LMFDB - Embedded newform 25.14.b.c.24.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,14,Mod(24,25)]

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([1]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$26.8077322380$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 35445x^{6} + 335091828x^{4} + 383886844480x^{2} + 107862016720896 $ x^8 + 35445x^6 + 335091828x^4 + 383886844480*x^2 + 107862016720896
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.5
Root			$21.1633i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.14.b.c.24.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.16335i q^{2} +1952.42i q^{3} +8165.34 q^{4} -10081.0 q^{6} +455997. i q^{7} +84458.7i q^{8} -2.21763e6 q^{9} +O(q^{10})$	\(q+5.16335i q^{2} +1952.42i q^{3} +8165.34 q^{4} -10081.0 q^{6} +455997. i q^{7} +84458.7i q^{8} -2.21763e6 q^{9} +8.01536e6 q^{11} +1.59422e7i q^{12} +2.30242e7i q^{13} -2.35447e6 q^{14} +6.64544e7 q^{16} -1.01602e8i q^{17} -1.14504e7i q^{18} +3.62454e7 q^{19} -8.90299e8 q^{21} +4.13861e7i q^{22} -1.39685e8i q^{23} -1.64899e8 q^{24} -1.18882e8 q^{26} -1.21696e9i q^{27} +3.72337e9i q^{28} -4.32031e9 q^{29} +3.49517e9 q^{31} +1.03501e9i q^{32} +1.56494e10i q^{33} +5.24608e8 q^{34} -1.81077e10 q^{36} -1.48718e10i q^{37} +1.87148e8i q^{38} -4.49530e10 q^{39} -5.64436e10 q^{41} -4.59692e9i q^{42} +2.37173e10i q^{43} +6.54482e10 q^{44} +7.21243e8 q^{46} -7.86799e10i q^{47} +1.29747e11i q^{48} -1.11044e11 q^{49} +1.98370e11 q^{51} +1.88000e11i q^{52} -1.63472e11i q^{53} +6.28359e9 q^{54} -3.85129e10 q^{56} +7.07664e10i q^{57} -2.23073e10i q^{58} +2.32502e11 q^{59} -5.37766e10 q^{61} +1.80468e10i q^{62} -1.01123e12i q^{63} +5.39050e11 q^{64} -8.08032e10 q^{66} -3.74139e11i q^{67} -8.29616e11i q^{68} +2.72724e11 q^{69} +1.60839e12 q^{71} -1.87298e11i q^{72} +1.25178e12i q^{73} +7.67883e10 q^{74} +2.95956e11 q^{76} +3.65498e12i q^{77} -2.32108e11i q^{78} +2.32330e11 q^{79} -1.15960e12 q^{81} -2.91438e11i q^{82} +1.83649e12i q^{83} -7.26959e12 q^{84} -1.22461e11 q^{86} -8.43507e12i q^{87} +6.76967e11i q^{88} +8.13439e12 q^{89} -1.04990e13 q^{91} -1.14058e12i q^{92} +6.82405e12i q^{93} +4.06252e11 q^{94} -2.02078e12 q^{96} -3.00647e9i q^{97} -5.73360e11i q^{98} -1.77751e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 7466 q^{4} + 80666 q^{6} - 95744 q^{9}+O(q^{10}) $ 8 * q - 7466 * q^4 + 80666 * q^6 - 95744 * q^9	$ 8 q - 7466 q^{4} + 80666 q^{6} - 95744 q^{9} + 13350856 q^{11} - 74206932 q^{14} - 16881502 q^{16} - 565297720 q^{19} - 877774944 q^{21} - 2830688910 q^{24} - 6534908744 q^{26} - 15261297680 q^{29} - 25432078064 q^{31} - 46246410042 q^{34} - 90995853812 q^{36} - 121383887248 q^{39} - 162509867224 q^{41} - 223233837362 q^{44} - 155877593604 q^{46} - 236142506856 q^{49} + 183907895336 q^{51} + 550485655330 q^{54} + 807926914620 q^{56} + 1716031630640 q^{59} + 1178411030656 q^{61} + 3033228117694 q^{64} + 2837643424762 q^{66} + 2972419500432 q^{69} + 1899364758896 q^{71} - 2006660960612 q^{74} + 3928235357890 q^{76} + 711630072320 q^{79} - 2301989080552 q^{81} - 18558672690612 q^{84} - 22033736493224 q^{86} - 5012165285640 q^{89} - 22184467676704 q^{91} - 30103143630072 q^{94} - 34691136857474 q^{96} - 2851279676608 q^{99}+O(q^{100}) $ 8 * q - 7466 * q^4 + 80666 * q^6 - 95744 * q^9 + 13350856 * q^11 - 74206932 * q^14 - 16881502 * q^16 - 565297720 * q^19 - 877774944 * q^21 - 2830688910 * q^24 - 6534908744 * q^26 - 15261297680 * q^29 - 25432078064 * q^31 - 46246410042 * q^34 - 90995853812 * q^36 - 121383887248 * q^39 - 162509867224 * q^41 - 223233837362 * q^44 - 155877593604 * q^46 - 236142506856 * q^49 + 183907895336 * q^51 + 550485655330 * q^54 + 807926914620 * q^56 + 1716031630640 * q^59 + 1178411030656 * q^61 + 3033228117694 * q^64 + 2837643424762 * q^66 + 2972419500432 * q^69 + 1899364758896 * q^71 - 2006660960612 * q^74 + 3928235357890 * q^76 + 711630072320 * q^79 - 2301989080552 * q^81 - 18558672690612 * q^84 - 22033736493224 * q^86 - 5012165285640 * q^89 - 22184467676704 * q^91 - 30103143630072 * q^94 - 34691136857474 * q^96 - 2851279676608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	5.16335i	0.0570475i	0.999593	+	0.0285237i	$0.00908062\pi$
$2$	5.16335i	0.0570475i	−0.999593	+	0.0285237i	$0.990919\pi$
$3$	1952.42i	1.54627i	0.634241	+	0.773136i	$0.281313\pi$
$3$	1952.42i	1.54627i	−0.634241	+	0.773136i	$0.718687\pi$
$4$	8165.34	0.996746
$5$	0	0
$5$	0	0
$6$	−10081.0	−0.0882109
$7$	455997.i	1.46496i	0.680790	+	0.732478i	$0.261636\pi$
$7$	455997.i	1.46496i	−0.680790	+	0.732478i	$0.738364\pi$
$8$	84458.7i	0.113909i
$9$	−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	$0.261072\pi$
$12$	1.59422e7i	1.54124i
$13$	2.30242e7i	1.32298i	0.749955	+	0.661489i	$0.230075\pi$
$13$	2.30242e7i	1.32298i	−0.749955	+	0.661489i	$0.769925\pi$
$14$	−2.35447e6	−0.0835721
$15$	0	0
$16$	6.64544e7	0.990247
$17$	− 1.01602e8i	− 1.02090i	−0.859906	−	0.510452i	$-0.829478\pi$
$17$	− 1.01602e8i	− 1.02090i	0.859906	−	0.510452i	$-0.170522\pi$
$18$	− 1.14504e7i	− 0.0793505i
$19$	3.62454e7	0.176748	0.0883740	−	0.996087i	$-0.471833\pi$
$19$	3.62454e7	0.176748	0.0883740	+	0.996087i	$0.471833\pi$
$20$	0	0
$21$	−8.90299e8	−2.26522
$22$	4.13861e7i	0.0778229i
$23$	− 1.39685e8i	− 0.196752i	−0.995149	−	0.0983760i	$-0.968635\pi$
$23$	− 1.39685e8i	− 0.196752i	0.995149	−	0.0983760i	$-0.0313648\pi$
$24$	−1.64899e8	−0.176135
$25$	0	0
$26$	−1.18882e8	−0.0754726
$27$	− 1.21696e9i	− 0.604521i
$28$	3.72337e9i	1.46019i
$29$	−4.32031e9	−1.34874	−0.674370	−	0.738394i	$-0.735585\pi$
$29$	−4.32031e9	−1.34874	−0.674370	+	0.738394i	$0.735585\pi$
$30$	0	0
$31$	3.49517e9	0.707322	0.353661	−	0.935374i	$-0.384937\pi$
$31$	3.49517e9	0.707322	0.353661	+	0.935374i	$0.384937\pi$
$32$	1.03501e9i	0.170400i
$33$	1.56494e10i	2.10939i
$34$	5.24608e8	0.0582400
$35$	0	0
$36$	−1.81077e10	−1.38643
$37$	− 1.48718e10i	− 0.952911i	−0.879199	−	0.476455i	$-0.841921\pi$
$37$	− 1.48718e10i	− 0.952911i	0.879199	−	0.476455i	$-0.158079\pi$
$38$	1.87148e8i	0.0100830i
$39$	−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	$0.878366\pi$
$42$	− 4.59692e9i	− 0.129225i
$43$	2.37173e10i	0.572164i	0.958205	+	0.286082i	$0.0923530\pi$
$43$	2.37173e10i	0.572164i	−0.958205	+	0.286082i	$0.907647\pi$
$44$	6.54482e10	1.35974
$45$	0	0
$46$	7.21243e8	0.0112242
$47$	− 7.86799e10i	− 1.06470i	−0.846524	−	0.532350i	$-0.821309\pi$
$47$	− 7.86799e10i	− 1.06470i	0.846524	−	0.532350i	$-0.178691\pi$
$48$	1.29747e11i	1.53119i
$49$	−1.11044e11	−1.14610
$50$	0	0
$51$	1.98370e11	1.57859
$52$	1.88000e11i	1.31867i
$53$	− 1.63472e11i	− 1.01309i	−0.862213	−	0.506546i	$-0.830922\pi$
$53$	− 1.63472e11i	− 1.01309i	0.862213	−	0.506546i	$-0.169078\pi$
$54$	6.28359e9	0.0344864
$55$	0	0
$56$	−3.85129e10	−0.166872
$57$	7.07664e10i	0.273300i
$58$	− 2.23073e10i	− 0.0769422i
$59$	2.32502e11	0.717610	0.358805	−	0.933413i	$-0.383184\pi$
$59$	2.32502e11	0.717610	0.358805	+	0.933413i	$0.383184\pi$
$60$	0	0
$61$	−5.37766e10	−0.133644	−0.0668220	−	0.997765i	$-0.521286\pi$
$61$	−5.37766e10	−0.133644	−0.0668220	+	0.997765i	$0.521286\pi$
$62$	1.80468e10i	0.0403510i
$63$	− 1.01123e12i	− 2.03769i
$64$	5.39050e11	0.980526
$65$	0	0
$66$	−8.08032e10	−0.120335
$67$	− 3.74139e11i	− 0.505298i	−0.967558	−	0.252649i	$-0.918698\pi$
$67$	− 3.74139e11i	− 0.505298i	0.967558	−	0.252649i	$-0.0813017\pi$
$68$	− 8.29616e11i	− 1.01758i
$69$	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	$0.232429\pi$
$72$	− 1.87298e11i	− 0.158443i
$73$	1.25178e12i	0.968122i	0.875034	+	0.484061i	$0.160839\pi$
$73$	1.25178e12i	0.968122i	−0.875034	+	0.484061i	$0.839161\pi$
$74$	7.67883e10	0.0543612
$75$	0	0
$76$	2.95956e11	0.176173
$77$	3.65498e12i	1.99846i
$78$	− 2.32108e11i	− 0.116701i
$79$	2.32330e11	0.107530	0.0537650	−	0.998554i	$-0.482878\pi$
$79$	2.32330e11	0.107530	0.0537650	+	0.998554i	$0.482878\pi$
$80$	0	0
$81$	−1.15960e12	−0.456200
$82$	− 2.91438e11i	− 0.105866i
$83$	1.83649e12i	0.616569i	0.951294	+	0.308284i	$0.0997549\pi$
$83$	1.83649e12i	0.616569i	−0.951294	+	0.308284i	$0.900245\pi$
$84$	−7.26959e12	−2.25785
$85$	0	0
$86$	−1.22461e11	−0.0326405
$87$	− 8.43507e12i	− 2.08552i
$88$	6.76967e11i	0.155393i
$89$	8.13439e12	1.73496	0.867481	−	0.497470i	$-0.165738\pi$
$89$	8.13439e12	1.73496	0.867481	+	0.497470i	$0.165738\pi$
$90$	0	0
$91$	−1.04990e13	−1.93811
$92$	− 1.14058e12i	− 0.196112i
$93$	6.82405e12i	1.09371i
$94$	4.06252e11	0.0607385
$95$	0	0
$96$	−2.02078e12	−0.263485
$97$	− 3.00647e9i	0 0.000366472i	−1.00000		0.000183236i	$-0.999942\pi$
$97$	− 3.00647e9i	0 0.000366472i	1.00000		0.000183236i	$-5.83259e-5\pi$
$98$	− 5.73360e11i	− 0.0653820i
$99$	−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	$0.394923\pi$
$102$	1.02426e12i	0.0900549i
$103$	1.27267e13i	1.05021i	0.851039	+	0.525103i	$0.175973\pi$
$103$	1.27267e13i	1.05021i	−0.851039	+	0.525103i	$0.824027\pi$
$104$	−1.94459e12	−0.150700
$105$	0	0
$106$	8.44061e11	0.0577944
$107$	9.16545e12i	0.590418i	0.955433	+	0.295209i	$0.0953892\pi$
$107$	9.16545e12i	0.590418i	−0.955433	+	0.295209i	$0.904611\pi$
$108$	− 9.93689e12i	− 0.602554i
$109$	1.13265e13	0.646879	0.323439	−	0.946249i	$-0.395161\pi$
$109$	1.13265e13	0.646879	0.323439	+	0.946249i	$0.395161\pi$
$110$	0	0
$111$	2.90360e13	1.47346
$112$	3.03030e13i	1.45067i
$113$	− 7.08078e12i	− 0.319942i	−0.987122	−	0.159971i	$-0.948860\pi$
$113$	− 7.08078e12i	− 0.319942i	0.987122	−	0.159971i	$-0.0511400\pi$
$114$	−3.65391e11	−0.0155911
$115$	0	0
$116$	−3.52768e13	−1.34435
$117$	− 5.10592e13i	− 1.84020i
$118$	1.20049e12i	0.0409378i
$119$	4.63303e13	1.49558
$120$	0	0
$121$	2.97234e13	0.860980
$122$	− 2.77668e11i	− 0.00762406i
$123$	− 1.10202e14i	− 2.86949i
$124$	2.85392e13	0.705020
$125$	0	0
$126$	5.22135e12	0.116245
$127$	− 1.25999e13i	− 0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$127$	− 1.25999e13i	− 0.266467i	0.991085	−	0.133233i	$-0.0425360\pi$
$128$	1.12621e13i	0.226337i
$129$	−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	$0.557994\pi$
$132$	1.27782e14i	2.10252i
$133$	1.65278e13i	0.258928i
$134$	1.93181e12	0.0288260
$135$	0	0
$136$	8.58118e12	0.116291
$137$	− 9.74113e12i	− 0.125871i	−0.998018	−	0.0629355i	$-0.979954\pi$
$137$	− 9.74113e12i	− 0.125871i	0.998018	−	0.0629355i	$-0.0200462\pi$
$138$	1.40817e12i	0.0173557i
$139$	5.63567e13	0.662750	0.331375	−	0.943499i	$-0.392488\pi$
$139$	5.63567e13	0.662750	0.331375	+	0.943499i	$0.392488\pi$
$140$	0	0
$141$	1.53616e14	1.64632
$142$	8.30466e12i	0.0850056i
$143$	1.84547e14i	1.80478i
$144$	−1.47371e14	−1.37739
$145$	0	0
$146$	−6.46339e12	−0.0552289
$147$	− 2.16805e14i	− 1.77218i
$148$	− 1.21433e14i	− 0.949810i
$149$	−3.57326e13	−0.267519	−0.133759	−	0.991014i	$-0.542705\pi$
$149$	−3.57326e13	−0.267519	−0.133759	+	0.991014i	$0.542705\pi$
$150$	0	0
$151$	−2.04240e14	−1.40214	−0.701068	−	0.713095i	$-0.747293\pi$
$151$	−2.04240e14	−1.40214	−0.701068	+	0.713095i	$0.747293\pi$
$152$	3.06124e12i	0.0201333i
$153$	2.25316e14i	1.42003i
$154$	−1.88720e13	−0.114007
$155$	0	0
$156$	−3.67056e14	−2.03903
$157$	1.14678e13i	0.0611129i	0.999533	+	0.0305565i	$0.00972794\pi$
$157$	1.14678e13i	0.0611129i	−0.999533	+	0.0305565i	$0.990272\pi$
$158$	1.19960e12i	0.00613432i
$159$	3.19165e14	1.56652
$160$	0	0
$161$	6.36960e13	0.288233
$162$	− 5.98742e12i	− 0.0260251i
$163$	2.83088e13i	0.118223i	0.998251	+	0.0591116i	$0.0188268\pi$
$163$	2.83088e13i	0.118223i	−0.998251	+	0.0591116i	$0.981173\pi$
$164$	−4.60881e14	−1.84971
$165$	0	0
$166$	−9.48245e12	−0.0351737
$167$	− 1.84618e14i	− 0.658593i	−0.944227	−	0.329296i	$-0.893189\pi$
$167$	− 1.84618e14i	− 0.658593i	0.944227	−	0.329296i	$-0.106811\pi$
$168$	− 7.51934e13i	− 0.258030i
$169$	−2.27238e14	−0.750271
$170$	0	0
$171$	−8.03789e13	−0.245848
$172$	1.93660e14i	0.570302i
$173$	2.26452e14i	0.642210i	0.947044	+	0.321105i	$0.104054\pi$
$173$	2.26452e14i	0.642210i	−0.947044	+	0.321105i	$0.895946\pi$
$174$	4.35532e13	0.118974
$175$	0	0
$176$	5.32656e14	1.35087
$177$	4.53942e14i	1.10962i
$178$	4.20007e13i	0.0989752i
$179$	5.84334e14	1.32775	0.663876	−	0.747843i	$-0.268910\pi$
$179$	5.84334e14	1.32775	0.663876	+	0.747843i	$0.268910\pi$
$180$	0	0
$181$	7.87444e14	1.66460	0.832298	−	0.554328i	$-0.187025\pi$
$181$	7.87444e14	1.66460	0.832298	+	0.554328i	$0.187025\pi$
$182$	− 5.42098e13i	− 0.110564i
$183$	− 1.04995e14i	− 0.206650i
$184$	1.17976e13	0.0224119
$185$	0	0
$186$	−3.52349e13	−0.0623935
$187$	− 8.14379e14i	− 1.39269i
$188$	− 6.42448e14i	− 1.06124i
$189$	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	$0.617519\pi$
$192$	1.05245e15i	1.51616i
$193$	− 1.05794e15i	− 1.47346i	−0.676190	−	0.736728i	$-0.736370\pi$
$193$	− 1.05794e15i	− 1.47346i	0.676190	−	0.736728i	$-0.263630\pi$
$194$	1.55235e10	2.09063e−5 0
$195$	0	0
$196$	−9.06714e14	−1.14237
$197$	− 1.64101e14i	− 0.200024i	−0.994986	−	0.100012i	$-0.968112\pi$
$197$	− 1.64101e14i	− 0.200024i	0.994986	−	0.100012i	$-0.0318881\pi$
$198$	− 9.17791e13i	− 0.108248i
$199$	−9.66561e14	−1.10328	−0.551638	−	0.834083i	$-0.685997\pi$
$199$	−9.66561e14	−1.10328	−0.551638	+	0.834083i	$0.685997\pi$
$200$	0	0
$201$	7.30478e14	0.781327
$202$	3.57102e13i	0.0369835i
$203$	− 1.97005e15i	− 1.97584i
$204$	1.61976e15	1.57346
$205$	0	0
$206$	−6.57125e13	−0.0599116
$207$	3.09770e14i	0.273673i
$208$	1.53006e15i	1.31008i
$209$	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	$0.455220\pi$
$212$	− 1.33480e15i	− 1.00980i
$213$	3.14025e15i	2.30407i
$214$	−4.73244e13	−0.0336818
$215$	0	0
$216$	1.02783e14	0.0688606
$217$	1.59379e15i	1.03620i
$218$	5.84826e13i	0.0369028i
$219$	−2.44401e15	−1.49698
$220$	0	0
$221$	2.33931e15	1.35063
$222$	1.49923e14i	0.0840571i
$223$	− 6.89603e14i	− 0.375507i	−0.982216	−	0.187753i	$-0.939879\pi$
$223$	− 6.89603e14i	− 0.375507i	0.982216	−	0.187753i	$-0.0601205\pi$
$224$	−4.71963e14	−0.249629
$225$	0	0
$226$	3.65605e13	0.0182519
$227$	− 2.31395e15i	− 1.12250i	−0.827647	−	0.561249i	$-0.810321\pi$
$227$	− 2.31395e15i	− 1.12250i	0.827647	−	0.561249i	$-0.189679\pi$
$228$	5.77831e14i	0.272411i
$229$	−1.93327e15	−0.885853	−0.442927	−	0.896558i	$-0.646060\pi$
$229$	−1.93327e15	−0.885853	−0.442927	+	0.896558i	$0.646060\pi$
$230$	0	0
$231$	−7.13607e15	−3.09016
$232$	− 3.64888e14i	− 0.153634i
$233$	4.01520e15i	1.64397i	0.569511	+	0.821984i	$0.307133\pi$
$233$	4.01520e15i	1.64397i	−0.569511	+	0.821984i	$0.692867\pi$
$234$	2.63636e14	0.104979
$235$	0	0
$236$	1.89846e15	0.715274
$237$	4.53607e14i	0.166271i
$238$	2.39219e14i	0.0853191i
$239$	2.64927e15	0.919476	0.459738	−	0.888054i	$-0.347943\pi$
$239$	2.64927e15	0.919476	0.459738	+	0.888054i	$0.347943\pi$
$240$	0	0
$241$	−5.31068e15	−1.74598	−0.872990	−	0.487739i	$-0.837822\pi$
$241$	−5.31068e15	−1.74598	−0.872990	+	0.487739i	$0.837822\pi$
$242$	1.53472e14i	0.0491167i
$243$	− 4.20426e15i	− 1.30993i
$244$	−4.39105e14	−0.133209
$245$	0	0
$246$	5.69010e14	0.163697
$247$	8.34521e14i	0.233834i
$248$	2.95197e14i	0.0805706i
$249$	−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	$0.441178\pi$
$252$	− 8.25706e15i	− 2.03106i
$253$	− 1.11963e15i	− 0.268405i
$254$	6.50577e13	0.0152013
$255$	0	0
$256$	4.35775e15	0.967614
$257$	4.64051e15i	1.00462i	0.864689	+	0.502308i	$0.167516\pi$
$257$	4.64051e15i	1.00462i	−0.864689	+	0.502308i	$0.832484\pi$
$258$	− 2.39095e14i	− 0.0504711i
$259$	6.78149e15	1.39597
$260$	0	0
$261$	9.58086e15	1.87604
$262$	− 1.08232e14i	− 0.0206727i
$263$	8.58684e15i	1.60000i	0.599997	+	0.800002i	$0.295168\pi$
$263$	8.58684e15i	1.60000i	−0.599997	+	0.800002i	$0.704832\pi$
$264$	−1.32173e15	−0.240279
$265$	0	0
$266$	−8.53388e13	−0.0147712
$267$	1.58818e16i	2.68272i
$268$	− 3.05498e15i	− 0.503653i
$269$	3.76914e15	0.606530	0.303265	−	0.952906i	$-0.401923\pi$
$269$	3.76914e15	0.606530	0.303265	+	0.952906i	$0.401923\pi$
$270$	0	0
$271$	−9.35477e14	−0.143461	−0.0717303	−	0.997424i	$-0.522852\pi$
$271$	−9.35477e14	−0.143461	−0.0717303	+	0.997424i	$0.522852\pi$
$272$	− 6.75191e15i	− 1.01095i
$273$	− 2.04984e16i	− 2.99684i
$274$	5.02969e13	0.00718063
$275$	0	0
$276$	2.22689e15	0.303242
$277$	8.86434e15i	1.17904i	0.807754	+	0.589519i	$0.200683\pi$
$277$	8.86434e15i	1.17904i	−0.807754	+	0.589519i	$0.799317\pi$
$278$	2.90990e14i	0.0378082i
$279$	−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	$0.624145\pi$
$282$	7.93175e14i	0.0939182i
$283$	1.05807e15i	0.122434i	0.998124	+	0.0612170i	$0.0194982\pi$
$283$	1.05807e15i	0.122434i	−0.998124	+	0.0612170i	$0.980502\pi$
$284$	1.31330e16	1.48524
$285$	0	0
$286$	−9.52882e14	−0.102958
$287$	− 2.57381e16i	− 2.71859i
$288$	− 2.29528e15i	− 0.237019i
$289$	−4.18426e14	−0.0422457
$290$	0	0
$291$	5.86991e12	0.000566666 0
$292$	1.02212e16i	0.964971i
$293$	− 5.99802e15i	− 0.553819i	−0.960896	−	0.276910i	$-0.910690\pi$
$293$	− 5.99802e15i	− 0.553819i	0.960896	−	0.276910i	$-0.0893103\pi$
$294$	1.11944e15	0.101098
$295$	0	0
$296$	1.25605e15	0.108545
$297$	− 9.75437e15i	− 0.824674i
$298$	− 1.84500e14i	− 0.0152613i
$299$	3.21614e15	0.260299
$300$	0	0
$301$	−1.08150e16	−0.838196
$302$	− 1.05456e15i	− 0.0799883i
$303$	1.35031e16i	1.00244i
$304$	2.40867e15	0.175024
$305$	0	0
$306$	−1.16339e15	−0.0810092
$307$	2.37996e16i	1.62244i	0.584739	+	0.811222i	$0.301197\pi$
$307$	2.37996e16i	1.62244i	−0.584739	+	0.811222i	$0.698803\pi$
$308$	2.98442e16i	1.99196i
$309$	−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	$0.296077\pi$
$312$	− 3.79667e15i	− 0.233022i
$313$	6.63166e15i	0.398643i	0.979934	+	0.199321i	$0.0638738\pi$
$313$	6.63166e15i	0.398643i	−0.979934	+	0.199321i	$0.936126\pi$
$314$	−5.92123e13	−0.00348634
$315$	0	0
$316$	1.89706e15	0.107180
$317$	− 1.98361e16i	− 1.09792i	−0.835848	−	0.548960i	$-0.815024\pi$
$317$	− 1.98361e16i	− 1.09792i	0.835848	−	0.548960i	$-0.184976\pi$
$318$	1.64796e15i	0.0893658i
$319$	−3.46289e16	−1.83992
$320$	0	0
$321$	−1.78948e16	−0.912946
$322$	3.28885e14i	0.0164430i
$323$	− 3.68261e15i	− 0.180443i
$324$	−9.46853e15	−0.454716
$325$	0	0
$326$	−1.46168e14	−0.00674434
$327$	2.21141e16i	1.00025i
$328$	− 4.76715e15i	− 0.211387i
$329$	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	$0.547248\pi$
$332$	1.49956e16i	0.614562i
$333$	3.29801e16i	1.32546i
$334$	9.53247e14	0.0375711
$335$	0	0
$336$	−5.91642e16	−2.24313
$337$	− 5.01755e16i	− 1.86594i	−0.359955	−	0.932970i	$-0.617208\pi$
$337$	− 5.01755e16i	− 1.86594i	0.359955	−	0.932970i	$-0.382792\pi$
$338$	− 1.17331e15i	− 0.0428011i
$339$	1.38247e16	0.494717
$340$	0	0
$341$	2.80151e16	0.964913
$342$	− 4.15025e14i	− 0.0140250i
$343$	− 6.45475e15i	− 0.214026i
$344$	−2.00313e15	−0.0651748
$345$	0	0
$346$	−1.16925e15	−0.0366365
$347$	− 5.89702e16i	− 1.81339i	−0.421788	−	0.906695i	$-0.638597\pi$
$347$	− 5.89702e16i	− 1.81339i	0.421788	−	0.906695i	$-0.361403\pi$
$348$	− 6.88752e16i	− 2.07873i
$349$	2.75077e16	0.814871	0.407435	−	0.913234i	$-0.366423\pi$
$349$	2.75077e16	0.814871	0.407435	+	0.913234i	$0.366423\pi$
$350$	0	0
$351$	2.80195e16	0.799769
$352$	8.29600e15i	0.232456i
$353$	− 3.11283e16i	− 0.856288i	−0.903711	−	0.428144i	$-0.859168\pi$
$353$	− 3.11283e16i	− 0.856288i	0.903711	−	0.428144i	$-0.140832\pi$
$354$	−2.34386e15	−0.0633010
$355$	0	0
$356$	6.64201e16	1.72932
$357$	9.04563e16i	2.31257i
$358$	3.01712e15i	0.0757449i
$359$	−5.75500e15	−0.141883	−0.0709416	−	0.997480i	$-0.522600\pi$
$359$	−5.75500e15	−0.141883	−0.0709416	+	0.997480i	$0.522600\pi$
$360$	0	0
$361$	−4.07393e16	−0.968760
$362$	4.06585e15i	0.0949611i
$363$	5.80325e16i	1.33131i
$364$	−8.57276e16	−1.93180
$365$	0	0
$366$	5.42124e14	0.0117889
$367$	7.60500e16i	1.62469i	0.583178	+	0.812344i	$0.301809\pi$
$367$	7.60500e16i	1.62469i	−0.583178	+	0.812344i	$0.698191\pi$
$368$	− 9.28269e15i	− 0.194833i
$369$	1.25171e17	2.58126
$370$	0	0
$371$	7.45425e16	1.48414
$372$	5.57207e16i	1.09015i
$373$	− 9.16071e16i	− 1.76125i	−0.473811	−	0.880627i	$-0.657122\pi$
$373$	− 9.16071e16i	− 1.76125i	0.473811	−	0.880627i	$-0.342878\pi$
$374$	4.20492e15	0.0794497
$375$	0	0
$376$	6.64520e15	0.121279
$377$	− 9.94717e16i	− 1.78435i
$378$	2.86530e15i	0.0505211i
$379$	−1.62258e16	−0.281223	−0.140612	−	0.990065i	$-0.544907\pi$
$379$	−1.62258e16	−0.281223	−0.140612	+	0.990065i	$0.544907\pi$
$380$	0	0
$381$	2.46003e16	0.412030
$382$	− 2.50048e15i	− 0.0411729i
$383$	2.15358e16i	0.348634i	0.984690	+	0.174317i	$0.0557717\pi$
$383$	2.15358e16i	0.348634i	−0.984690	+	0.174317i	$0.944228\pi$
$384$	−2.19884e16	−0.349978
$385$	0	0
$386$	5.46249e15	0.0840569
$387$	− 5.25963e16i	− 0.795854i
$388$	− 2.45489e13i	0 0.000365280i
$389$	4.79874e16	0.702190	0.351095	−	0.936340i	$-0.385809\pi$
$389$	4.79874e16	0.702190	0.351095	+	0.936340i	$0.385809\pi$
$390$	0	0
$391$	−1.41923e16	−0.200865
$392$	− 9.37865e15i	− 0.130551i
$393$	− 4.09258e16i	− 0.560332i
$394$	8.47313e14	0.0114109
$395$	0	0
$396$	−1.45140e17	−1.89133
$397$	− 2.77596e16i	− 0.355857i	−0.984043	−	0.177929i	$-0.943060\pi$
$397$	− 2.77596e16i	− 0.355857i	0.984043	−	0.177929i	$-0.0569396\pi$
$398$	− 4.99069e15i	− 0.0629392i
$399$	−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	$0.670705\pi$
$402$	3.77172e15i	0.0445728i
$403$	8.04735e16i	0.935772i
$404$	5.64722e16	0.646183
$405$	0	0
$406$	1.01721e16	0.112717
$407$	− 1.19203e17i	− 1.29994i
$408$	1.67541e16i	0.179817i
$409$	−8.53238e16	−0.901298	−0.450649	−	0.892701i	$-0.648807\pi$
$409$	−8.53238e16	−0.901298	−0.450649	+	0.892701i	$0.648807\pi$
$410$	0	0
$411$	1.90188e16	0.194631
$412$	1.03918e17i	1.04679i
$413$	1.06020e17i	1.05127i
$414$	−1.59945e15	−0.0156124
$415$	0	0
$416$	−2.38303e16	−0.225436
$417$	1.10032e17i	1.02479i
$418$	1.50006e15i	0.0137550i
$419$	−9.30449e16	−0.840043	−0.420021	−	0.907514i	$-0.637977\pi$
$419$	−9.30449e16	−0.840043	−0.420021	+	0.907514i	$0.637977\pi$
$420$	0	0
$421$	8.75821e16	0.766623	0.383312	−	0.923619i	$-0.374784\pi$
$421$	8.75821e16	0.766623	0.383312	+	0.923619i	$0.374784\pi$
$422$	1.85609e15i	0.0159981i
$423$	1.74483e17i	1.48095i
$424$	1.38066e16	0.115401
$425$	0	0
$426$	−1.62142e16	−0.131442
$427$	− 2.45220e16i	− 0.195783i
$428$	7.48390e16i	0.588496i
$429$	−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	$0.625707\pi$
$432$	− 8.08723e16i	− 0.598626i
$433$	− 1.26034e17i	− 0.919004i	−0.888177	−	0.459502i	$-0.848028\pi$
$433$	− 1.26034e17i	− 0.919004i	0.888177	−	0.459502i	$-0.151972\pi$
$434$	−8.22928e15	−0.0591124
$435$	0	0
$436$	9.24846e16	0.644773
$437$	− 5.06295e15i	− 0.0347755i
$438$	− 1.26193e16i	− 0.0853989i
$439$	2.13985e17	1.42680	0.713400	−	0.700757i	$-0.247154\pi$
$439$	2.13985e17	1.42680	0.713400	+	0.700757i	$0.247154\pi$
$440$	0	0
$441$	2.46255e17	1.59417
$442$	1.20787e16i	0.0770503i
$443$	2.47490e16i	0.155572i	0.996970	+	0.0777862i	$0.0247852\pi$
$443$	2.47490e16i	0.155572i	−0.996970	+	0.0777862i	$0.975215\pi$
$444$	2.37089e17	1.46866
$445$	0	0
$446$	3.56066e15	0.0214217
$447$	− 6.97651e16i	− 0.413656i
$448$	2.45805e17i	1.43643i
$449$	2.16659e17	1.24789	0.623943	−	0.781470i	$-0.285530\pi$
$449$	2.16659e17	1.24789	0.623943	+	0.781470i	$0.285530\pi$
$450$	0	0
$451$	−4.52416e17	−2.53157
$452$	− 5.78169e16i	− 0.318901i
$453$	− 3.98762e17i	− 2.16808i
$454$	1.19477e16	0.0640357
$455$	0	0
$456$	−5.97683e15	−0.0311315
$457$	− 1.98785e16i	− 0.102077i	−0.998697	−	0.0510386i	$-0.983747\pi$
$457$	− 1.98785e16i	− 0.102077i	0.998697	−	0.0510386i	$-0.0162531\pi$
$458$	− 9.98214e15i	− 0.0505357i
$459$	−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	$0.425040\pi$
$462$	− 3.68460e16i	− 0.176286i
$463$	− 3.62569e17i	− 1.71046i	−0.518245	−	0.855232i	$-0.673414\pi$
$463$	− 3.62569e17i	− 1.71046i	0.518245	−	0.855232i	$-0.326586\pi$
$464$	−2.87104e17	−1.33559
$465$	0	0
$466$	−2.07319e16	−0.0937842
$467$	2.50232e17i	1.11631i	0.829738	+	0.558153i	$0.188490\pi$
$467$	2.50232e17i	1.11631i	−0.829738	+	0.558153i	$0.811510\pi$
$468$	− 4.16915e17i	− 1.83421i
$469$	1.70606e17	0.740239
$470$	0	0
$471$	−2.23900e16	−0.0944971
$472$	1.96368e16i	0.0817424i
$473$	1.90103e17i	0.780533i
$474$	−2.34213e15	−0.00948532
$475$	0	0
$476$	3.78303e17	1.49071
$477$	3.62519e17i	1.40917i
$478$	1.36791e16i	0.0524538i
$479$	2.97588e17	1.12573	0.562865	−	0.826549i	$-0.309699\pi$
$479$	2.97588e17	1.12573	0.562865	+	0.826549i	$0.309699\pi$
$480$	0	0
$481$	3.42411e17	1.26068
$482$	− 2.74209e16i	− 0.0996037i
$483$	1.24362e17i	0.445687i
$484$	2.42701e17	0.858178
$485$	0	0
$486$	2.17080e16	0.0747283
$487$	2.49951e17i	0.849017i	0.905424	+	0.424508i	$0.139553\pi$
$487$	2.49951e17i	0.849017i	−0.905424	+	0.424508i	$0.860447\pi$
$488$	− 4.54190e15i	− 0.0152233i
$489$	−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	$0.616729\pi$
$492$	− 8.99834e17i	− 2.86015i
$493$	4.38953e17i	1.37693i
$494$	−4.30893e15	−0.0133396
$495$	0	0
$496$	2.32269e17	0.700424
$497$	7.33419e17i	2.18291i
$498$	− 1.85138e16i	− 0.0543881i
$499$	−5.94401e17	−1.72356	−0.861779	−	0.507284i	$-0.830650\pi$
$499$	−5.94401e17	−1.72356	−0.861779	+	0.507284i	$0.830650\pi$
$500$	0	0
$501$	3.60452e17	1.01836
$502$	7.51720e15i	0.0209644i
$503$	− 2.62564e17i	− 0.722843i	−0.932403	−	0.361421i	$-0.882292\pi$
$503$	− 2.62564e17i	− 0.722843i	0.932403	−	0.361421i	$-0.117708\pi$
$504$	8.54074e16	0.232112
$505$	0	0
$506$	5.78103e15	0.0153118
$507$	− 4.43665e17i	− 1.16012i
$508$	− 1.02882e17i	− 0.265600i
$509$	2.63270e17	0.671022	0.335511	−	0.942036i	$-0.391091\pi$
$509$	2.63270e17	0.671022	0.335511	+	0.942036i	$0.391091\pi$
$510$	0	0
$511$	−5.70809e17	−1.41826
$512$	1.14760e17i	0.281537i
$513$	− 4.41092e16i	− 0.106848i
$514$	−2.39606e16	−0.0573109
$515$	0	0
$516$	−3.78106e17	−0.881842
$517$	− 6.30648e17i	− 1.45244i
$518$	3.50152e16i	0.0796367i
$519$	−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	$0.878751\pi$
$522$	4.94693e16i	0.107023i
$523$	4.84028e17i	1.03421i	0.855922	+	0.517106i	$0.172991\pi$
$523$	4.84028e17i	1.03421i	−0.855922	+	0.517106i	$0.827009\pi$
$524$	−1.71158e17	−0.361197
$525$	0	0
$526$	−4.43369e16	−0.0912762
$527$	− 3.55117e17i	− 0.722108i
$528$	1.03997e18i	2.08882i
$529$	4.84524e17	0.961289
$530$	0	0
$531$	−5.15603e17	−0.998162
$532$	1.34955e17i	0.258086i
$533$	− 1.29957e18i	− 2.45512i
$534$	−8.20031e16	−0.153043
$535$	0	0
$536$	3.15993e16	0.0575581
$537$	1.14087e18i	2.05306i
$538$	1.94614e16i	0.0346010i
$539$	−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	$0.284118\pi$
$542$	− 4.83019e15i	− 0.00818407i
$543$	1.53742e18i	2.57392i
$544$	1.05160e17	0.173963
$545$	0	0
$546$	1.05840e17	0.170962
$547$	− 1.09459e18i	− 1.74716i	−0.486682	−	0.873579i	$-0.661793\pi$
$547$	− 1.09459e18i	− 1.74716i	0.486682	−	0.873579i	$-0.338207\pi$
$548$	− 7.95397e16i	− 0.125461i
$549$	1.19257e17	0.185893
$550$	0	0
$551$	−1.56591e17	−0.238387
$552$	2.30339e16i	0.0346549i
$553$	1.05942e17i	0.157527i
$554$	−4.57697e16	−0.0672612
$555$	0	0
$556$	4.60172e17	0.660593
$557$	− 7.41551e15i	− 0.0105216i	−0.999986	−	0.00526080i	$-0.998325\pi$
$557$	− 7.41551e15i	− 0.0105216i	0.999986	−	0.00526080i	$-0.00167457\pi$
$558$	− 4.00211e16i	− 0.0561263i
$559$	−5.46072e17	−0.756961
$560$	0	0
$561$	1.59001e18	2.15348
$562$	− 3.24014e16i	− 0.0433788i
$563$	− 3.72192e15i	− 0.00492564i	−0.999997	−	0.00246282i	$-0.999216\pi$
$563$	− 3.72192e15i	− 0.00492564i	0.999997	−	0.00246282i	$-0.000783941\pi$
$564$	1.25433e18	1.64096
$565$	0	0
$566$	−5.46318e15	−0.00698456
$567$	− 5.28774e17i	− 0.668314i
$568$	1.35842e17i	0.169735i
$569$	−9.30899e17	−1.14993	−0.574967	−	0.818177i	$-0.694985\pi$
$569$	−9.30899e17	−1.14993	−0.574967	+	0.818177i	$0.694985\pi$
$570$	0	0
$571$	−8.21061e16	−0.0991382	−0.0495691	−	0.998771i	$-0.515785\pi$
$571$	−8.21061e16	−0.0991382	−0.0495691	+	0.998771i	$0.515785\pi$
$572$	1.50689e18i	1.79890i
$573$	− 9.45510e17i	− 1.11599i
$574$	1.32895e17	0.155089
$575$	0	0
$576$	−1.19541e18	−1.36387
$577$	8.28701e17i	0.934878i	0.884025	+	0.467439i	$0.154823\pi$
$577$	8.28701e17i	0.934878i	−0.884025	+	0.467439i	$0.845177\pi$
$578$	− 2.16048e15i	− 0.00241001i
$579$	2.06554e18	2.27836
$580$	0	0
$581$	−8.37435e17	−0.903247
$582$	3.03084e13i	0 3.23268e-5i
$583$	− 1.31028e18i	− 1.38204i
$584$	−1.05724e17	−0.110278
$585$	0	0
$586$	3.09699e16	0.0315940
$587$	6.35978e17i	0.641645i	0.947139	+	0.320822i	$0.103959\pi$
$587$	6.35978e17i	0.641645i	−0.947139	+	0.320822i	$0.896041\pi$
$588$	− 1.77029e18i	− 1.76641i
$589$	1.26684e17	0.125018
$590$	0	0
$591$	3.20395e17	0.309291
$592$	− 9.88296e17i	− 0.943617i
$593$	− 6.83014e17i	− 0.645021i	−0.946566	−	0.322511i	$-0.895473\pi$
$593$	− 6.83014e17i	− 0.645021i	0.946566	−	0.322511i	$-0.104527\pi$
$594$	5.03652e16	0.0470456
$595$	0	0
$596$	−2.91769e17	−0.266648
$597$	− 1.88714e18i	− 1.70596i
$598$	1.66060e16i	0.0148494i
$599$	−1.20464e18	−1.06558	−0.532788	−	0.846249i	$-0.678856\pi$
$599$	−1.20464e18	−1.06558	−0.532788	+	0.846249i	$0.678856\pi$
$600$	0	0
$601$	1.16803e18	1.01104	0.505520	−	0.862815i	$-0.331301\pi$
$601$	1.16803e18	1.01104	0.505520	+	0.862815i	$0.331301\pi$
$602$	− 5.58418e16i	− 0.0478170i
$603$	8.29703e17i	0.702846i
$604$	−1.66769e18	−1.39757
$605$	0	0
$606$	−6.97213e16	−0.0571865
$607$	− 2.08566e17i	− 0.169245i	−0.996413	−	0.0846226i	$-0.973032\pi$
$607$	− 2.08566e17i	− 0.169245i	0.996413	−	0.0846226i	$-0.0269685\pi$
$608$	3.75145e16i	0.0301179i
$609$	3.84637e18	3.05519
$610$	0	0
$611$	1.81154e18	1.40858
$612$	1.83978e18i	1.41541i
$613$	− 1.08956e18i	− 0.829385i	−0.909962	−	0.414693i	$-0.863889\pi$
$613$	− 1.08956e18i	− 0.829385i	0.909962	−	0.414693i	$-0.136111\pi$
$614$	−1.22885e17	−0.0925563
$615$	0	0
$616$	−3.08695e17	−0.227643
$617$	8.64512e17i	0.630837i	0.948953	+	0.315419i	$0.102145\pi$
$617$	8.64512e17i	0.630837i	−0.948953	+	0.315419i	$0.897855\pi$
$618$	− 1.28299e17i	− 0.0926397i
$619$	2.59466e18	1.85392	0.926961	−	0.375157i	$-0.122411\pi$
$619$	2.59466e18	1.85392	0.926961	+	0.375157i	$0.122411\pi$
$620$	0	0
$621$	−1.69991e17	−0.118941
$622$	9.84906e16i	0.0681957i
$623$	3.70926e18i	2.54164i
$624$	−2.98732e18	−2.02573
$625$	0	0
$626$	−3.42416e16	−0.0227416
$627$	5.67218e17i	0.372830i
$628$	9.36386e16i	0.0609140i
$629$	−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	$0.504728\pi$
$632$	1.96223e16i	0.0122487i
$633$	7.01846e17i	0.433629i
$634$	1.02421e17	0.0626336
$635$	0	0
$636$	2.60609e18	1.56142
$637$	− 2.55670e18i	− 1.51626i
$638$	− 1.78801e17i	− 0.104963i
$639$	−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	$0.732297\pi$
$642$	− 9.23973e16i	− 0.0520813i
$643$	2.28715e18i	1.27621i	0.769948	+	0.638106i	$0.220282\pi$
$643$	2.28715e18i	1.27621i	−0.769948	+	0.638106i	$0.779718\pi$
$644$	5.20100e17	0.287295
$645$	0	0
$646$	1.90146e16	0.0102938
$647$	1.51642e18i	0.812723i	0.913712	+	0.406362i	$0.133203\pi$
$647$	1.51642e18i	0.812723i	−0.913712	+	0.406362i	$0.866797\pi$
$648$	− 9.79383e16i	− 0.0519655i
$649$	1.86359e18	0.978947
$650$	0	0
$651$	−3.11175e18	−1.60224
$652$	2.31151e17i	0.117838i
$653$	− 3.90116e18i	− 1.96906i	−0.175228	−	0.984528i	$-0.556066\pi$
$653$	− 3.90116e18i	− 1.96906i	0.175228	−	0.984528i	$-0.443934\pi$
$654$	−1.14183e17	−0.0570617
$655$	0	0
$656$	−3.75092e18	−1.83765
$657$	− 2.77599e18i	− 1.34661i
$658$	1.85250e17i	0.0889793i
$659$	−1.75617e18	−0.835241	−0.417620	−	0.908622i	$-0.637136\pi$
$659$	−1.75617e18	−0.835241	−0.417620	+	0.908622i	$0.637136\pi$
$660$	0	0
$661$	−2.35537e17	−0.109837	−0.0549187	−	0.998491i	$-0.517490\pi$
$661$	−2.35537e17	−0.109837	−0.0549187	+	0.998491i	$0.517490\pi$
$662$	− 3.65410e16i	− 0.0168735i
$663$	4.56732e18i	2.08845i
$664$	−1.55108e17	−0.0702329
$665$	0	0
$666$	−1.70288e17	−0.0756139
$667$	6.03483e17i	0.265367i
$668$	− 1.50747e18i	− 0.656449i
$669$	1.34640e18	0.580635
$670$	0	0
$671$	−4.31039e17	−0.182314
$672$	− 9.21470e17i	− 0.385994i
$673$	1.28360e18i	0.532514i	0.963902	+	0.266257i	$0.0857870\pi$
$673$	1.28360e18i	0.532514i	−0.963902	+	0.266257i	$0.914213\pi$
$674$	2.59074e17	0.106447
$675$	0	0
$676$	−1.85548e18	−0.747829
$677$	− 1.71378e18i	− 0.684114i	−0.939679	−	0.342057i	$-0.888876\pi$
$677$	− 1.71378e18i	− 0.684114i	0.939679	−	0.342057i	$-0.111124\pi$
$678$	7.13816e16i	0.0282224i
$679$	1.37094e15	0.000536866 0
$680$	0	0
$681$	4.51780e18	1.73569
$682$	1.44652e17i	0.0550459i
$683$	2.51565e18i	0.948236i	0.880461	+	0.474118i	$0.157233\pi$
$683$	2.51565e18i	0.948236i	−0.880461	+	0.474118i	$0.842767\pi$
$684$	−6.56321e17	−0.245048
$685$	0	0
$686$	3.33281e16	0.0122097
$687$	− 3.77456e18i	− 1.36977i
$688$	1.57612e18i	0.566584i
$689$	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	$0.225998\pi$
$692$	1.84906e18i	0.640120i
$693$	− 8.10540e18i	− 2.77977i
$694$	3.04484e17	0.103449
$695$	0	0
$696$	7.12415e17	0.237560
$697$	5.73479e18i	1.89454i
$698$	1.42032e17i	0.0464863i
$699$	−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	$0.438024\pi$
$702$	1.44675e17i	0.0456248i
$703$	− 5.39034e17i	− 0.168425i
$704$	4.32068e18	1.33761
$705$	0	0
$706$	1.60726e17	0.0488491
$707$	3.15371e18i	0.949721i
$708$	3.70659e18i	1.10601i
$709$	−4.65855e18	−1.37737	−0.688684	−	0.725061i	$-0.741811\pi$
$709$	−4.65855e18	−1.37737	−0.688684	+	0.725061i	$0.741811\pi$
$710$	0	0
$711$	−5.15223e17	−0.149569
$712$	6.87020e17i	0.197628i
$713$	− 4.88223e17i	− 0.139167i
$714$	−4.67058e17	−0.131926
$715$	0	0
$716$	4.77129e18	1.32343
$717$	5.17250e18i	1.42176i
$718$	− 2.97151e16i	− 0.00809408i
$719$	5.22159e18	1.40950	0.704750	−	0.709456i	$-0.251059\pi$
$719$	5.22159e18	1.40950	0.704750	+	0.709456i	$0.251059\pi$
$720$	0	0
$721$	−5.80335e18	−1.53851
$722$	− 2.10351e17i	− 0.0552653i
$723$	− 1.03687e19i	− 2.69976i
$724$	6.42975e18	1.65918
$725$	0	0
$726$	−2.99642e17	−0.0759478
$727$	− 5.29220e18i	− 1.32942i	−0.747101	−	0.664710i	$-0.768555\pi$
$727$	− 5.29220e18i	− 1.32942i	0.747101	−	0.664710i	$-0.231445\pi$
$728$	− 8.86728e17i	− 0.220768i
$729$	6.35971e18	1.56931
$730$	0	0
$731$	2.40973e18	0.584125
$732$	− 8.57318e17i	− 0.205977i
$733$	− 5.48494e16i	− 0.0130616i	−0.999979	−	0.00653080i	$-0.997921\pi$
$733$	− 5.48494e16i	− 0.0130616i	0.999979	−	0.00653080i	$-0.00207883\pi$
$734$	−3.92673e17	−0.0926844
$735$	0	0
$736$	1.44576e17	0.0335266
$737$	− 2.99886e18i	− 0.689316i
$738$	6.46301e17i	0.147255i
$739$	−3.79938e18	−0.858073	−0.429037	−	0.903287i	$-0.641147\pi$
$739$	−3.79938e18	−0.858073	−0.429037	+	0.903287i	$0.641147\pi$
$740$	0	0
$741$	−1.62934e18	−0.361570
$742$	3.84889e17i	0.0846662i
$743$	− 8.77336e17i	− 0.191310i	−0.995415	−	0.0956552i	$-0.969505\pi$
$743$	− 8.77336e17i	− 0.191310i	0.995415	−	0.0956552i	$-0.0304946\pi$
$744$	−5.76350e17	−0.124584
$745$	0	0
$746$	4.73000e17	0.100475
$747$	− 4.07266e18i	− 0.857619i
$748$	− 6.64968e18i	− 1.38816i
$749$	−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	$0.700300\pi$
$752$	− 5.22862e18i	− 1.05432i
$753$	2.84249e18i	0.568239i
$754$	5.13607e17	0.101793
$755$	0	0
$756$	4.53119e18	0.882715
$757$	6.83799e18i	1.32070i	0.750956	+	0.660352i	$0.229593\pi$
$757$	6.83799e18i	1.32070i	−0.750956	+	0.660352i	$0.770407\pi$
$758$	− 8.37795e16i	− 0.0160431i
$759$	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	$0.429549\pi$
$762$	1.27020e17i	0.0235053i
$763$	5.16484e18i	0.947649i
$764$	−3.95427e18	−0.719382
$765$	0	0
$766$	−1.11197e17	−0.0198887
$767$	5.35317e18i	0.949382i
$768$	8.50817e18i	1.49619i
$769$	6.22288e18	1.08510	0.542550	−	0.840023i	$-0.317459\pi$
$769$	6.22288e18	1.08510	0.542550	+	0.840023i	$0.317459\pi$
$770$	0	0
$771$	−9.06023e18	−1.55341
$772$	− 8.63841e18i	− 1.46866i
$773$	4.84793e18i	0.817315i	0.912688	+	0.408657i	$0.134003\pi$
$773$	4.84793e18i	0.817315i	−0.912688	+	0.408657i	$0.865997\pi$
$774$	2.71573e17	0.0454015
$775$	0	0
$776$	2.53923e14	4.17446e−5 0
$777$	1.32403e19i	2.15855i
$778$	2.47776e17i	0.0400582i
$779$	−2.04582e18	−0.328000
$780$	0	0
$781$	1.28918e19	2.03274
$782$	− 7.32799e16i	− 0.0114588i
$783$	5.25764e18i	0.815342i
$784$	−7.37938e18	−1.13492
$785$	0	0
$786$	2.11314e17	0.0319655
$787$	1.58990e18i	0.238525i	0.992863	+	0.119262i	$0.0380530\pi$
$787$	1.58990e18i	0.238525i	−0.992863	+	0.119262i	$0.961947\pi$
$788$	− 1.33994e18i	− 0.199373i
$789$	−1.67651e19	−2.47404
$790$	0	0
$791$	3.22881e18	0.468701
$792$	− 1.50126e18i	− 0.216144i
$793$	− 1.23816e18i	− 0.176808i
$794$	1.43333e17	0.0203008
$795$	0	0
$796$	−7.89230e18	−1.09969
$797$	− 1.21837e19i	− 1.68384i	−0.539603	−	0.841919i	$-0.681426\pi$
$797$	− 1.21837e19i	− 1.68384i	0.539603	−	0.841919i	$-0.318574\pi$
$798$	− 1.66617e17i	− 0.0228403i
$799$	−7.99405e18	−1.08696
$800$	0	0
$801$	−1.80391e19	−2.41325
$802$	− 4.39315e17i	− 0.0582965i
$803$	1.00335e19i	1.32069i
$804$	5.96460e18	0.778785
$805$	0	0
$806$	−4.15513e17	−0.0533834
$807$	7.35896e18i	0.937860i
$808$	5.84123e17i	0.0738466i
$809$	9.03249e18	1.13277	0.566386	−	0.824140i	$-0.308341\pi$
$809$	9.03249e18	1.13277	0.566386	+	0.824140i	$0.308341\pi$
$810$	0	0
$811$	−4.13436e18	−0.510238	−0.255119	−	0.966910i	$-0.582115\pi$
$811$	−4.13436e18	−0.510238	−0.255119	+	0.966910i	$0.582115\pi$
$812$	− 1.60861e19i	− 1.96941i
$813$	− 1.82645e18i	− 0.221829i
$814$	6.15486e17	0.0741583
$815$	0	0
$816$	1.31826e19	1.56320
$817$	8.59644e17i	0.101129i
$818$	− 4.40557e17i	− 0.0514168i
$819$	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	$0.468013\pi$
$822$	9.82008e16i	0.0111032i
$823$	− 1.43607e19i	− 1.61093i	−0.592643	−	0.805465i	$-0.701916\pi$
$823$	− 1.43607e19i	− 1.61093i	0.592643	−	0.805465i	$-0.298084\pi$
$824$	−1.07488e18	−0.119628
$825$	0	0
$826$	−5.47419e17	−0.0599721
$827$	− 1.24592e19i	− 1.35427i	−0.735861	−	0.677133i	$-0.763222\pi$
$827$	− 1.24592e19i	− 1.35427i	0.735861	−	0.677133i	$-0.236778\pi$
$828$	2.52938e18i	0.272783i
$829$	−1.21281e19	−1.29774	−0.648870	−	0.760900i	$-0.724758\pi$
$829$	−1.21281e19	−1.29774	−0.648870	+	0.760900i	$0.724758\pi$
$830$	0	0
$831$	−1.73069e19	−1.82311
$832$	1.24112e19i	1.29721i
$833$	1.12823e19i	1.17006i
$834$	−5.68134e17	−0.0584617
$835$	0	0
$836$	2.37220e18	0.240331
$837$	− 4.25348e18i	− 0.427591i
$838$	− 4.80423e17i	− 0.0479223i
$839$	−2.65901e17	−0.0263188	−0.0131594	−	0.999913i	$-0.504189\pi$
$839$	−2.65901e17	−0.0263188	−0.0131594	+	0.999913i	$0.504189\pi$
$840$	0	0
$841$	8.40447e18	0.819098
$842$	4.52217e17i	0.0437339i
$843$	− 1.22520e19i	− 1.17578i
$844$	2.93523e18	0.279522
$845$	0	0
$846$	−9.00916e17	−0.0844845
$847$	1.35538e19i	1.26130i
$848$	− 1.08634e19i	− 1.00321i
$849$	−2.06580e18	−0.189316
$850$	0	0
$851$	−2.07737e18	−0.187487
$852$	2.56412e19i	2.29658i
$853$	− 9.22242e18i	− 0.819740i	−0.912144	−	0.409870i	$-0.865574\pi$
$853$	− 9.22242e18i	− 0.819740i	0.912144	−	0.409870i	$-0.134426\pi$
$854$	1.26616e17	0.0111689
$855$	0	0
$856$	−7.74102e17	−0.0672541
$857$	− 4.41223e18i	− 0.380437i	−0.981742	−	0.190218i	$-0.939080\pi$
$857$	− 4.41223e18i	− 0.380437i	0.981742	−	0.190218i	$-0.0609196\pi$
$858$	− 1.86043e18i	− 0.159201i
$859$	−4.93717e18	−0.419298	−0.209649	−	0.977777i	$-0.567232\pi$
$859$	−4.93717e18	−0.419298	−0.209649	+	0.977777i	$0.567232\pi$
$860$	0	0
$861$	5.02516e19	4.20368
$862$	− 5.28717e17i	− 0.0438961i
$863$	− 4.02787e18i	− 0.331899i	−0.986134	−	0.165949i	$-0.946931\pi$
$863$	− 4.02787e18i	− 0.331899i	0.986134	−	0.165949i	$-0.0530688\pi$
$864$	1.25957e18	0.103011
$865$	0	0
$866$	6.50759e17	0.0524269
$867$	− 8.16944e17i	− 0.0653233i
$868$	1.30138e19i	1.03282i
$869$	1.86221e18	0.146690
$870$	0	0
$871$	8.61426e18	0.668498
$872$	9.56619e17i	0.0736855i
$873$	6.66725e15i	0 0.000509746i
$874$	2.61418e16	0.00198386
$875$	0	0
$876$	−1.99561e19	−1.49211
$877$	1.30375e18i	0.0967599i	0.998829	+	0.0483800i	$0.0154058\pi$
$877$	1.30375e18i	0.0967599i	−0.998829	+	0.0483800i	$0.984594\pi$
$878$	1.10488e18i	0.0813954i
$879$	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	$0.449345\pi$
$882$	1.27150e18i	0.0909434i
$883$	− 7.36283e18i	− 0.522758i	−0.965236	−	0.261379i	$-0.915823\pi$
$883$	− 7.36283e18i	− 0.522758i	0.965236	−	0.261379i	$-0.0841772\pi$
$884$	1.91012e19	1.34624
$885$	0	0
$886$	−1.27788e17	−0.00887502
$887$	− 1.03361e19i	− 0.712614i	−0.934369	−	0.356307i	$-0.884036\pi$
$887$	− 1.03361e19i	− 0.712614i	0.934369	−	0.356307i	$-0.115964\pi$
$888$	2.45234e18i	0.167841i
$889$	5.74552e18	0.390362
$890$	0	0
$891$	−9.29462e18	−0.622338
$892$	− 5.63084e18i	− 0.374284i
$893$	− 2.85178e18i	− 0.188184i
$894$	3.60222e17	0.0235980
$895$	0	0
$896$	−5.13550e18	−0.331574
$897$	6.27926e18i	0.402492i
$898$	1.11869e18i	0.0711888i
$899$	−1.51002e19	−0.953993
$900$	0	0
$901$	−1.66091e19	−1.03427
$902$	− 2.33598e18i	− 0.144420i
$903$	− 2.11155e19i	− 1.29608i
$904$	5.98033e17	0.0364444
$905$	0	0
$906$	2.05895e18	0.123684
$907$	− 2.42647e19i	− 1.44720i	−0.690221	−	0.723599i	$-0.742487\pi$
$907$	− 2.42647e19i	− 1.44720i	0.690221	−	0.723599i	$-0.257513\pi$
$908$	− 1.88942e19i	− 1.11884i
$909$	−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	$0.186727\pi$
$912$	4.70273e18i	0.270635i
$913$	1.47202e19i	0.841109i
$914$	1.02640e17	0.00582325
$915$	0	0
$916$	−1.57858e19	−0.882970
$917$	− 9.55840e18i	− 0.530866i
$918$	− 6.38426e17i	− 0.0352073i
$919$	2.65496e19	1.45381	0.726905	−	0.686738i	$-0.240958\pi$
$919$	2.65496e19	1.45381	0.726905	+	0.686738i	$0.240958\pi$
$920$	0	0
$921$	−4.64668e19	−2.50874
$922$	4.96562e17i	0.0266209i
$923$	3.70318e19i	1.97135i
$924$	−5.82684e19	−3.08010
$925$	0	0
$926$	1.87207e18	0.0975777
$927$	− 2.82232e19i	− 1.46079i
$928$	− 4.47158e18i	− 0.229826i
$929$	2.35245e19	1.20065	0.600327	−	0.799754i	$-0.295037\pi$
$929$	2.35245e19	1.20065	0.600327	+	0.799754i	$0.295037\pi$
$930$	0	0
$931$	−4.02484e18	−0.202571
$932$	3.27854e19i	1.63862i
$933$	3.72423e19i	1.84844i
$934$	−1.29204e18	−0.0636825
$935$	0	0
$936$	4.31239e18	0.209616
$937$	3.40251e19i	1.64245i	0.570605	+	0.821225i	$0.306709\pi$
$937$	3.40251e19i	1.64245i	−0.570605	+	0.821225i	$0.693291\pi$
$938$	8.80901e17i	0.0422288i
$939$	−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	$0.551228\pi$
$942$	− 1.15608e17i	− 0.00539082i
$943$	7.88433e18i	0.365123i
$944$	1.54508e19	0.710611
$945$	0	0
$946$	−9.81568e17	−0.0445275
$947$	3.03102e19i	1.36557i	0.730620	+	0.682784i	$0.239231\pi$
$947$	3.03102e19i	1.36557i	−0.730620	+	0.682784i	$0.760769\pi$
$948$	3.70385e18i	0.165729i
$949$	−2.88213e19	−1.28080
$950$	0	0
$951$	3.87284e19	1.69768
$952$	3.91299e18i	0.170361i
$953$	2.84246e19i	1.22911i	0.788875	+	0.614554i	$0.210664\pi$
$953$	2.84246e19i	1.22911i	−0.788875	+	0.614554i	$0.789336\pi$
$954$	−1.87181e18	−0.0803893
$955$	0	0
$956$	2.16322e19	0.916484
$957$	− 6.76102e19i	− 2.84501i
$958$	1.53655e18i	0.0642200i
$959$	4.44193e18	0.184396
$960$	0	0
$961$	−1.22013e19	−0.499695
$962$	1.76799e18i	0.0719186i
$963$	− 2.03256e19i	− 0.821244i
$964$	−4.33635e19	−1.74030
$965$	0	0
$966$	−6.42122e17	−0.0254253
$967$	− 4.24114e18i	− 0.166806i	−0.996516	−	0.0834028i	$-0.973421\pi$
$967$	− 4.24114e18i	− 0.166806i	0.996516	−	0.0834028i	$-0.0265788\pi$
$968$	2.51039e18i	0.0980736i
$969$	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	$0.473600\pi$
$972$	− 3.43292e19i	− 1.30567i
$973$	2.56985e19i	0.970900i
$974$	−1.29058e18	−0.0484343
$975$	0	0
$976$	−3.57369e18	−0.132341
$977$	− 2.00848e19i	− 0.738843i	−0.929262	−	0.369422i	$-0.879556\pi$
$977$	− 2.00848e19i	− 0.738843i	0.929262	−	0.369422i	$-0.120444\pi$
$978$	− 2.85383e17i	− 0.0104286i
$979$	6.52001e19	2.36680
$980$	0	0
$981$	−2.51180e19	−0.899779
$982$	− 1.14959e18i	− 0.0409089i
$983$	− 4.85500e19i	− 1.71629i	−0.513404	−	0.858147i	$-0.671616\pi$
$983$	− 4.85500e19i	− 1.71629i	0.513404	−	0.858147i	$-0.328384\pi$
$984$	9.30749e18	0.326862
$985$	0	0
$986$	−2.26647e18	−0.0785506
$987$	7.00486e19i	2.41178i
$988$	6.81415e18i	0.233073i
$989$	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	$0.367532\pi$
$992$	3.61754e18i	0.120528i
$993$	− 1.38173e19i	− 0.457355i
$994$	−3.78690e18	−0.124529
$995$	0	0
$996$	−2.92777e19	−0.950280
$997$	9.00367e18i	0.290336i	0.989407	+	0.145168i	$0.0463723\pi$
$997$	9.00367e18i	0.290336i	−0.989407	+	0.145168i	$0.953628\pi$
$998$	− 3.06910e18i	− 0.0983247i
$999$	−1.80984e19	−0.576055

Twists

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

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

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.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+5.16335i q^{2} +1952.42i q^{3} +8165.34 q^{4} -10081.0 q^{6} +455997. i q^{7} +84458.7i q^{8} -2.21763e6 q^{9} +O(q^{10})\)	\(q+5.16335i q^{2} +1952.42i q^{3} +8165.34 q^{4} -10081.0 q^{6} +455997. i q^{7} +84458.7i q^{8} -2.21763e6 q^{9} +8.01536e6 q^{11} +1.59422e7i q^{12} +2.30242e7i q^{13} -2.35447e6 q^{14} +6.64544e7 q^{16} -1.01602e8i q^{17} -1.14504e7i q^{18} +3.62454e7 q^{19} -8.90299e8 q^{21} +4.13861e7i q^{22} -1.39685e8i q^{23} -1.64899e8 q^{24} -1.18882e8 q^{26} -1.21696e9i q^{27} +3.72337e9i q^{28} -4.32031e9 q^{29} +3.49517e9 q^{31} +1.03501e9i q^{32} +1.56494e10i q^{33} +5.24608e8 q^{34} -1.81077e10 q^{36} -1.48718e10i q^{37} +1.87148e8i q^{38} -4.49530e10 q^{39} -5.64436e10 q^{41} -4.59692e9i q^{42} +2.37173e10i q^{43} +6.54482e10 q^{44} +7.21243e8 q^{46} -7.86799e10i q^{47} +1.29747e11i q^{48} -1.11044e11 q^{49} +1.98370e11 q^{51} +1.88000e11i q^{52} -1.63472e11i q^{53} +6.28359e9 q^{54} -3.85129e10 q^{56} +7.07664e10i q^{57} -2.23073e10i q^{58} +2.32502e11 q^{59} -5.37766e10 q^{61} +1.80468e10i q^{62} -1.01123e12i q^{63} +5.39050e11 q^{64} -8.08032e10 q^{66} -3.74139e11i q^{67} -8.29616e11i q^{68} +2.72724e11 q^{69} +1.60839e12 q^{71} -1.87298e11i q^{72} +1.25178e12i q^{73} +7.67883e10 q^{74} +2.95956e11 q^{76} +3.65498e12i q^{77} -2.32108e11i q^{78} +2.32330e11 q^{79} -1.15960e12 q^{81} -2.91438e11i q^{82} +1.83649e12i q^{83} -7.26959e12 q^{84} -1.22461e11 q^{86} -8.43507e12i q^{87} +6.76967e11i q^{88} +8.13439e12 q^{89} -1.04990e13 q^{91} -1.14058e12i q^{92} +6.82405e12i q^{93} +4.06252e11 q^{94} -2.02078e12 q^{96} -3.00647e9i q^{97} -5.73360e11i q^{98} -1.77751e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 7466 q^{4} + 80666 q^{6} - 95744 q^{9}+O(q^{10}) \) 8 * q - 7466 * q^4 + 80666 * q^6 - 95744 * q^9	\( 8 q - 7466 q^{4} + 80666 q^{6} - 95744 q^{9} + 13350856 q^{11} - 74206932 q^{14} - 16881502 q^{16} - 565297720 q^{19} - 877774944 q^{21} - 2830688910 q^{24} - 6534908744 q^{26} - 15261297680 q^{29} - 25432078064 q^{31} - 46246410042 q^{34} - 90995853812 q^{36} - 121383887248 q^{39} - 162509867224 q^{41} - 223233837362 q^{44} - 155877593604 q^{46} - 236142506856 q^{49} + 183907895336 q^{51} + 550485655330 q^{54} + 807926914620 q^{56} + 1716031630640 q^{59} + 1178411030656 q^{61} + 3033228117694 q^{64} + 2837643424762 q^{66} + 2972419500432 q^{69} + 1899364758896 q^{71} - 2006660960612 q^{74} + 3928235357890 q^{76} + 711630072320 q^{79} - 2301989080552 q^{81} - 18558672690612 q^{84} - 22033736493224 q^{86} - 5012165285640 q^{89} - 22184467676704 q^{91} - 30103143630072 q^{94} - 34691136857474 q^{96} - 2851279676608 q^{99}+O(q^{100}) \) 8 * q - 7466 * q^4 + 80666 * q^6 - 95744 * q^9 + 13350856 * q^11 - 74206932 * q^14 - 16881502 * q^16 - 565297720 * q^19 - 877774944 * q^21 - 2830688910 * q^24 - 6534908744 * q^26 - 15261297680 * q^29 - 25432078064 * q^31 - 46246410042 * q^34 - 90995853812 * q^36 - 121383887248 * q^39 - 162509867224 * q^41 - 223233837362 * q^44 - 155877593604 * q^46 - 236142506856 * q^49 + 183907895336 * q^51 + 550485655330 * q^54 + 807926914620 * q^56 + 1716031630640 * q^59 + 1178411030656 * q^61 + 3033228117694 * q^64 + 2837643424762 * q^66 + 2972419500432 * q^69 + 1899364758896 * q^71 - 2006660960612 * q^74 + 3928235357890 * q^76 + 711630072320 * q^79 - 2301989080552 * q^81 - 18558672690612 * q^84 - 22033736493224 * q^86 - 5012165285640 * q^89 - 22184467676704 * q^91 - 30103143630072 * q^94 - 34691136857474 * q^96 - 2851279676608 * q^99

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