.855232	+	0.518245i	$0.826586\pi$
$464$	2.87104e17	1.33559
$465$	0	0
$466$	−2.07319e16	−0.0937842
$467$	−2.50232e17	−1.11631	−0.558153	−	0.829738i	$-0.688490\pi$
$467$	−2.50232e17	−1.11631	−0.558153	+	0.829738i	$0.688490\pi$
$468$	−4.16915e17	−1.83421
$469$	−1.70606e17	−0.740239
$470$	0	0
$471$	−2.23900e16	−0.0944971
$472$	−1.96368e16	−0.0817424
$473$	1.90103e17	0.780533
$474$	2.34213e15	0.00948532
$475$	0	0
$476$	3.78303e17	1.49071
$477$	−3.62519e17	−1.40917
$478$	1.36791e16	0.0524538
$479$	−2.97588e17	−1.12573	−0.562865	−	0.826549i	$-0.690301\pi$
$479$	−2.97588e17	−1.12573	−0.562865	+	0.826549i	$0.690301\pi$
$480$	0	0
$481$	3.42411e17	1.26068
$482$	2.74209e16	0.0996037
$483$	1.24362e17	0.445687
$484$	−2.42701e17	−0.858178
$485$	0	0
$486$	2.17080e16	0.0747283
$487$	−2.49951e17	−0.849017	−0.424508	−	0.905424i	$-0.639553\pi$
$487$	−2.49951e17	−0.849017	−0.424508	+	0.905424i	$0.639553\pi$
$488$	−4.54190e15	−0.0152233
$489$	5.52708e16	0.182805
$490$	0	0
$491$	−2.22644e17	−0.717103	−0.358551	−	0.933510i	$-0.616729\pi$
$491$	−2.22644e17	−0.717103	−0.358551	+	0.933510i	$0.616729\pi$
$492$	8.99834e17	2.86015
$493$	4.38953e17	1.37693
$494$	4.30893e15	0.0133396
$495$	0	0
$496$	2.32269e17	0.700424
$497$	−7.33419e17	−2.18291
$498$	−1.85138e16	−0.0543881
$499$	5.94401e17	1.72356	0.861779	−	0.507284i	$-0.169350\pi$
$499$	5.94401e17	1.72356	0.861779	+	0.507284i	$0.169350\pi$
$500$	0	0
$501$	3.60452e17	1.01836
$502$	−7.51720e15	−0.0209644
$503$	−2.62564e17	−0.722843	−0.361421	−	0.932403i	$-0.617708\pi$
$503$	−2.62564e17	−0.722843	−0.361421	+	0.932403i	$0.617708\pi$
$504$	−8.54074e16	−0.232112
$505$	0	0
$506$	5.78103e15	0.0153118
$507$	4.43665e17	1.16012
$508$	−1.02882e17	−0.265600
$509$	−2.63270e17	−0.671022	−0.335511	−	0.942036i	$-0.608909\pi$
$509$	−2.63270e17	−0.671022	−0.335511	+	0.942036i	$0.608909\pi$
$510$	0	0
$511$	−5.70809e17	−1.41826
$512$	−1.14760e17	−0.281537
$513$	−4.41092e16	−0.106848
$514$	2.39606e16	0.0573109
$515$	0	0
$516$	−3.78106e17	−0.881842
$517$	6.30648e17	1.45244
$518$	3.50152e16	0.0796367
$519$	4.42131e17	0.993031
$520$	0	0
$521$	−8.47569e17	−1.85665	−0.928325	−	0.371769i	$-0.878751\pi$
$521$	−8.47569e17	−1.85665	−0.928325	+	0.371769i	$0.878751\pi$
$522$	−4.94693e16	−0.107023
$523$	4.84028e17	1.03421	0.517106	−	0.855922i	$-0.327009\pi$
$523$	4.84028e17	1.03421	0.517106	+	0.855922i	$0.327009\pi$
$524$	1.71158e17	0.361197
$525$	0	0
$526$	−4.43369e16	−0.0912762
$527$	3.55117e17	0.722108
$528$	1.03997e18	2.08882
$529$	−4.84524e17	−0.961289
$530$	0	0
$531$	−5.15603e17	−0.998162
$532$	−1.34955e17	−0.258086
$533$	−1.29957e18	−2.45512
$534$	8.20031e16	0.153043
$535$	0	0
$536$	3.15993e16	0.0575581
$537$	−1.14087e18	−2.05306
$538$	1.94614e16	0.0346010
$539$	8.90060e17	1.56348
$540$	0	0
$541$	7.31743e17	1.25481	0.627403	−	0.778695i	$-0.284118\pi$
$541$	7.31743e17	1.25481	0.627403	+	0.778695i	$0.284118\pi$
$542$	4.83019e15	0.00818407
$543$	1.53742e18	2.57392
$544$	−1.05160e17	−0.173963
$545$	0	0
$546$	1.05840e17	0.170962
$547$	1.09459e18	1.74716	0.873579	−	0.486682i	$-0.161793\pi$
$547$	1.09459e18	1.74716	0.873579	+	0.486682i	$0.161793\pi$
$548$	−7.95397e16	−0.125461
$549$	−1.19257e17	−0.185893
$550$	0	0
$551$	−1.56591e17	−0.238387
$552$	−2.30339e16	−0.0346549
$553$	1.05942e17	0.157527
$554$	4.57697e16	0.0672612
$555$	0	0
$556$	4.60172e17	0.660593
$557$	7.41551e15	0.0105216	0.00526080	−	0.999986i	$-0.498325\pi$
$557$	7.41551e15	0.0105216	0.00526080	+	0.999986i	$0.498325\pi$
$558$	−4.00211e16	−0.0561263
$559$	5.46072e17	0.756961
$560$	0	0
$561$	1.59001e18	2.15348
$562$	3.24014e16	0.0433788
$563$	−3.72192e15	−0.00492564	−0.00246282	−	0.999997i	$-0.500784\pi$
$563$	−3.72192e15	−0.00492564	−0.00246282	+	0.999997i	$0.500784\pi$
$564$	−1.25433e18	−1.64096
$565$	0	0
$566$	−5.46318e15	−0.00698456
$567$	5.28774e17	0.668314
$568$	1.35842e17	0.169735
$569$	9.30899e17	1.14993	0.574967	−	0.818177i	$-0.305015\pi$
$569$	9.30899e17	1.14993	0.574967	+	0.818177i	$0.305015\pi$
$570$	0	0
$571$	−8.21061e16	−0.0991382	−0.0495691	−	0.998771i	$-0.515785\pi$
$571$	−8.21061e16	−0.0991382	−0.0495691	+	0.998771i	$0.515785\pi$
$572$	−1.50689e18	−1.79890
$573$	−9.45510e17	−1.11599
$574$	−1.32895e17	−0.155089
$575$	0	0
$576$	−1.19541e18	−1.36387
$577$	−8.28701e17	−0.934878	−0.467439	−	0.884025i	$-0.654823\pi$
$577$	−8.28701e17	−0.934878	−0.467439	+	0.884025i	$0.654823\pi$
$578$	−2.16048e15	−0.00241001
$579$	−2.06554e18	−2.27836
$580$	0	0
$581$	−8.37435e17	−0.903247
$582$	−3.03084e13	−3.23268e−5 0
$583$	−1.31028e18	−1.38204
$584$	1.05724e17	0.110278
$585$	0	0
$586$	3.09699e16	0.0315940
$587$	−6.35978e17	−0.641645	−0.320822	−	0.947139i	$-0.603959\pi$
$587$	−6.35978e17	−0.641645	−0.320822	+	0.947139i	$0.603959\pi$
$588$	−1.77029e18	−1.76641
$589$	−1.26684e17	−0.125018
$590$	0	0
$591$	3.20395e17	0.309291
$592$	9.88296e17	0.943617
$593$	−6.83014e17	−0.645021	−0.322511	−	0.946566i	$-0.604527\pi$
$593$	−6.83014e17	−0.645021	−0.322511	+	0.946566i	$0.604527\pi$
$594$	−5.03652e16	−0.0470456
$595$	0	0
$596$	−2.91769e17	−0.266648
$597$	1.88714e18	1.70596
$598$	1.66060e16	0.0148494
$599$	1.20464e18	1.06558	0.532788	−	0.846249i	$-0.321144\pi$
$599$	1.20464e18	1.06558	0.532788	+	0.846249i	$0.321144\pi$
$600$	0	0
$601$	1.16803e18	1.01104	0.505520	−	0.862815i	$-0.331301\pi$
$601$	1.16803e18	1.01104	0.505520	+	0.862815i	$0.331301\pi$
$602$	5.58418e16	0.0478170
$603$	8.29703e17	0.702846
$604$	1.66769e18	1.39757
$605$	0	0
$606$	−6.97213e16	−0.0571865
$607$	2.08566e17	0.169245	0.0846226	−	0.996413i	$-0.473032\pi$
$607$	2.08566e17	0.169245	0.0846226	+	0.996413i	$0.473032\pi$
$608$	3.75145e16	0.0301179
$609$	−3.84637e18	−3.05519
$610$	0	0
$611$	1.81154e18	1.40858
$612$	−1.83978e18	−1.41541
$613$	−1.08956e18	−0.829385	−0.414693	−	0.909962i	$-0.636111\pi$
$613$	−1.08956e18	−0.829385	−0.414693	+	0.909962i	$0.636111\pi$
$614$	1.22885e17	0.0925563
$615$	0	0
$616$	−3.08695e17	−0.227643
$617$	−8.64512e17	−0.630837	−0.315419	−	0.948953i	$-0.602145\pi$
$617$	−8.64512e17	−0.630837	−0.315419	+	0.948953i	$0.602145\pi$
$618$	−1.28299e17	−0.0926397
$619$	−2.59466e18	−1.85392	−0.926961	−	0.375157i	$-0.877589\pi$
$619$	−2.59466e18	−1.85392	−0.926961	+	0.375157i	$0.877589\pi$
$620$	0	0
$621$	−1.69991e17	−0.118941
$622$	−9.84906e16	−0.0681957
$623$	3.70926e18	2.54164
$624$	2.98732e18	2.02573
$625$	0	0
$626$	−3.42416e16	−0.0227416
$627$	−5.67218e17	−0.372830
$628$	9.36386e16	0.0609140
$629$	1.51101e18	0.972831
$630$	0	0
$631$	−4.70988e16	−0.0297043	−0.0148522	−	0.999890i	$-0.504728\pi$
$631$	−4.70988e16	−0.0297043	−0.0148522	+	0.999890i	$0.504728\pi$
$632$	−1.96223e16	−0.0122487
$633$	7.01846e17	0.433629
$634$	−1.02421e17	−0.0626336
$635$	0	0
$636$	2.60609e18	1.56142
$637$	2.55670e18	1.51626
$638$	−1.78801e17	−0.104963
$639$	3.56680e18	2.07264
$640$	0	0
$641$	−2.34176e18	−1.33342	−0.666708	−	0.745319i	$-0.732297\pi$
$641$	−2.34176e18	−1.33342	−0.666708	+	0.745319i	$0.732297\pi$
$642$	9.23973e16	0.0520813
$643$	2.28715e18	1.27621	0.638106	−	0.769948i	$-0.279718\pi$
$643$	2.28715e18	1.27621	0.638106	+	0.769948i	$0.279718\pi$
$644$	−5.20100e17	−0.287295
$645$	0	0
$646$	1.90146e16	0.0102938
$647$	−1.51642e18	−0.812723	−0.406362	−	0.913712i	$-0.633203\pi$
$647$	−1.51642e18	−0.812723	−0.406362	+	0.913712i	$0.633203\pi$
$648$	−9.79383e16	−0.0519655
$649$	−1.86359e18	−0.978947
$650$	0	0
$651$	−3.11175e18	−1.60224
$652$	−2.31151e17	−0.117838
$653$	−3.90116e18	−1.96906	−0.984528	−	0.175228i	$-0.943934\pi$
$653$	−3.90116e18	−1.96906	−0.984528	+	0.175228i	$0.943934\pi$
$654$	1.14183e17	0.0570617
$655$	0	0
$656$	−3.75092e18	−1.83765
$657$	2.77599e18	1.34661
$658$	1.85250e17	0.0889793
$659$	1.75617e18	0.835241	0.417620	−	0.908622i	$-0.362864\pi$
$659$	1.75617e18	0.835241	0.417620	+	0.908622i	$0.362864\pi$
$660$	0	0
$661$	−2.35537e17	−0.109837	−0.0549187	−	0.998491i	$-0.517490\pi$
$661$	−2.35537e17	−0.109837	−0.0549187	+	0.998491i	$0.517490\pi$
$662$	3.65410e16	0.0168735
$663$	4.56732e18	2.08845
$664$	1.55108e17	0.0702329
$665$	0	0
$666$	−1.70288e17	−0.0756139
$667$	−6.03483e17	−0.265367
$668$	−1.50747e18	−0.656449
$669$	−1.34640e18	−0.580635
$670$	0	0
$671$	−4.31039e17	−0.182314
$672$	9.21470e17	0.385994
$673$	1.28360e18	0.532514	0.266257	−	0.963902i	$-0.414213\pi$
$673$	1.28360e18	0.532514	0.266257	+	0.963902i	$0.414213\pi$
$674$	−2.59074e17	−0.106447
$675$	0	0
$676$	−1.85548e18	−0.747829
$677$	1.71378e18	0.684114	0.342057	−	0.939679i	$-0.388876\pi$
$677$	1.71378e18	0.684114	0.342057	+	0.939679i	$0.388876\pi$
$678$	7.13816e16	0.0282224
$679$	−1.37094e15	−0.000536866 0
$680$	0	0
$681$	4.51780e18	1.73569
$682$	−1.44652e17	−0.0550459
$683$	2.51565e18	0.948236	0.474118	−	0.880461i	$-0.342767\pi$
$683$	2.51565e18	0.948236	0.474118	+	0.880461i	$0.342767\pi$
$684$	6.56321e17	0.245048
$685$	0	0
$686$	3.33281e16	0.0122097
$687$	3.77456e18	1.36977
$688$	1.57612e18	0.566584
$689$	−3.76380e18	−1.34030
$690$	0	0
$691$	4.34027e18	1.51673	0.758366	−	0.651829i	$-0.225998\pi$
$691$	4.34027e18	1.51673	0.758366	+	0.651829i	$0.225998\pi$
$692$	−1.84906e18	−0.640120
$693$	−8.10540e18	−2.77977
$694$	−3.04484e17	−0.103449
$695$	0	0
$696$	7.12415e17	0.237560
$697$	−5.73479e18	−1.89454
$698$	1.42032e17	0.0464863
$699$	7.83936e18	2.54202
$700$	0	0
$701$	1.21569e18	0.386951	0.193476	−	0.981105i	$-0.438024\pi$
$701$	1.21569e18	0.386951	0.193476	+	0.981105i	$0.438024\pi$
$702$	−1.44675e17	−0.0456248
$703$	−5.39034e17	−0.168425
$704$	−4.32068e18	−1.33761
$705$	0	0
$706$	1.60726e17	0.0488491
$707$	−3.15371e18	−0.949721
$708$	3.70659e18	1.10601
$709$	4.65855e18	1.37737	0.688684	−	0.725061i	$-0.258189\pi$
$709$	4.65855e18	1.37737	0.688684	+	0.725061i	$0.258189\pi$
$710$	0	0
$711$	−5.15223e17	−0.149569
$712$	−6.87020e17	−0.197628
$713$	−4.88223e17	−0.139167
$714$	4.67058e17	0.131926
$715$	0	0
$716$	4.77129e18	1.32343
$717$	−5.17250e18	−1.42176
$718$	−2.97151e16	−0.00809408
$719$	−5.22159e18	−1.40950	−0.704750	−	0.709456i	$-0.748941\pi$
$719$	−5.22159e18	−1.40950	−0.704750	+	0.709456i	$0.748941\pi$
$720$	0	0
$721$	−5.80335e18	−1.53851
$722$	2.10351e17	0.0552653
$723$	−1.03687e19	−2.69976
$724$	−6.42975e18	−1.65918
$725$	0	0
$726$	−2.99642e17	−0.0759478
$727$	5.29220e18	1.32942	0.664710	−	0.747101i	$-0.268555\pi$
$727$	5.29220e18	1.32942	0.664710	+	0.747101i	$0.268555\pi$
$728$	−8.86728e17	−0.220768
$729$	−6.35971e18	−1.56931
$730$	0	0
$731$	2.40973e18	0.584125
$732$	8.57318e17	0.205977
$733$	−5.48494e16	−0.0130616	−0.00653080	−	0.999979i	$-0.502079\pi$
$733$	−5.48494e16	−0.0130616	−0.00653080	+	0.999979i	$0.502079\pi$
$734$	3.92673e17	0.0926844
$735$	0	0
$736$	1.44576e17	0.0335266
$737$	2.99886e18	0.689316
$738$	6.46301e17	0.147255
$739$	3.79938e18	0.858073	0.429037	−	0.903287i	$-0.358853\pi$
$739$	3.79938e18	0.858073	0.429037	+	0.903287i	$0.358853\pi$
$740$	0	0
$741$	−1.62934e18	−0.361570
$742$	−3.84889e17	−0.0846662
$743$	−8.77336e17	−0.191310	−0.0956552	−	0.995415i	$-0.530495\pi$
$743$	−8.77336e17	−0.191310	−0.0956552	+	0.995415i	$0.530495\pi$
$744$	5.76350e17	0.124584
$745$	0	0
$746$	4.73000e17	0.100475
$747$	4.07266e18	0.857619
$748$	−6.64968e18	−1.38816
$749$	4.17942e18	0.864936
$750$	0	0
$751$	−5.78723e18	−1.17709	−0.588547	−	0.808463i	$-0.700300\pi$
$751$	−5.78723e18	−1.17709	−0.588547	+	0.808463i	$0.700300\pi$
$752$	5.22862e18	1.05432
$753$	2.84249e18	0.568239
$754$	−5.13607e17	−0.101793
$755$	0	0
$756$	4.53119e18	0.882715
$757$	−6.83799e18	−1.32070	−0.660352	−	0.750956i	$-0.729593\pi$
$757$	−6.83799e18	−1.32070	−0.660352	+	0.750956i	$0.729593\pi$
$758$	−8.37795e16	−0.0160431
$759$	−2.18599e18	−0.415026
$760$	0	0
$761$	2.35241e18	0.439049	0.219525	−	0.975607i	$-0.429549\pi$
$761$	2.35241e18	0.439049	0.219525	+	0.975607i	$0.429549\pi$
$762$	−1.27020e17	−0.0235053
$763$	5.16484e18	0.947649
$764$	3.95427e18	0.719382
$765$	0	0
$766$	−1.11197e17	−0.0198887
$767$	−5.35317e18	−0.949382
$768$	8.50817e18	1.49619
$769$	−6.22288e18	−1.08510	−0.542550	−	0.840023i	$-0.682541\pi$
$769$	−6.22288e18	−1.08510	−0.542550	+	0.840023i	$0.682541\pi$
$770$	0	0
$771$	−9.06023e18	−1.55341
$772$	8.63841e18	1.46866
$773$	4.84793e18	0.817315	0.408657	−	0.912688i	$-0.365997\pi$
$773$	4.84793e18	0.817315	0.408657	+	0.912688i	$0.365997\pi$
$774$	−2.71573e17	−0.0454015
$775$	0	0
$776$	2.53923e14	4.17446e−5 0
$777$	−1.32403e19	−2.15855
$778$	2.47776e17	0.0400582
$779$	2.04582e18	0.328000
$780$	0	0
$781$	1.28918e19	2.03274
$782$	7.32799e16	0.0114588
$783$	5.25764e18	0.815342
$784$	7.37938e18	1.13492
$785$	0	0
$786$	2.11314e17	0.0319655
$787$	−1.58990e18	−0.238525	−0.119262	−	0.992863i	$-0.538053\pi$
$787$	−1.58990e18	−0.238525	−0.119262	+	0.992863i	$0.538053\pi$
$788$	−1.33994e18	−0.199373
$789$	1.67651e19	2.47404
$790$	0	0
$791$	3.22881e18	0.468701
$792$	1.50126e18	0.216144
$793$	−1.23816e18	−0.176808
$794$	−1.43333e17	−0.0203008
$795$	0	0
$796$	−7.89230e18	−1.09969
$797$	1.21837e19	1.68384	0.841919	−	0.539603i	$-0.181426\pi$
$797$	1.21837e19	1.68384	0.841919	+	0.539603i	$0.181426\pi$
$798$	−1.66617e17	−0.0228403
$799$	7.99405e18	1.08696
$800$	0	0
$801$	−1.80391e19	−2.41325
$802$	4.39315e17	0.0582965
$803$	1.00335e19	1.32069
$804$	−5.96460e18	−0.778785
$805$	0	0
$806$	−4.15513e17	−0.0533834
$807$	−7.35896e18	−0.937860
$808$	5.84123e17	0.0738466
$809$	−9.03249e18	−1.13277	−0.566386	−	0.824140i	$-0.691659\pi$
$809$	−9.03249e18	−1.13277	−0.566386	+	0.824140i	$0.691659\pi$
$810$	0	0
$811$	−4.13436e18	−0.510238	−0.255119	−	0.966910i	$-0.582115\pi$
$811$	−4.13436e18	−0.510238	−0.255119	+	0.966910i	$0.582115\pi$
$812$	1.60861e19	1.96941
$813$	−1.82645e18	−0.221829
$814$	−6.15486e17	−0.0741583
$815$	0	0
$816$	1.31826e19	1.56320
$817$	−8.59644e17	−0.101129
$818$	−4.40557e17	−0.0514168
$819$	−2.32828e19	−2.69582
$820$	0	0
$821$	1.76054e18	0.200639	0.100320	−	0.994955i	$-0.468013\pi$
$821$	1.76054e18	0.200639	0.100320	+	0.994955i	$0.468013\pi$
$822$	−9.82008e16	−0.0111032
$823$	−1.43607e19	−1.61093	−0.805465	−	0.592643i	$-0.798084\pi$
$823$	−1.43607e19	−1.61093	−0.805465	+	0.592643i	$0.798084\pi$
$824$	1.07488e18	0.119628
$825$	0	0
$826$	−5.47419e17	−0.0599721
$827$	1.24592e19	1.35427	0.677133	−	0.735861i	$-0.263222\pi$
$827$	1.24592e19	1.35427	0.677133	+	0.735861i	$0.263222\pi$
$828$	2.52938e18	0.272783
$829$	1.21281e19	1.29774	0.648870	−	0.760900i	$-0.275242\pi$
$829$	1.21281e19	1.29774	0.648870	+	0.760900i	$0.275242\pi$
$830$	0	0
$831$	−1.73069e19	−1.82311
$832$	−1.24112e19	−1.29721
$833$	1.12823e19	1.17006
$834$	5.68134e17	0.0584617
$835$	0	0
$836$	2.37220e18	0.240331
$837$	4.25348e18	0.427591
$838$	−4.80423e17	−0.0479223
$839$	2.65901e17	0.0263188	0.0131594	−	0.999913i	$-0.495811\pi$
$839$	2.65901e17	0.0263188	0.0131594	+	0.999913i	$0.495811\pi$
$840$	0	0
$841$	8.40447e18	0.819098
$842$	−4.52217e17	−0.0437339
$843$	−1.22520e19	−1.17578
$844$	−2.93523e18	−0.279522
$845$	0	0
$846$	−9.00916e17	−0.0844845
$847$	−1.35538e19	−1.26130
$848$	−1.08634e19	−1.00321
$849$	2.06580e18	0.189316
$850$	0	0
$851$	−2.07737e18	−0.187487
$852$	−2.56412e19	−2.29658
$853$	−9.22242e18	−0.819740	−0.409870	−	0.912144i	$-0.634426\pi$
$853$	−9.22242e18	−0.819740	−0.409870	+	0.912144i	$0.634426\pi$
$854$	−1.26616e17	−0.0111689
$855$	0	0
$856$	−7.74102e17	−0.0672541
$857$	4.41223e18	0.380437	0.190218	−	0.981742i	$-0.439080\pi$
$857$	4.41223e18	0.380437	0.190218	+	0.981742i	$0.439080\pi$
$858$	−1.86043e18	−0.159201
$859$	4.93717e18	0.419298	0.209649	−	0.977777i	$-0.432768\pi$
$859$	4.93717e18	0.419298	0.209649	+	0.977777i	$0.432768\pi$
$860$	0	0
$861$	5.02516e19	4.20368
$862$	5.28717e17	0.0438961
$863$	−4.02787e18	−0.331899	−0.165949	−	0.986134i	$-0.553069\pi$
$863$	−4.02787e18	−0.331899	−0.165949	+	0.986134i	$0.553069\pi$
$864$	−1.25957e18	−0.103011
$865$	0	0
$866$	6.50759e17	0.0524269
$867$	8.16944e17	0.0653233
$868$	1.30138e19	1.03282
$869$	−1.86221e18	−0.146690
$870$	0	0
$871$	8.61426e18	0.668498
$872$	−9.56619e17	−0.0736855
$873$	6.66725e15	0.000509746 0
$874$	−2.61418e16	−0.00198386
$875$	0	0
$876$	−1.99561e19	−1.49211
$877$	−1.30375e18	−0.0967599	−0.0483800	−	0.998829i	$-0.515406\pi$
$877$	−1.30375e18	−0.0967599	−0.0483800	+	0.998829i	$0.515406\pi$
$878$	1.10488e18	0.0813954
$879$	−1.17107e19	−0.856355
$880$	0	0
$881$	4.39860e18	0.316936	0.158468	−	0.987364i	$-0.449345\pi$
$881$	4.39860e18	0.316936	0.158468	+	0.987364i	$0.449345\pi$
$882$	−1.27150e18	−0.0909434
$883$	−7.36283e18	−0.522758	−0.261379	−	0.965236i	$-0.584177\pi$
$883$	−7.36283e18	−0.522758	−0.261379	+	0.965236i	$0.584177\pi$
$884$	−1.91012e19	−1.34624
$885$	0	0
$886$	−1.27788e17	−0.00887502
$887$	1.03361e19	0.712614	0.356307	−	0.934369i	$-0.384036\pi$
$887$	1.03361e19	0.712614	0.356307	+	0.934369i	$0.384036\pi$
$888$	2.45234e18	0.167841
$889$	−5.74552e18	−0.390362
$890$	0	0
$891$	−9.29462e18	−0.622338
$892$	5.63084e18	0.374284
$893$	−2.85178e18	−0.188184
$894$	−3.60222e17	−0.0235980
$895$	0	0
$896$	−5.13550e18	−0.331574
$897$	−6.27926e18	−0.402492
$898$	1.11869e18	0.0711888
$899$	1.51002e19	0.953993
$900$	0	0
$901$	−1.66091e19	−1.03427
$902$	2.33598e18	0.144420
$903$	−2.11155e19	−1.29608
$904$	−5.98033e17	−0.0364444
$905$	0	0
$906$	2.05895e18	0.123684
$907$	2.42647e19	1.44720	0.723599	−	0.690221i	$-0.242487\pi$
$907$	2.42647e19	1.44720	0.723599	+	0.690221i	$0.242487\pi$
$908$	−1.88942e19	−1.11884
$909$	1.53373e19	0.901746
$910$	0	0
$911$	2.87375e19	1.66563	0.832816	−	0.553549i	$-0.186727\pi$
$911$	2.87375e19	1.66563	0.832816	+	0.553549i	$0.186727\pi$
$912$	−4.70273e18	−0.270635
$913$	1.47202e19	0.841109
$914$	−1.02640e17	−0.00582325
$915$	0	0
$916$	−1.57858e19	−0.882970
$917$	9.55840e18	0.530866
$918$	−6.38426e17	−0.0352073
$919$	−2.65496e19	−1.45381	−0.726905	−	0.686738i	$-0.759042\pi$
$919$	−2.65496e19	−1.45381	−0.726905	+	0.686738i	$0.759042\pi$
$920$	0	0
$921$	−4.64668e19	−2.50874
$922$	−4.96562e17	−0.0266209
$923$	3.70318e19	1.97135
$924$	5.82684e19	3.08010
$925$	0	0
$926$	1.87207e18	0.0975777
$927$	2.82232e19	1.46079
$928$	−4.47158e18	−0.229826
$929$	−2.35245e19	−1.20065	−0.600327	−	0.799754i	$-0.704963\pi$
$929$	−2.35245e19	−1.20065	−0.600327	+	0.799754i	$0.704963\pi$
$930$	0	0
$931$	−4.02484e18	−0.202571
$932$	−3.27854e19	−1.63862
$933$	3.72423e19	1.84844
$934$	1.29204e18	0.0636825
$935$	0	0
$936$	4.31239e18	0.209616
$937$	−3.40251e19	−1.64245	−0.821225	−	0.570605i	$-0.806709\pi$
$937$	−3.40251e19	−1.64245	−0.821225	+	0.570605i	$0.806709\pi$
$938$	8.80901e17	0.0422288
$939$	1.29478e19	0.616410
$940$	0	0
$941$	−6.82569e18	−0.320490	−0.160245	−	0.987077i	$-0.551228\pi$
$941$	−6.82569e18	−0.320490	−0.160245	+	0.987077i	$0.551228\pi$
$942$	1.15608e17	0.00539082
$943$	7.88433e18	0.365123
$944$	−1.54508e19	−0.710611
$945$	0	0
$946$	−9.81568e17	−0.0445275
$947$	−3.03102e19	−1.36557	−0.682784	−	0.730620i	$-0.739231\pi$
$947$	−3.03102e19	−1.36557	−0.682784	+	0.730620i	$0.739231\pi$
$948$	3.70385e18	0.165729
$949$	2.88213e19	1.28080
$950$	0	0
$951$	3.87284e19	1.69768
$952$	−3.91299e18	−0.170361
$953$	2.84246e19	1.22911	0.614554	−	0.788875i	$-0.289336\pi$
$953$	2.84246e19	1.22911	0.614554	+	0.788875i	$0.289336\pi$
$954$	1.87181e18	0.0803893
$955$	0	0
$956$	2.16322e19	0.916484
$957$	6.76102e19	2.84501
$958$	1.53655e18	0.0642200
$959$	−4.44193e18	−0.184396
$960$	0	0
$961$	−1.22013e19	−0.499695
$962$	−1.76799e18	−0.0719186
$963$	−2.03256e19	−0.821244
$964$	4.33635e19	1.74030
$965$	0	0
$966$	−6.42122e17	−0.0254253
$967$	4.24114e18	0.166806	0.0834028	−	0.996516i	$-0.473421\pi$
$967$	4.24114e18	0.166806	0.0834028	+	0.996516i	$0.473421\pi$
$968$	2.51039e18	0.0980736
$969$	−7.19002e18	−0.279014
$970$	0	0
$971$	4.32725e18	0.165686	0.0828432	−	0.996563i	$-0.473600\pi$
$971$	4.32725e18	0.165686	0.0828432	+	0.996563i	$0.473600\pi$
$972$	3.43292e19	1.30567
$973$	2.56985e19	0.970900
$974$	1.29058e18	0.0484343
$975$	0	0
$976$	−3.57369e18	−0.132341
$977$	2.00848e19	0.738843	0.369422	−	0.929262i	$-0.379556\pi$
$977$	2.00848e19	0.738843	0.369422	+	0.929262i	$0.379556\pi$
$978$	−2.85383e17	−0.0104286
$979$	−6.52001e19	−2.36680
$980$	0	0
$981$	−2.51180e19	−0.899779
$982$	1.14959e18	0.0409089
$983$	−4.85500e19	−1.71629	−0.858147	−	0.513404i	$-0.828384\pi$
$983$	−4.85500e19	−1.71629	−0.858147	+	0.513404i	$0.828384\pi$
$984$	−9.30749e18	−0.326862
$985$	0	0
$986$	−2.26647e18	−0.0785506
$987$	−7.00486e19	−2.41178
$988$	6.81415e18	0.233073
$989$	−3.31296e18	−0.112575
$990$	0	0
$991$	2.41079e19	0.808502	0.404251	−	0.914648i	$-0.367532\pi$
$991$	2.41079e19	0.808502	0.404251	+	0.914648i	$0.367532\pi$
$992$	−3.61754e18	−0.120528
$993$	−1.38173e19	−0.457355
$994$	3.78690e18	0.124529
$995$	0	0
$996$	−2.92777e19	−0.950280
$997$	−9.00367e18	−0.290336	−0.145168	−	0.989407i	$-0.546372\pi$
$997$	−9.00367e18	−0.290336	−0.145168	+	0.989407i	$0.546372\pi$
$998$	−3.06910e18	−0.0983247
$999$	1.80984e19	0.576055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.a.d.1.2	yes	4
5.2	odd	4		25.14.b.c.24.4		8
5.3	odd	4		25.14.b.c.24.5		8
5.4	even	2		25.14.a.c.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.14.a.c.1.3	✓	4	5.4	even	2
25.14.a.d.1.2	yes	4	1.1	even	1	trivial
25.14.b.c.24.4		8	5.2	odd	4
25.14.b.c.24.5		8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-5.16335 q^{2} +1952.42 q^{3} -8165.34 q^{4} -10081.0 q^{6} -455997. q^{7} +84458.7 q^{8} +2.21763e6 q^{9} +O(q^{10})\)	\(q-5.16335 q^{2} +1952.42 q^{3} -8165.34 q^{4} -10081.0 q^{6} -455997. q^{7} +84458.7 q^{8} +2.21763e6 q^{9} +8.01536e6 q^{11} -1.59422e7 q^{12} +2.30242e7 q^{13} +2.35447e6 q^{14} +6.64544e7 q^{16} +1.01602e8 q^{17} -1.14504e7 q^{18} -3.62454e7 q^{19} -8.90299e8 q^{21} -4.13861e7 q^{22} -1.39685e8 q^{23} +1.64899e8 q^{24} -1.18882e8 q^{26} +1.21696e9 q^{27} +3.72337e9 q^{28} +4.32031e9 q^{29} +3.49517e9 q^{31} -1.03501e9 q^{32} +1.56494e10 q^{33} -5.24608e8 q^{34} -1.81077e10 q^{36} +1.48718e10 q^{37} +1.87148e8 q^{38} +4.49530e10 q^{39} -5.64436e10 q^{41} +4.59692e9 q^{42} +2.37173e10 q^{43} -6.54482e10 q^{44} +7.21243e8 q^{46} +7.86799e10 q^{47} +1.29747e11 q^{48} +1.11044e11 q^{49} +1.98370e11 q^{51} -1.88000e11 q^{52} -1.63472e11 q^{53} -6.28359e9 q^{54} -3.85129e10 q^{56} -7.07664e10 q^{57} -2.23073e10 q^{58} -2.32502e11 q^{59} -5.37766e10 q^{61} -1.80468e10 q^{62} -1.01123e12 q^{63} -5.39050e11 q^{64} -8.08032e10 q^{66} +3.74139e11 q^{67} -8.29616e11 q^{68} -2.72724e11 q^{69} +1.60839e12 q^{71} +1.87298e11 q^{72} +1.25178e12 q^{73} -7.67883e10 q^{74} +2.95956e11 q^{76} -3.65498e12 q^{77} -2.32108e11 q^{78} -2.32330e11 q^{79} -1.15960e12 q^{81} +2.91438e11 q^{82} +1.83649e12 q^{83} +7.26959e12 q^{84} -1.22461e11 q^{86} +8.43507e12 q^{87} +6.76967e11 q^{88} -8.13439e12 q^{89} -1.04990e13 q^{91} +1.14058e12 q^{92} +6.82405e12 q^{93} -4.06252e11 q^{94} -2.02078e12 q^{96} +3.00647e9 q^{97} -5.73360e11 q^{98} +1.77751e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9}+O(q^{10}) \) 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9} + 6675428 q^{11} - 520595 q^{12} + 4926920 q^{13} + 37103466 q^{14} - 8440751 q^{16} + 50416220 q^{17} + 22302110 q^{18} + 282648860 q^{19} - 438887472 q^{21} + 969439305 q^{22} + 1208437080 q^{23} + 1415344455 q^{24} - 3267454372 q^{26} + 1714727420 q^{27} + 11782380170 q^{28} + 7630648840 q^{29} - 12716039032 q^{31} + 5288310415 q^{32} + 36748956820 q^{33} + 23123205021 q^{34} - 45497926906 q^{36} + 38137910960 q^{37} + 99584060705 q^{38} + 60691943624 q^{39} - 81254933612 q^{41} + 62466915570 q^{42} + 97224763400 q^{43} + 111616918681 q^{44} - 77938796802 q^{46} + 69940090280 q^{47} + 107001227905 q^{48} + 118071253428 q^{49} + 91953947668 q^{51} - 165428401300 q^{52} - 179518658440 q^{53} - 275242827665 q^{54} + 403963457310 q^{56} - 99736967860 q^{57} - 810275460480 q^{58} - 858015815320 q^{59} + 589205515328 q^{61} - 942802276470 q^{62} - 2020360823760 q^{63} - 1516614058847 q^{64} + 1418821712381 q^{66} - 685669480180 q^{67} - 2270111055215 q^{68} - 1486209750216 q^{69} + 949682379448 q^{71} - 1359611223390 q^{72} - 1688808513820 q^{73} + 1003330480306 q^{74} + 1964117678945 q^{76} + 2180313451200 q^{77} + 171961033900 q^{78} - 355815036160 q^{79} - 1150994540276 q^{81} - 224361325395 q^{82} + 8420327909340 q^{83} + 9279336345306 q^{84} - 11016868246612 q^{86} + 9035391325160 q^{87} + 12729770641515 q^{88} + 2506082642820 q^{89} - 11092233838352 q^{91} + 403195163070 q^{92} + 17882711708520 q^{93} + 15051571815036 q^{94} - 17345568428737 q^{96} + 12121501720280 q^{97} + 19722093248605 q^{98} + 1425639838304 q^{99}+O(q^{100}) \) 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9 + 6675428 * q^11 - 520595 * q^12 + 4926920 * q^13 + 37103466 * q^14 - 8440751 * q^16 + 50416220 * q^17 + 22302110 * q^18 + 282648860 * q^19 - 438887472 * q^21 + 969439305 * q^22 + 1208437080 * q^23 + 1415344455 * q^24 - 3267454372 * q^26 + 1714727420 * q^27 + 11782380170 * q^28 + 7630648840 * q^29 - 12716039032 * q^31 + 5288310415 * q^32 + 36748956820 * q^33 + 23123205021 * q^34 - 45497926906 * q^36 + 38137910960 * q^37 + 99584060705 * q^38 + 60691943624 * q^39 - 81254933612 * q^41 + 62466915570 * q^42 + 97224763400 * q^43 + 111616918681 * q^44 - 77938796802 * q^46 + 69940090280 * q^47 + 107001227905 * q^48 + 118071253428 * q^49 + 91953947668 * q^51 - 165428401300 * q^52 - 179518658440 * q^53 - 275242827665 * q^54 + 403963457310 * q^56 - 99736967860 * q^57 - 810275460480 * q^58 - 858015815320 * q^59 + 589205515328 * q^61 - 942802276470 * q^62 - 2020360823760 * q^63 - 1516614058847 * q^64 + 1418821712381 * q^66 - 685669480180 * q^67 - 2270111055215 * q^68 - 1486209750216 * q^69 + 949682379448 * q^71 - 1359611223390 * q^72 - 1688808513820 * q^73 + 1003330480306 * q^74 + 1964117678945 * q^76 + 2180313451200 * q^77 + 171961033900 * q^78 - 355815036160 * q^79 - 1150994540276 * q^81 - 224361325395 * q^82 + 8420327909340 * q^83 + 9279336345306 * q^84 - 11016868246612 * q^86 + 9035391325160 * q^87 + 12729770641515 * q^88 + 2506082642820 * q^89 - 11092233838352 * q^91 + 403195163070 * q^92 + 17882711708520 * q^93 + 15051571815036 * q^94 - 17345568428737 * q^96 + 12121501720280 * q^97 + 19722093248605 * q^98 + 1425639838304 * q^99

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