LMFDB - Embedded newform 75.14.b.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,14,Mod(49,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.49");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	75.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:	$80.4231967139$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{1969})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 985x^{2} + 242064 $ x^4 + 985*x^2 + 242064
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-22.6867i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.14.b.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-160.120i q^{2} -729.000i q^{3} -17446.5 q^{4} -116728. q^{6} +449560. i q^{7} +1.48183e6i q^{8} -531441. q^{9} +O(q^{10})$	\(q-160.120i q^{2} -729.000i q^{3} -17446.5 q^{4} -116728. q^{6} +449560. i q^{7} +1.48183e6i q^{8} -531441. q^{9} +5.20947e6 q^{11} +1.27185e7i q^{12} +3.19535e6i q^{13} +7.19836e7 q^{14} +9.43496e7 q^{16} +3.22068e7i q^{17} +8.50945e7i q^{18} -2.60127e7 q^{19} +3.27729e8 q^{21} -8.34142e8i q^{22} -9.21991e8i q^{23} +1.08026e9 q^{24} +5.11640e8 q^{26} +3.87420e8i q^{27} -7.84324e9i q^{28} +3.17741e9 q^{29} -7.65586e9 q^{31} -2.96811e9i q^{32} -3.79770e9i q^{33} +5.15697e9 q^{34} +9.27178e9 q^{36} +1.60133e10i q^{37} +4.16515e9i q^{38} +2.32941e9 q^{39} -5.42402e9 q^{41} -5.24760e10i q^{42} -3.58248e10i q^{43} -9.08870e10 q^{44} -1.47629e11 q^{46} -1.26460e11i q^{47} -6.87809e10i q^{48} -1.05215e11 q^{49} +2.34788e10 q^{51} -5.57477e10i q^{52} -6.08596e10i q^{53} +6.20339e10 q^{54} -6.66172e11 q^{56} +1.89632e10i q^{57} -5.08767e11i q^{58} +4.10975e11 q^{59} -1.17141e11 q^{61} +1.22586e12i q^{62} -2.38914e11i q^{63} +2.97657e11 q^{64} -6.08089e11 q^{66} -1.16014e12i q^{67} -5.61896e11i q^{68} -6.72131e11 q^{69} +2.58837e11 q^{71} -7.87506e11i q^{72} -1.87421e12i q^{73} +2.56405e12 q^{74} +4.53830e11 q^{76} +2.34197e12i q^{77} -3.72986e11i q^{78} +2.22847e11 q^{79} +2.82430e11 q^{81} +8.68495e11i q^{82} +2.08940e12i q^{83} -5.71772e12 q^{84} -5.73628e12 q^{86} -2.31633e12i q^{87} +7.71956e12i q^{88} +1.34175e12 q^{89} -1.43650e12 q^{91} +1.60855e13i q^{92} +5.58112e12i q^{93} -2.02488e13 q^{94} -2.16376e12 q^{96} -3.12485e9i q^{97} +1.68470e13i q^{98} -2.76853e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 41032 q^{4} - 78732 q^{6} - 2125764 q^{9}+O(q^{10}) $ 4 * q - 41032 * q^4 - 78732 * q^6 - 2125764 * q^9	$ 4 q - 41032 q^{4} - 78732 q^{6} - 2125764 q^{9} + 1344816 q^{11} + 243840672 q^{14} + 23034400 q^{16} - 512587088 q^{19} - 30629664 q^{21} + 2953079856 q^{24} + 5422592088 q^{26} + 9456950664 q^{29} - 11965103296 q^{31} - 644414184 q^{34} + 21806087112 q^{36} - 25562536632 q^{39} + 30517948584 q^{41} - 153920882016 q^{44} - 308504493216 q^{46} - 459519253860 q^{49} + 122236626312 q^{51} + 41841412812 q^{54} - 820741991040 q^{56} + 1855641648528 q^{59} + 358790922680 q^{61} + 158678840192 q^{64} - 1918167766416 q^{66} - 1253270462688 q^{69} - 1568917099872 q^{71} + 2708999602632 q^{74} + 2321356801952 q^{76} + 1428050940160 q^{79} + 1129718145924 q^{81} - 9329490850752 q^{84} - 21477442268304 q^{86} - 6540357403368 q^{89} - 22380807889856 q^{91} - 52685591533632 q^{94} - 10650886375104 q^{96} - 714690359856 q^{99}+O(q^{100}) $ 4 * q - 41032 * q^4 - 78732 * q^6 - 2125764 * q^9 + 1344816 * q^11 + 243840672 * q^14 + 23034400 * q^16 - 512587088 * q^19 - 30629664 * q^21 + 2953079856 * q^24 + 5422592088 * q^26 + 9456950664 * q^29 - 11965103296 * q^31 - 644414184 * q^34 + 21806087112 * q^36 - 25562536632 * q^39 + 30517948584 * q^41 - 153920882016 * q^44 - 308504493216 * q^46 - 459519253860 * q^49 + 122236626312 * q^51 + 41841412812 * q^54 - 820741991040 * q^56 + 1855641648528 * q^59 + 358790922680 * q^61 + 158678840192 * q^64 - 1918167766416 * q^66 - 1253270462688 * q^69 - 1568917099872 * q^71 + 2708999602632 * q^74 + 2321356801952 * q^76 + 1428050940160 * q^79 + 1129718145924 * q^81 - 9329490850752 * q^84 - 21477442268304 * q^86 - 6540357403368 * q^89 - 22380807889856 * q^91 - 52685591533632 * q^94 - 10650886375104 * q^96 - 714690359856 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 160.120i	− 1.76910i	−0.466450	−	0.884548i	$-0.654467\pi$
$2$	− 160.120i	− 1.76910i	0.466450	−	0.884548i	$-0.345533\pi$
$3$	− 729.000i	− 0.577350i
$3$	− 729.000i	− 0.577350i
$4$	−17446.5	−2.12970
$5$	0	0
$5$	0	0
$6$	−116728.	−1.02139
$7$	449560.i	1.44428i	0.691749	+	0.722138i	$0.256840\pi$
$7$	449560.i	1.44428i	−0.691749	+	0.722138i	$0.743160\pi$
$8$	1.48183e6i	1.99855i
$9$	−531441.	−0.333333
$10$	0	0
$11$	5.20947e6	0.886627	0.443314	−	0.896367i	$-0.353803\pi$
$11$	5.20947e6	0.886627	0.443314	+	0.896367i	$0.353803\pi$
$12$	1.27185e7i	1.22958i
$13$	3.19535e6i	0.183606i	0.995777	+	0.0918030i	$0.0292630\pi$
$13$	3.19535e6i	0.183606i	−0.995777	+	0.0918030i	$0.970737\pi$
$14$	7.19836e7	2.55506
$15$	0	0
$16$	9.43496e7	1.40592
$17$	3.22068e7i	0.323616i	0.986822	+	0.161808i	$0.0517325\pi$
$17$	3.22068e7i	0.323616i	−0.986822	+	0.161808i	$0.948267\pi$
$18$	8.50945e7i	0.589699i
$19$	−2.60127e7	−0.126849	−0.0634244	−	0.997987i	$-0.520202\pi$
$19$	−2.60127e7	−0.126849	−0.0634244	+	0.997987i	$0.520202\pi$
$20$	0	0
$21$	3.27729e8	0.833853
$22$	− 8.34142e8i	− 1.56853i
$23$	− 9.21991e8i	− 1.29866i	−0.760507	−	0.649330i	$-0.775049\pi$
$23$	− 9.21991e8i	− 1.29866i	0.760507	−	0.649330i	$-0.224951\pi$
$24$	1.08026e9	1.15386
$25$	0	0
$26$	5.11640e8	0.324816
$27$	3.87420e8i	0.192450i
$28$	− 7.84324e9i	− 3.07587i
$29$	3.17741e9	0.991942	0.495971	−	0.868339i	$-0.334812\pi$
$29$	3.17741e9	0.991942	0.495971	+	0.868339i	$0.334812\pi$
$30$	0	0
$31$	−7.65586e9	−1.54933	−0.774663	−	0.632374i	$-0.782081\pi$
$31$	−7.65586e9	−1.54933	−0.774663	+	0.632374i	$0.782081\pi$
$32$	− 2.96811e9i	− 0.488659i
$33$	− 3.79770e9i	− 0.511894i
$34$	5.15697e9	0.572508
$35$	0	0
$36$	9.27178e9	0.709900
$37$	1.60133e10i	1.02605i	0.858373	+	0.513026i	$0.171475\pi$
$37$	1.60133e10i	1.02605i	−0.858373	+	0.513026i	$0.828525\pi$
$38$	4.16515e9i	0.224408i
$39$	2.32941e9	0.106005
$40$	0	0
$41$	−5.42402e9	−0.178331	−0.0891653	−	0.996017i	$-0.528420\pi$
$41$	−5.42402e9	−0.178331	−0.0891653	+	0.996017i	$0.528420\pi$
$42$	− 5.24760e10i	− 1.47517i
$43$	− 3.58248e10i	− 0.864250i	−0.901814	−	0.432125i	$-0.857764\pi$
$43$	− 3.58248e10i	− 0.864250i	0.901814	−	0.432125i	$-0.142236\pi$
$44$	−9.08870e10	−1.88825
$45$	0	0
$46$	−1.47629e11	−2.29745
$47$	− 1.26460e11i	− 1.71127i	−0.517582	−	0.855633i	$-0.673168\pi$
$47$	− 1.26460e11i	− 1.71127i	0.517582	−	0.855633i	$-0.326832\pi$
$48$	− 6.87809e10i	− 0.811707i
$49$	−1.05215e11	−1.08593
$50$	0	0
$51$	2.34788e10	0.186840
$52$	− 5.57477e10i	− 0.391025i
$53$	− 6.08596e10i	− 0.377169i	−0.982057	−	0.188585i	$-0.939610\pi$
$53$	− 6.08596e10i	− 0.377169i	0.982057	−	0.188585i	$-0.0603900\pi$
$54$	6.20339e10	0.340463
$55$	0	0
$56$	−6.66172e11	−2.88645
$57$	1.89632e10i	0.0732362i
$58$	− 5.08767e11i	− 1.75484i
$59$	4.10975e11	1.26846	0.634230	−	0.773144i	$-0.281317\pi$
$59$	4.10975e11	1.26846	0.634230	+	0.773144i	$0.281317\pi$
$60$	0	0
$61$	−1.17141e11	−0.291116	−0.145558	−	0.989350i	$-0.546498\pi$
$61$	−1.17141e11	−0.291116	−0.145558	+	0.989350i	$0.546498\pi$
$62$	1.22586e12i	2.74091i
$63$	− 2.38914e11i	− 0.481425i
$64$	2.97657e11	0.541434
$65$	0	0
$66$	−6.08089e11	−0.905590
$67$	− 1.16014e12i	− 1.56684i	−0.621494	−	0.783419i	$-0.713474\pi$
$67$	− 1.16014e12i	− 1.56684i	0.621494	−	0.783419i	$-0.286526\pi$
$68$	− 5.61896e11i	− 0.689205i
$69$	−6.72131e11	−0.749782
$70$	0	0
$71$	2.58837e11	0.239799	0.119899	−	0.992786i	$-0.461743\pi$
$71$	2.58837e11	0.239799	0.119899	+	0.992786i	$0.461743\pi$
$72$	− 7.87506e11i	− 0.666182i
$73$	− 1.87421e12i	− 1.44950i	−0.689010	−	0.724752i	$-0.741954\pi$
$73$	− 1.87421e12i	− 1.44950i	0.689010	−	0.724752i	$-0.258046\pi$
$74$	2.56405e12	1.81518
$75$	0	0
$76$	4.53830e11	0.270150
$77$	2.34197e12i	1.28053i
$78$	− 3.72986e11i	− 0.187533i
$79$	2.22847e11	0.103141	0.0515704	−	0.998669i	$-0.483577\pi$
$79$	2.22847e11	0.103141	0.0515704	+	0.998669i	$0.483577\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	8.68495e11i	0.315484i
$83$	2.08940e12i	0.701477i	0.936473	+	0.350739i	$0.114069\pi$
$83$	2.08940e12i	0.701477i	−0.936473	+	0.350739i	$0.885931\pi$
$84$	−5.71772e12	−1.77586
$85$	0	0
$86$	−5.73628e12	−1.52894
$87$	− 2.31633e12i	− 0.572698i
$88$	7.71956e12i	1.77196i
$89$	1.34175e12	0.286177	0.143089	−	0.989710i	$-0.454297\pi$
$89$	1.34175e12	0.286177	0.143089	+	0.989710i	$0.454297\pi$
$90$	0	0
$91$	−1.43650e12	−0.265178
$92$	1.60855e13i	2.76576i
$93$	5.58112e12i	0.894504i
$94$	−2.02488e13	−3.02739
$95$	0	0
$96$	−2.16376e12	−0.282127
$97$	− 3.12485e9i	0 0.000380902i	−1.00000		0.000190451i	$-0.999939\pi$
$97$	− 3.12485e9i	0 0.000380902i	1.00000		0.000190451i	$-6.06224e-5\pi$
$98$	1.68470e13i	1.92112i
$99$	−2.76853e12	−0.295542
$100$	0	0
$101$	1.35294e13	1.26820	0.634102	−	0.773249i	$-0.281370\pi$
$101$	1.35294e13	1.26820	0.634102	+	0.773249i	$0.281370\pi$
$102$	− 3.75943e12i	− 0.330537i
$103$	− 3.69605e12i	− 0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$103$	− 3.69605e12i	− 0.304997i	0.988304	−	0.152499i	$-0.0487320\pi$
$104$	−4.73497e12	−0.366945
$105$	0	0
$106$	−9.74486e12	−0.667248
$107$	7.56519e12i	0.487332i	0.969859	+	0.243666i	$0.0783501\pi$
$107$	7.56519e12i	0.487332i	−0.969859	+	0.243666i	$0.921650\pi$
$108$	− 6.75913e12i	− 0.409861i
$109$	2.05699e13	1.17479	0.587394	−	0.809301i	$-0.300154\pi$
$109$	2.05699e13	1.17479	0.587394	+	0.809301i	$0.300154\pi$
$110$	0	0
$111$	1.16737e13	0.592391
$112$	4.24158e13i	2.03053i
$113$	1.50599e13i	0.680475i	0.940340	+	0.340238i	$0.110507\pi$
$113$	1.50599e13i	0.680475i	−0.940340	+	0.340238i	$0.889493\pi$
$114$	3.03640e12	0.129562
$115$	0	0
$116$	−5.54346e13	−2.11254
$117$	− 1.69814e12i	− 0.0612020i
$118$	− 6.58054e13i	− 2.24403i
$119$	−1.44789e13	−0.467391
$120$	0	0
$121$	−7.38413e12	−0.213892
$122$	1.87567e13i	0.515012i
$123$	3.95411e12i	0.102959i
$124$	1.33568e14	3.29960
$125$	0	0
$126$	−3.82550e13	−0.851687
$127$	3.25187e13i	0.687717i	0.939022	+	0.343858i	$0.111734\pi$
$127$	3.25187e13i	0.687717i	−0.939022	+	0.343858i	$0.888266\pi$
$128$	− 7.19757e13i	− 1.44651i
$129$	−2.61163e13	−0.498975
$130$	0	0
$131$	−4.24335e13	−0.733577	−0.366788	−	0.930304i	$-0.619543\pi$
$131$	−4.24335e13	−0.733577	−0.366788	+	0.930304i	$0.619543\pi$
$132$	6.62566e13i	1.09018i
$133$	− 1.16942e13i	− 0.183205i
$134$	−1.85762e14	−2.77188
$135$	0	0
$136$	−4.77251e13	−0.646761
$137$	− 1.38138e14i	− 1.78496i	−0.451085	−	0.892481i	$-0.648963\pi$
$137$	− 1.38138e14i	− 1.78496i	0.451085	−	0.892481i	$-0.351037\pi$
$138$	1.07622e14i	1.32644i
$139$	−6.55318e13	−0.770648	−0.385324	−	0.922781i	$-0.625910\pi$
$139$	−6.55318e13	−0.770648	−0.385324	+	0.922781i	$0.625910\pi$
$140$	0	0
$141$	−9.21895e13	−0.988000
$142$	− 4.14450e13i	− 0.424227i
$143$	1.66461e13i	0.162790i
$144$	−5.01412e13	−0.468639
$145$	0	0
$146$	−3.00099e14	−2.56431
$147$	7.67016e13i	0.626963i
$148$	− 2.79376e14i	− 2.18518i
$149$	−1.62826e14	−1.21902	−0.609512	−	0.792777i	$-0.708635\pi$
$149$	−1.62826e14	−1.21902	−0.609512	+	0.792777i	$0.708635\pi$
$150$	0	0
$151$	7.18136e13	0.493011	0.246505	−	0.969141i	$-0.420718\pi$
$151$	7.18136e13	0.493011	0.246505	+	0.969141i	$0.420718\pi$
$152$	− 3.85464e13i	− 0.253513i
$153$	− 1.71160e13i	− 0.107872i
$154$	3.74996e14	2.26539
$155$	0	0
$156$	−4.06400e13	−0.225759
$157$	− 4.46499e13i	− 0.237943i	−0.992898	−	0.118971i	$-0.962040\pi$
$157$	− 4.46499e13i	− 0.237943i	0.992898	−	0.118971i	$-0.0379597\pi$
$158$	− 3.56823e13i	− 0.182466i
$159$	−4.43667e13	−0.217759
$160$	0	0
$161$	4.14490e14	1.87562
$162$	− 4.52227e13i	− 0.196566i
$163$	7.29720e13i	0.304745i	0.988323	+	0.152373i	$0.0486914\pi$
$163$	7.29720e13i	0.304745i	−0.988323	+	0.152373i	$0.951309\pi$
$164$	9.46301e13	0.379790
$165$	0	0
$166$	3.34555e14	1.24098
$167$	− 5.24603e14i	− 1.87143i	−0.352757	−	0.935715i	$-0.614756\pi$
$167$	− 5.24603e14i	− 1.87143i	0.352757	−	0.935715i	$-0.385244\pi$
$168$	4.85639e14i	1.66649i
$169$	2.92665e14	0.966289
$170$	0	0
$171$	1.38242e13	0.0422829
$172$	6.25018e14i	1.84059i
$173$	− 3.74739e14i	− 1.06275i	−0.847138	−	0.531373i	$-0.821676\pi$
$173$	− 3.74739e14i	− 1.06275i	0.847138	−	0.531373i	$-0.178324\pi$
$174$	−3.70891e14	−1.01316
$175$	0	0
$176$	4.91511e14	1.24653
$177$	− 2.99601e14i	− 0.732346i
$178$	− 2.14841e14i	− 0.506275i
$179$	−1.41559e14	−0.321657	−0.160828	−	0.986982i	$-0.551417\pi$
$179$	−1.41559e14	−0.321657	−0.160828	+	0.986982i	$0.551417\pi$
$180$	0	0
$181$	2.66316e14	0.562973	0.281486	−	0.959565i	$-0.409173\pi$
$181$	2.66316e14	0.562973	0.281486	+	0.959565i	$0.409173\pi$
$182$	2.30013e14i	0.469124i
$183$	8.53960e13i	0.168076i
$184$	1.36624e15	2.59543
$185$	0	0
$186$	8.93651e14	1.58246
$187$	1.67781e14i	0.286927i
$188$	2.20629e15i	3.64448i
$189$	−1.74169e14	−0.277951
$190$	0	0
$191$	−1.59059e14	−0.237051	−0.118526	−	0.992951i	$-0.537817\pi$
$191$	−1.59059e14	−0.237051	−0.118526	+	0.992951i	$0.537817\pi$
$192$	− 2.16992e14i	− 0.312597i
$193$	− 5.78312e14i	− 0.805452i	−0.915320	−	0.402726i	$-0.868063\pi$
$193$	− 5.78312e14i	− 0.805452i	0.915320	−	0.402726i	$-0.131937\pi$
$194$	−5.00352e11	−0.000673852 0
$195$	0	0
$196$	1.83563e15	2.31271
$197$	7.45344e14i	0.908503i	0.890873	+	0.454252i	$0.150093\pi$
$197$	7.45344e14i	0.908503i	−0.890873	+	0.454252i	$0.849907\pi$
$198$	4.43297e14i	0.522843i
$199$	−9.14435e14	−1.04378	−0.521889	−	0.853014i	$-0.674772\pi$
$199$	−9.14435e14	−1.04378	−0.521889	+	0.853014i	$0.674772\pi$
$200$	0	0
$201$	−8.45741e14	−0.904614
$202$	− 2.16633e15i	− 2.24358i
$203$	1.42843e15i	1.43264i
$204$	−4.09622e14	−0.397912
$205$	0	0
$206$	−5.91812e14	−0.539569
$207$	4.89984e14i	0.432887i
$208$	3.01480e14i	0.258135i
$209$	−1.35512e14	−0.112468
$210$	0	0
$211$	4.28835e14	0.334545	0.167272	−	0.985911i	$-0.446504\pi$
$211$	4.28835e14	0.334545	0.167272	+	0.985911i	$0.446504\pi$
$212$	1.06179e15i	0.803257i
$213$	− 1.88692e14i	− 0.138448i
$214$	1.21134e15	0.862137
$215$	0	0
$216$	−5.74092e14	−0.384620
$217$	− 3.44177e15i	− 2.23765i
$218$	− 3.29365e15i	− 2.07831i
$219$	−1.36630e15	−0.836871
$220$	0	0
$221$	−1.02912e14	−0.0594178
$222$	− 1.86919e15i	− 1.04800i
$223$	− 2.03442e15i	− 1.10779i	−0.832585	−	0.553897i	$-0.813140\pi$
$223$	− 2.03442e15i	− 1.10779i	0.832585	−	0.553897i	$-0.186860\pi$
$224$	1.33434e15	0.705758
$225$	0	0
$226$	2.41139e15	1.20383
$227$	− 2.60190e15i	− 1.26218i	−0.775708	−	0.631091i	$-0.782607\pi$
$227$	− 2.60190e15i	− 1.26218i	0.775708	−	0.631091i	$-0.217393\pi$
$228$	− 3.30842e14i	− 0.155971i
$229$	−7.15955e14	−0.328061	−0.164031	−	0.986455i	$-0.552450\pi$
$229$	−7.15955e14	−0.328061	−0.164031	+	0.986455i	$0.552450\pi$
$230$	0	0
$231$	1.70729e15	0.739317
$232$	4.70838e15i	1.98244i
$233$	− 2.42556e15i	− 0.993112i	−0.868005	−	0.496556i	$-0.834598\pi$
$233$	− 2.42556e15i	− 0.993112i	0.868005	−	0.496556i	$-0.165402\pi$
$234$	−2.71907e14	−0.108272
$235$	0	0
$236$	−7.17007e15	−2.70144
$237$	− 1.62455e14i	− 0.0595483i
$238$	2.31836e15i	0.826859i
$239$	2.17202e15	0.753836	0.376918	−	0.926247i	$-0.376984\pi$
$239$	2.17202e15	0.753836	0.376918	+	0.926247i	$0.376984\pi$
$240$	0	0
$241$	−4.62659e15	−1.52108	−0.760538	−	0.649294i	$-0.775065\pi$
$241$	−4.62659e15	−1.52108	−0.760538	+	0.649294i	$0.775065\pi$
$242$	1.18235e15i	0.378396i
$243$	− 2.05891e14i	− 0.0641500i
$244$	2.04371e15	0.619990
$245$	0	0
$246$	6.33133e14	0.182145
$247$	− 8.31196e13i	− 0.0232902i
$248$	− 1.13447e16i	− 3.09640i
$249$	1.52317e15	0.404998
$250$	0	0
$251$	5.16492e15	1.30372	0.651860	−	0.758339i	$-0.273989\pi$
$251$	5.16492e15	1.30372	0.651860	+	0.758339i	$0.273989\pi$
$252$	4.16822e15i	1.02529i
$253$	− 4.80308e15i	− 1.15143i
$254$	5.20691e15	1.21664
$255$	0	0
$256$	−9.08636e15	−2.01758
$257$	− 6.62253e15i	− 1.43370i	−0.697227	−	0.716851i	$-0.745583\pi$
$257$	− 6.62253e15i	− 1.43370i	0.697227	−	0.716851i	$-0.254417\pi$
$258$	4.18175e15i	0.882734i
$259$	−7.19892e15	−1.48190
$260$	0	0
$261$	−1.68861e15	−0.330647
$262$	6.79447e15i	1.29777i
$263$	− 8.43203e14i	− 0.157116i	−0.996910	−	0.0785579i	$-0.974968\pi$
$263$	− 8.43203e14i	− 0.157116i	0.996910	−	0.0785579i	$-0.0250315\pi$
$264$	5.62756e15	1.02304
$265$	0	0
$266$	−1.87248e15	−0.324106
$267$	− 9.78133e14i	− 0.165225i
$268$	2.02404e16i	3.33689i
$269$	−1.22523e16	−1.97164	−0.985821	−	0.167803i	$-0.946333\pi$
$269$	−1.22523e16	−1.97164	−0.985821	+	0.167803i	$0.946333\pi$
$270$	0	0
$271$	−2.29585e14	−0.0352082	−0.0176041	−	0.999845i	$-0.505604\pi$
$271$	−2.29585e14	−0.0352082	−0.0176041	+	0.999845i	$0.505604\pi$
$272$	3.03870e15i	0.454978i
$273$	1.04721e15i	0.153100i
$274$	−2.21187e16	−3.15777
$275$	0	0
$276$	1.17263e16	1.59681
$277$	− 2.21417e15i	− 0.294505i	−0.989099	−	0.147252i	$-0.952957\pi$
$277$	− 2.21417e15i	− 0.294505i	0.989099	−	0.147252i	$-0.0470430\pi$
$278$	1.04930e16i	1.36335i
$279$	4.06864e15	0.516442
$280$	0	0
$281$	−3.89035e15	−0.471409	−0.235704	−	0.971825i	$-0.575740\pi$
$281$	−3.89035e15	−0.471409	−0.235704	+	0.971825i	$0.575740\pi$
$282$	1.47614e16i	1.74787i
$283$	1.39198e16i	1.61072i	0.592783	+	0.805362i	$0.298029\pi$
$283$	1.39198e16i	1.61072i	−0.592783	+	0.805362i	$0.701971\pi$
$284$	−4.51580e15	−0.510699
$285$	0	0
$286$	2.66538e15	0.287991
$287$	− 2.43842e15i	− 0.257558i
$288$	1.57738e15i	0.162886i
$289$	8.86730e15	0.895273
$290$	0	0
$291$	−2.27802e12	−0.000219914 0
$292$	3.26984e16i	3.08701i
$293$	− 1.52234e16i	− 1.40563i	−0.711371	−	0.702817i	$-0.751925\pi$
$293$	− 1.52234e16i	− 1.40563i	0.711371	−	0.702817i	$-0.248075\pi$
$294$	1.22815e16	1.10916
$295$	0	0
$296$	−2.37290e16	−2.05061
$297$	2.01826e15i	0.170631i
$298$	2.60717e16i	2.15657i
$299$	2.94608e15	0.238442
$300$	0	0
$301$	1.61054e16	1.24821
$302$	− 1.14988e16i	− 0.872183i
$303$	− 9.86293e15i	− 0.732198i
$304$	−2.45428e15	−0.178339
$305$	0	0
$306$	−2.74062e15	−0.190836
$307$	− 8.48697e14i	− 0.0578566i	−0.999581	−	0.0289283i	$-0.990791\pi$
$307$	− 8.48697e14i	− 0.0578566i	0.999581	−	0.0289283i	$-0.00920945\pi$
$308$	− 4.08591e16i	− 2.72715i
$309$	−2.69442e15	−0.176090
$310$	0	0
$311$	−2.48376e15	−0.155657	−0.0778283	−	0.996967i	$-0.524799\pi$
$311$	−2.48376e15	−0.155657	−0.0778283	+	0.996967i	$0.524799\pi$
$312$	3.45179e15i	0.211856i
$313$	− 4.39913e15i	− 0.264441i	−0.991220	−	0.132220i	$-0.957789\pi$
$313$	− 4.39913e15i	− 0.264441i	0.991220	−	0.132220i	$-0.0422107\pi$
$314$	−7.14935e15	−0.420944
$315$	0	0
$316$	−3.88789e15	−0.219659
$317$	2.19567e16i	1.21530i	0.794206	+	0.607648i	$0.207887\pi$
$317$	2.19567e16i	1.21530i	−0.794206	+	0.607648i	$0.792113\pi$
$318$	7.10400e15i	0.385236i
$319$	1.65526e16	0.879482
$320$	0	0
$321$	5.51502e15	0.281361
$322$	− 6.63682e16i	− 3.31816i
$323$	− 8.37785e14i	− 0.0410503i
$324$	−4.92741e15	−0.236633
$325$	0	0
$326$	1.16843e16	0.539124
$327$	− 1.49954e16i	− 0.678264i
$328$	− 8.03748e15i	− 0.356402i
$329$	5.68514e16	2.47154
$330$	0	0
$331$	2.65474e16	1.10953	0.554767	−	0.832006i	$-0.312808\pi$
$331$	2.65474e16	1.10953	0.554767	+	0.832006i	$0.312808\pi$
$332$	− 3.64527e16i	− 1.49394i
$333$	− 8.51011e15i	− 0.342017i
$334$	−8.39995e16	−3.31074
$335$	0	0
$336$	3.09211e16	1.17233
$337$	1.40823e16i	0.523697i	0.965109	+	0.261848i	$0.0843320\pi$
$337$	1.40823e16i	0.523697i	−0.965109	+	0.261848i	$0.915668\pi$
$338$	− 4.68616e16i	− 1.70946i
$339$	1.09787e16	0.392872
$340$	0	0
$341$	−3.98830e16	−1.37368
$342$	− 2.21353e15i	− 0.0748025i
$343$	− 3.74294e15i	− 0.124108i
$344$	5.30864e16	1.72724
$345$	0	0
$346$	−6.00033e16	−1.88010
$347$	4.85833e16i	1.49398i	0.664834	+	0.746992i	$0.268502\pi$
$347$	4.85833e16i	1.49398i	−0.664834	+	0.746992i	$0.731498\pi$
$348$	4.04119e16i	1.21967i
$349$	−1.20256e16	−0.356239	−0.178119	−	0.984009i	$-0.557001\pi$
$349$	−1.20256e16	−0.356239	−0.178119	+	0.984009i	$0.557001\pi$
$350$	0	0
$351$	−1.23794e15	−0.0353350
$352$	− 1.54623e16i	− 0.433258i
$353$	3.68917e16i	1.01483i	0.861702	+	0.507415i	$0.169399\pi$
$353$	3.68917e16i	1.01483i	−0.861702	+	0.507415i	$0.830601\pi$
$354$	−4.79721e16	−1.29559
$355$	0	0
$356$	−2.34088e16	−0.609472
$357$	1.05551e16i	0.269848i
$358$	2.26664e16i	0.569041i
$359$	−2.30169e16	−0.567456	−0.283728	−	0.958905i	$-0.591571\pi$
$359$	−2.30169e16	−0.567456	−0.283728	+	0.958905i	$0.591571\pi$
$360$	0	0
$361$	−4.13763e16	−0.983909
$362$	− 4.26427e16i	− 0.995952i
$363$	5.38303e15i	0.123491i
$364$	2.50619e16	0.564748
$365$	0	0
$366$	1.36736e16	0.297342
$367$	6.59133e15i	0.140813i	0.997518	+	0.0704066i	$0.0224297\pi$
$367$	6.59133e15i	0.140813i	−0.997518	+	0.0704066i	$0.977570\pi$
$368$	− 8.69895e16i	− 1.82581i
$369$	2.88254e15	0.0594435
$370$	0	0
$371$	2.73600e16	0.544736
$372$	− 9.73710e16i	− 1.90502i
$373$	− 9.60592e15i	− 0.184685i	−0.995727	−	0.0923425i	$-0.970565\pi$
$373$	− 9.60592e15i	− 0.184685i	0.995727	−	0.0923425i	$-0.0294355\pi$
$374$	2.68651e16	0.507601
$375$	0	0
$376$	1.87393e17	3.42004
$377$	1.01529e16i	0.182126i
$378$	2.78879e16i	0.491722i
$379$	8.91020e16	1.54430	0.772151	−	0.635439i	$-0.219181\pi$
$379$	8.91020e16	1.54430	0.772151	+	0.635439i	$0.219181\pi$
$380$	0	0
$381$	2.37062e16	0.397053
$382$	2.54686e16i	0.419366i
$383$	− 7.32809e16i	− 1.18631i	−0.805088	−	0.593156i	$-0.797882\pi$
$383$	− 7.32809e16i	− 1.18631i	0.805088	−	0.593156i	$-0.202118\pi$
$384$	−5.24703e16	−0.835142
$385$	0	0
$386$	−9.25995e16	−1.42492
$387$	1.90388e16i	0.288083i
$388$	5.45177e13i	0 0.000811206i
$389$	4.08834e16	0.598239	0.299119	−	0.954216i	$-0.403307\pi$
$389$	4.08834e16	0.598239	0.299119	+	0.954216i	$0.403307\pi$
$390$	0	0
$391$	2.96944e16	0.420267
$392$	− 1.55911e17i	− 2.17028i
$393$	3.09340e16i	0.423531i
$394$	1.19345e17	1.60723
$395$	0	0
$396$	4.83011e16	0.629416
$397$	− 1.12376e16i	− 0.144058i	−0.997403	−	0.0720289i	$-0.977053\pi$
$397$	− 1.12376e16i	− 0.144058i	0.997403	−	0.0720289i	$-0.0229474\pi$
$398$	1.46420e17i	1.84654i
$399$	−8.52510e15	−0.105773
$400$	0	0
$401$	1.32254e17	1.58844	0.794219	−	0.607632i	$-0.207880\pi$
$401$	1.32254e17	1.58844	0.794219	+	0.607632i	$0.207880\pi$
$402$	1.35420e17i	1.60035i
$403$	− 2.44632e16i	− 0.284466i
$404$	−2.36040e17	−2.70089
$405$	0	0
$406$	2.28721e17	2.53447
$407$	8.34207e16i	0.909725i
$408$	3.47916e16i	0.373408i
$409$	1.13059e17	1.19428	0.597139	−	0.802138i	$-0.296304\pi$
$409$	1.13059e17	1.19428	0.597139	+	0.802138i	$0.296304\pi$
$410$	0	0
$411$	−1.00703e17	−1.03055
$412$	6.44831e16i	0.649552i
$413$	1.84758e17i	1.83201i
$414$	7.84563e16	0.765818
$415$	0	0
$416$	9.48417e15	0.0897207
$417$	4.77727e16i	0.444934i
$418$	2.16982e16i	0.198966i
$419$	6.14346e16	0.554654	0.277327	−	0.960776i	$-0.410552\pi$
$419$	6.14346e16	0.554654	0.277327	+	0.960776i	$0.410552\pi$
$420$	0	0
$421$	1.62906e17	1.42595	0.712974	−	0.701190i	$-0.247348\pi$
$421$	1.62906e17	1.42595	0.712974	+	0.701190i	$0.247348\pi$
$422$	− 6.86651e16i	− 0.591841i
$423$	6.72061e16i	0.570422i
$424$	9.01838e16	0.753790
$425$	0	0
$426$	−3.02134e16	−0.244927
$427$	− 5.26620e16i	− 0.420452i
$428$	− 1.31986e17i	− 1.03787i
$429$	1.21350e16	0.0939869
$430$	0	0
$431$	−2.03574e17	−1.52975	−0.764875	−	0.644179i	$-0.777199\pi$
$431$	−2.03574e17	−1.52975	−0.764875	+	0.644179i	$0.777199\pi$
$432$	3.65530e16i	0.270569i
$433$	− 1.73408e17i	− 1.26444i	−0.774791	−	0.632218i	$-0.782145\pi$
$433$	− 1.73408e17i	− 1.26444i	0.774791	−	0.632218i	$-0.217855\pi$
$434$	−5.51096e17	−3.95862
$435$	0	0
$436$	−3.58872e17	−2.50195
$437$	2.39834e16i	0.164734i
$438$	2.18772e17i	1.48050i
$439$	7.14926e16	0.476696	0.238348	−	0.971180i	$-0.423394\pi$
$439$	7.14926e16	0.476696	0.238348	+	0.971180i	$0.423394\pi$
$440$	0	0
$441$	5.59155e16	0.361977
$442$	1.64783e16i	0.105116i
$443$	− 2.09427e17i	− 1.31646i	−0.752816	−	0.658231i	$-0.771305\pi$
$443$	− 2.09427e17i	− 1.31646i	0.752816	−	0.658231i	$-0.228695\pi$
$444$	−2.03665e17	−1.26161
$445$	0	0
$446$	−3.25752e17	−1.95979
$447$	1.18700e17i	0.703804i
$448$	1.33814e17i	0.781980i
$449$	−4.62356e16	−0.266302	−0.133151	−	0.991096i	$-0.542510\pi$
$449$	−4.62356e16	−0.266302	−0.133151	+	0.991096i	$0.542510\pi$
$450$	0	0
$451$	−2.82562e16	−0.158113
$452$	− 2.62742e17i	− 1.44921i
$453$	− 5.23521e16i	− 0.284640i
$454$	−4.16617e17	−2.23292
$455$	0	0
$456$	−2.81003e16	−0.146366
$457$	3.28135e17i	1.68499i	0.538706	+	0.842494i	$0.318913\pi$
$457$	3.28135e17i	1.68499i	−0.538706	+	0.842494i	$0.681087\pi$
$458$	1.14639e17i	0.580371i
$459$	−1.24776e16	−0.0622799
$460$	0	0
$461$	7.87892e16	0.382306	0.191153	−	0.981560i	$-0.438777\pi$
$461$	7.87892e16	0.382306	0.191153	+	0.981560i	$0.438777\pi$
$462$	− 2.73372e17i	− 1.30792i
$463$	− 6.33656e16i	− 0.298935i	−0.988767	−	0.149468i	$-0.952244\pi$
$463$	− 6.33656e16i	− 0.298935i	0.988767	−	0.149468i	$-0.0477560\pi$
$464$	2.99787e17	1.39459
$465$	0	0
$466$	−3.88381e17	−1.75691
$467$	− 2.32240e17i	− 1.03604i	−0.855368	−	0.518020i	$-0.826669\pi$
$467$	− 2.32240e17i	− 1.03604i	0.855368	−	0.518020i	$-0.173331\pi$
$468$	2.96266e16i	0.130342i
$469$	5.21552e17	2.26294
$470$	0	0
$471$	−3.25498e16	−0.137376
$472$	6.08995e17i	2.53508i
$473$	− 1.86628e17i	− 0.766268i
$474$	−2.60124e16	−0.105347
$475$	0	0
$476$	2.52606e17	0.995401
$477$	3.23433e16i	0.125723i
$478$	− 3.47784e17i	− 1.33361i
$479$	4.79339e17	1.81327	0.906634	−	0.421919i	$-0.138643\pi$
$479$	4.79339e17	1.81327	0.906634	+	0.421919i	$0.138643\pi$
$480$	0	0
$481$	−5.11680e16	−0.188389
$482$	7.40811e17i	2.69093i
$483$	− 3.02163e17i	− 1.08289i
$484$	1.28827e17	0.455526
$485$	0	0
$486$	−3.29673e16	−0.113488
$487$	− 2.92692e17i	− 0.994197i	−0.867694	−	0.497098i	$-0.834399\pi$
$487$	− 2.92692e17i	− 0.994197i	0.867694	−	0.497098i	$-0.165601\pi$
$488$	− 1.73584e17i	− 0.581809i
$489$	5.31966e16	0.175945
$490$	0	0
$491$	6.92352e16	0.222996	0.111498	−	0.993765i	$-0.464435\pi$
$491$	6.92352e16	0.222996	0.111498	+	0.993765i	$0.464435\pi$
$492$	− 6.89853e16i	− 0.219272i
$493$	1.02334e17i	0.321008i
$494$	−1.33091e16	−0.0412026
$495$	0	0
$496$	−7.22327e17	−2.17823
$497$	1.16363e17i	0.346335i
$498$	− 2.43891e17i	− 0.716480i
$499$	−4.50229e17	−1.30551	−0.652755	−	0.757569i	$-0.726387\pi$
$499$	−4.50229e17	−1.30551	−0.652755	+	0.757569i	$0.726387\pi$
$500$	0	0
$501$	−3.82435e17	−1.08047
$502$	− 8.27008e17i	− 2.30641i
$503$	− 3.62365e17i	− 0.997596i	−0.866718	−	0.498798i	$-0.833775\pi$
$503$	− 3.62365e17i	− 0.997596i	0.866718	−	0.498798i	$-0.166225\pi$
$504$	3.54031e17	0.962150
$505$	0	0
$506$	−7.69071e17	−2.03699
$507$	− 2.13353e17i	− 0.557887i
$508$	− 5.67338e17i	− 1.46463i
$509$	4.92663e16	0.125569	0.0627847	−	0.998027i	$-0.480002\pi$
$509$	4.92663e16	0.125569	0.0627847	+	0.998027i	$0.480002\pi$
$510$	0	0
$511$	8.42568e17	2.09348
$512$	8.65285e17i	2.12278i
$513$	− 1.00778e16i	− 0.0244121i
$514$	−1.06040e18	−2.53636
$515$	0	0
$516$	4.55638e17	1.06267
$517$	− 6.58791e17i	− 1.51726i
$518$	1.15269e18i	2.62162i
$519$	−2.73185e17	−0.613576
$520$	0	0
$521$	8.86374e16	0.194165	0.0970826	−	0.995276i	$-0.469049\pi$
$521$	8.86374e16	0.194165	0.0970826	+	0.995276i	$0.469049\pi$
$522$	2.70380e17i	0.584946i
$523$	8.32000e16i	0.177772i	0.996042	+	0.0888858i	$0.0283306\pi$
$523$	8.32000e16i	0.177772i	−0.996042	+	0.0888858i	$0.971669\pi$
$524$	7.40316e17	1.56230
$525$	0	0
$526$	−1.35014e17	−0.277953
$527$	− 2.46571e17i	− 0.501387i
$528$	− 3.58312e17i	− 0.719682i
$529$	−3.46031e17	−0.686519
$530$	0	0
$531$	−2.18409e17	−0.422820
$532$	2.04023e17i	0.390171i
$533$	− 1.73316e16i	− 0.0327426i
$534$	−1.56619e17	−0.292298
$535$	0	0
$536$	1.71913e18	3.13140
$537$	1.03196e17i	0.185709i
$538$	1.96184e18i	3.48802i
$539$	−5.48113e17	−0.962816
$540$	0	0
$541$	−4.36899e16	−0.0749201	−0.0374601	−	0.999298i	$-0.511927\pi$
$541$	−4.36899e16	−0.0749201	−0.0374601	+	0.999298i	$0.511927\pi$
$542$	3.67612e16i	0.0622866i
$543$	− 1.94145e17i	− 0.325032i
$544$	9.55935e16	0.158138
$545$	0	0
$546$	1.67679e17	0.270849
$547$	− 3.78763e17i	− 0.604575i	−0.953217	−	0.302287i	$-0.902250\pi$
$547$	− 3.78763e17i	− 0.604575i	0.953217	−	0.302287i	$-0.0977502\pi$
$548$	2.41002e18i	3.80143i
$549$	6.22537e16	0.0970387
$550$	0	0
$551$	−8.26528e16	−0.125827
$552$	− 9.95986e17i	− 1.49847i
$553$	1.00183e17i	0.148964i
$554$	−3.54534e17	−0.521007
$555$	0	0
$556$	1.14330e18	1.64125
$557$	6.88487e17i	0.976871i	0.872600	+	0.488435i	$0.162432\pi$
$557$	6.88487e17i	0.976871i	−0.872600	+	0.488435i	$0.837568\pi$
$558$	− 6.51471e17i	− 0.913636i
$559$	1.14473e17	0.158681
$560$	0	0
$561$	1.22312e17	0.165657
$562$	6.22924e17i	0.833967i
$563$	2.26569e17i	0.299844i	0.988698	+	0.149922i	$0.0479023\pi$
$563$	2.26569e17i	0.299844i	−0.988698	+	0.149922i	$0.952098\pi$
$564$	1.60838e18	2.10414
$565$	0	0
$566$	2.22884e18	2.84953
$567$	1.26969e17i	0.160475i
$568$	3.83553e17i	0.479249i
$569$	−7.35304e17	−0.908316	−0.454158	−	0.890921i	$-0.650060\pi$
$569$	−7.35304e17	−0.908316	−0.454158	+	0.890921i	$0.650060\pi$
$570$	0	0
$571$	4.30093e16	0.0519311	0.0259655	−	0.999663i	$-0.491734\pi$
$571$	4.30093e16	0.0519311	0.0259655	+	0.999663i	$0.491734\pi$
$572$	− 2.90416e17i	− 0.346694i
$573$	1.15954e17i	0.136862i
$574$	−3.90440e17	−0.455646
$575$	0	0
$576$	−1.58187e17	−0.180478
$577$	− 1.37324e18i	− 1.54919i	−0.632458	−	0.774594i	$-0.717954\pi$
$577$	− 1.37324e18i	− 1.54919i	0.632458	−	0.774594i	$-0.282046\pi$
$578$	− 1.41983e18i	− 1.58382i
$579$	−4.21590e17	−0.465028
$580$	0	0
$581$	−9.39309e17	−1.01313
$582$	3.64757e14i	0 0.000389049i
$583$	− 3.17047e17i	− 0.334409i
$584$	2.77726e18	2.89690
$585$	0	0
$586$	−2.43758e18	−2.48670
$587$	− 6.95010e17i	− 0.701203i	−0.936525	−	0.350601i	$-0.885977\pi$
$587$	− 6.95010e17i	− 0.701203i	0.936525	−	0.350601i	$-0.114023\pi$
$588$	− 1.33817e18i	− 1.33524i
$589$	1.99149e17	0.196530
$590$	0	0
$591$	5.43356e17	0.524525
$592$	1.51085e18i	1.44254i
$593$	− 1.10257e18i	− 1.04124i	−0.853789	−	0.520620i	$-0.825701\pi$
$593$	− 1.10257e18i	− 1.04124i	0.853789	−	0.520620i	$-0.174299\pi$
$594$	3.23164e17	0.301863
$595$	0	0
$596$	2.84074e18	2.59616
$597$	6.66623e17i	0.602625i
$598$	− 4.71728e17i	− 0.421826i
$599$	9.09357e17	0.804377	0.402189	−	0.915557i	$-0.368250\pi$
$599$	9.09357e17	0.804377	0.402189	+	0.915557i	$0.368250\pi$
$600$	0	0
$601$	1.26383e18	1.09397	0.546984	−	0.837143i	$-0.315776\pi$
$601$	1.26383e18	1.09397	0.546984	+	0.837143i	$0.315776\pi$
$602$	− 2.57880e18i	− 2.20821i
$603$	6.16546e17i	0.522279i
$604$	−1.25290e18	−1.04996
$605$	0	0
$606$	−1.57925e18	−1.29533
$607$	− 2.53124e17i	− 0.205403i	−0.994712	−	0.102701i	$-0.967251\pi$
$607$	− 2.53124e17i	− 0.205403i	0.994712	−	0.102701i	$-0.0327486\pi$
$608$	7.72085e16i	0.0619858i
$609$	1.04133e18	0.827133
$610$	0	0
$611$	4.04085e17	0.314199
$612$	2.98615e17i	0.229735i
$613$	− 2.18461e18i	− 1.66295i	−0.555560	−	0.831476i	$-0.687496\pi$
$613$	− 2.18461e18i	− 1.66295i	0.555560	−	0.831476i	$-0.312504\pi$
$614$	−1.35894e17	−0.102354
$615$	0	0
$616$	−3.47040e18	−2.55920
$617$	1.93526e17i	0.141217i	0.997504	+	0.0706083i	$0.0224941\pi$
$617$	1.93526e17i	0.141217i	−0.997504	+	0.0706083i	$0.977506\pi$
$618$	4.31431e17i	0.311520i
$619$	−1.78009e17	−0.127190	−0.0635948	−	0.997976i	$-0.520257\pi$
$619$	−1.78009e17	−0.127190	−0.0635948	+	0.997976i	$0.520257\pi$
$620$	0	0
$621$	3.57198e17	0.249927
$622$	3.97701e17i	0.275371i
$623$	6.03195e17i	0.413319i
$624$	2.19779e17	0.149034
$625$	0	0
$626$	−7.04389e17	−0.467821
$627$	9.87884e16i	0.0649332i
$628$	7.78984e17i	0.506747i
$629$	−5.15737e17	−0.332047
$630$	0	0
$631$	1.13174e18	0.713769	0.356884	−	0.934149i	$-0.383839\pi$
$631$	1.13174e18	0.713769	0.356884	+	0.934149i	$0.383839\pi$
$632$	3.30221e17i	0.206131i
$633$	− 3.12621e17i	− 0.193149i
$634$	3.51571e18	2.14998
$635$	0	0
$636$	7.74043e17	0.463761
$637$	− 3.36198e17i	− 0.199383i
$638$	− 2.65041e18i	− 1.55589i
$639$	−1.37557e17	−0.0799329
$640$	0	0
$641$	−2.32314e18	−1.32281	−0.661406	−	0.750028i	$-0.730040\pi$
$641$	−2.32314e18	−1.32281	−0.661406	+	0.750028i	$0.730040\pi$
$642$	− 8.83067e17i	− 0.497755i
$643$	2.63934e18i	1.47273i	0.676583	+	0.736366i	$0.263460\pi$
$643$	2.63934e18i	1.47273i	−0.676583	+	0.736366i	$0.736540\pi$
$644$	−7.23139e18	−3.99451
$645$	0	0
$646$	−1.34146e17	−0.0726219
$647$	1.32570e18i	0.710503i	0.934771	+	0.355251i	$0.115605\pi$
$647$	1.32570e18i	0.710503i	−0.934771	+	0.355251i	$0.884395\pi$
$648$	4.18513e17i	0.222061i
$649$	2.14096e18	1.12465
$650$	0	0
$651$	−2.50905e18	−1.29191
$652$	− 1.27311e18i	− 0.649016i
$653$	2.10774e18i	1.06385i	0.846791	+	0.531926i	$0.178532\pi$
$653$	2.10774e18i	1.06385i	−0.846791	+	0.531926i	$0.821468\pi$
$654$	−2.40107e18	−1.19991
$655$	0	0
$656$	−5.11754e17	−0.250718
$657$	9.96031e17i	0.483168i
$658$	− 9.10306e18i	− 4.37239i
$659$	−2.06081e18	−0.980126	−0.490063	−	0.871687i	$-0.663026\pi$
$659$	−2.06081e18	−0.980126	−0.490063	+	0.871687i	$0.663026\pi$
$660$	0	0
$661$	2.22419e18	1.03720	0.518600	−	0.855017i	$-0.326453\pi$
$661$	2.22419e18	1.03720	0.518600	+	0.855017i	$0.326453\pi$
$662$	− 4.25078e18i	− 1.96287i
$663$	7.50229e16i	0.0343049i
$664$	−3.09614e18	−1.40193
$665$	0	0
$666$	−1.36264e18	−0.605061
$667$	− 2.92954e18i	− 1.28820i
$668$	9.15248e18i	3.98558i
$669$	−1.48309e18	−0.639585
$670$	0	0
$671$	−6.10244e17	−0.258111
$672$	− 9.72737e17i	− 0.407469i
$673$	3.24859e18i	1.34771i	0.738863	+	0.673856i	$0.235363\pi$
$673$	3.24859e18i	1.34771i	−0.738863	+	0.673856i	$0.764637\pi$
$674$	2.25486e18	0.926470
$675$	0	0
$676$	−5.10598e18	−2.05790
$677$	3.36868e18i	1.34472i	0.740222	+	0.672362i	$0.234720\pi$
$677$	3.36868e18i	1.34472i	−0.740222	+	0.672362i	$0.765280\pi$
$678$	− 1.75791e18i	− 0.695029i
$679$	1.40481e15	0.000550127 0
$680$	0	0
$681$	−1.89678e18	−0.728722
$682$	6.38607e18i	2.43016i
$683$	− 5.02495e18i	− 1.89408i	−0.321122	−	0.947038i	$-0.604060\pi$
$683$	− 5.02495e18i	− 1.89408i	0.321122	−	0.947038i	$-0.395940\pi$
$684$	−2.41184e17	−0.0900499
$685$	0	0
$686$	−5.99320e17	−0.219559
$687$	5.21931e17i	0.189406i
$688$	− 3.38006e18i	− 1.21506i
$689$	1.94468e17	0.0692505
$690$	0	0
$691$	3.84714e18	1.34441	0.672204	−	0.740366i	$-0.265348\pi$
$691$	3.84714e18	1.34441	0.672204	+	0.740366i	$0.265348\pi$
$692$	6.53788e18i	2.26333i
$693$	− 1.24462e18i	− 0.426845i
$694$	7.77917e18	2.64300
$695$	0	0
$696$	3.43241e18	1.14456
$697$	− 1.74690e17i	− 0.0577106i
$698$	1.92554e18i	0.630220i
$699$	−1.76823e18	−0.573373
$700$	0	0
$701$	−3.06033e18	−0.974095	−0.487048	−	0.873375i	$-0.661926\pi$
$701$	−3.06033e18	−0.974095	−0.487048	+	0.873375i	$0.661926\pi$
$702$	1.98220e17i	0.0625110i
$703$	− 4.16548e17i	− 0.130153i
$704$	1.55063e18	0.480050
$705$	0	0
$706$	5.90711e18	1.79533
$707$	6.08227e18i	1.83164i
$708$	5.22698e18i	1.55968i
$709$	2.08211e18	0.615605	0.307803	−	0.951450i	$-0.400406\pi$
$709$	2.08211e18	0.615605	0.307803	+	0.951450i	$0.400406\pi$
$710$	0	0
$711$	−1.18430e17	−0.0343802
$712$	1.98824e18i	0.571938i
$713$	7.05863e18i	2.01205i
$714$	1.69009e18	0.477387
$715$	0	0
$716$	2.46971e18	0.685032
$717$	− 1.58340e18i	− 0.435227i
$718$	3.68547e18i	1.00388i
$719$	3.53851e18	0.955175	0.477588	−	0.878584i	$-0.341511\pi$
$719$	3.53851e18	0.955175	0.477588	+	0.878584i	$0.341511\pi$
$720$	0	0
$721$	1.66159e18	0.440500
$722$	6.62519e18i	1.74063i
$723$	3.37279e18i	0.878193i
$724$	−4.64629e18	−1.19896
$725$	0	0
$726$	8.61933e17	0.218467
$727$	1.72239e17i	0.0432671i	0.999766	+	0.0216335i	$0.00688670\pi$
$727$	1.72239e17i	0.0432671i	−0.999766	+	0.0216335i	$0.993113\pi$
$728$	− 2.12865e18i	− 0.529969i
$729$	−1.50095e17	−0.0370370
$730$	0	0
$731$	1.15380e18	0.279685
$732$	− 1.48986e18i	− 0.357951i
$733$	− 4.07961e18i	− 0.971501i	−0.874097	−	0.485751i	$-0.838546\pi$
$733$	− 4.07961e18i	− 0.971501i	0.874097	−	0.485751i	$-0.161454\pi$
$734$	1.05541e18	0.249112
$735$	0	0
$736$	−2.73657e18	−0.634602
$737$	− 6.04371e18i	− 1.38920i
$738$	− 4.61554e17i	− 0.105161i
$739$	−2.80600e18	−0.633722	−0.316861	−	0.948472i	$-0.602629\pi$
$739$	−2.80600e18	−0.633722	−0.316861	+	0.948472i	$0.602629\pi$
$740$	0	0
$741$	−6.05942e16	−0.0134466
$742$	− 4.38090e18i	− 0.963690i
$743$	3.51196e18i	0.765813i	0.923787	+	0.382907i	$0.125077\pi$
$743$	3.51196e18i	0.765813i	−0.923787	+	0.382907i	$0.874923\pi$
$744$	−8.27028e18	−1.78771
$745$	0	0
$746$	−1.53810e18	−0.326725
$747$	− 1.11039e18i	− 0.233826i
$748$	− 2.92718e18i	− 0.611068i
$749$	−3.40100e18	−0.703842
$750$	0	0
$751$	−1.57963e18	−0.321289	−0.160644	−	0.987012i	$-0.551357\pi$
$751$	−1.57963e18	−0.321289	−0.160644	+	0.987012i	$0.551357\pi$
$752$	− 1.19315e19i	− 2.40590i
$753$	− 3.76523e18i	− 0.752703i
$754$	1.62569e18	0.322199
$755$	0	0
$756$	3.03863e18	0.591952
$757$	4.57886e18i	0.884371i	0.896924	+	0.442185i	$0.145797\pi$
$757$	4.57886e18i	0.884371i	−0.896924	+	0.442185i	$0.854203\pi$
$758$	− 1.42670e19i	− 2.73202i
$759$	−3.50145e18	−0.664777
$760$	0	0
$761$	−3.19192e18	−0.595733	−0.297867	−	0.954608i	$-0.596275\pi$
$761$	−3.19192e18	−0.595733	−0.297867	+	0.954608i	$0.596275\pi$
$762$	− 3.79584e18i	− 0.702425i
$763$	9.24739e18i	1.69672i
$764$	2.77503e18	0.504848
$765$	0	0
$766$	−1.17338e19	−2.09870
$767$	1.31321e18i	0.232897i
$768$	6.62395e18i	1.16485i
$769$	2.98686e18	0.520827	0.260414	−	0.965497i	$-0.416141\pi$
$769$	2.98686e18	0.520827	0.260414	+	0.965497i	$0.416141\pi$
$770$	0	0
$771$	−4.82783e18	−0.827748
$772$	1.00895e19i	1.71537i
$773$	6.01573e18i	1.01420i	0.861888	+	0.507098i	$0.169282\pi$
$773$	6.01573e18i	1.01420i	−0.861888	+	0.507098i	$0.830718\pi$
$774$	3.04850e18	0.509647
$775$	0	0
$776$	4.63050e15	0.000761250 0
$777$	5.24801e18i	0.855576i
$778$	− 6.54626e18i	− 1.05834i
$779$	1.41093e17	0.0226210
$780$	0	0
$781$	1.34840e18	0.212612
$782$	− 4.75467e18i	− 0.743493i
$783$	1.23099e18i	0.190899i
$784$	−9.92697e18	−1.52673
$785$	0	0
$786$	4.95317e18	0.749266
$787$	− 8.17242e18i	− 1.22607i	−0.790056	−	0.613034i	$-0.789949\pi$
$787$	− 8.17242e18i	− 1.22607i	0.790056	−	0.613034i	$-0.210051\pi$
$788$	− 1.30036e19i	− 1.93484i
$789$	−6.14695e17	−0.0907108
$790$	0	0
$791$	−6.77032e18	−0.982793
$792$	− 4.10249e18i	− 0.590655i
$793$	− 3.74308e17i	− 0.0534506i
$794$	−1.79937e18	−0.254852
$795$	0	0
$796$	1.59537e19	2.22293
$797$	1.06035e19i	1.46545i	0.680523	+	0.732726i	$0.261752\pi$
$797$	1.06035e19i	1.46545i	−0.680523	+	0.732726i	$0.738248\pi$
$798$	1.36504e18i	0.187123i
$799$	4.07288e18	0.553793
$800$	0	0
$801$	−7.13059e17	−0.0953925
$802$	− 2.11765e19i	− 2.81010i
$803$	− 9.76363e18i	− 1.28517i
$804$	1.47552e19	1.92656
$805$	0	0
$806$	−3.91705e18	−0.503247
$807$	8.93193e18i	1.13833i
$808$	2.00483e19i	2.53456i
$809$	−9.68399e18	−1.21448	−0.607238	−	0.794520i	$-0.707722\pi$
$809$	−9.68399e18	−1.21448	−0.607238	+	0.794520i	$0.707722\pi$
$810$	0	0
$811$	−5.91477e18	−0.729966	−0.364983	−	0.931014i	$-0.618925\pi$
$811$	−5.91477e18	−0.729966	−0.364983	+	0.931014i	$0.618925\pi$
$812$	− 2.49212e19i	− 3.05108i
$813$	1.67368e17i	0.0203275i
$814$	1.33573e19	1.60939
$815$	0	0
$816$	2.21521e18	0.262681
$817$	9.31899e17i	0.109629i
$818$	− 1.81031e19i	− 2.11279i
$819$	7.63415e17	0.0883925
$820$	0	0
$821$	7.57709e17	0.0863519	0.0431759	−	0.999067i	$-0.486252\pi$
$821$	7.57709e17	0.0863519	0.0431759	+	0.999067i	$0.486252\pi$
$822$	1.61245e19i	1.82314i
$823$	− 1.14913e19i	− 1.28905i	−0.764585	−	0.644523i	$-0.777056\pi$
$823$	− 1.14913e19i	− 1.28905i	0.764585	−	0.644523i	$-0.222944\pi$
$824$	5.47692e18	0.609551
$825$	0	0
$826$	2.95834e19	3.24099
$827$	− 1.01647e19i	− 1.10486i	−0.833559	−	0.552430i	$-0.813701\pi$
$827$	− 1.01647e19i	− 1.10486i	0.833559	−	0.552430i	$-0.186299\pi$
$828$	− 8.54850e18i	− 0.921919i
$829$	−2.72808e18	−0.291913	−0.145956	−	0.989291i	$-0.546626\pi$
$829$	−2.72808e18	−0.291913	−0.145956	+	0.989291i	$0.546626\pi$
$830$	0	0
$831$	−1.61413e18	−0.170033
$832$	9.51118e17i	0.0994106i
$833$	− 3.38863e18i	− 0.351425i
$834$	7.64938e18	0.787130
$835$	0	0
$836$	2.36421e18	0.239522
$837$	− 2.96604e18i	− 0.298168i
$838$	− 9.83692e18i	− 0.981235i
$839$	1.69983e19	1.68249	0.841245	−	0.540655i	$-0.181823\pi$
$839$	1.69983e19	1.68249	0.841245	+	0.540655i	$0.181823\pi$
$840$	0	0
$841$	−1.64704e17	−0.0160520
$842$	− 2.60846e19i	− 2.52264i
$843$	2.83606e18i	0.272168i
$844$	−7.48166e18	−0.712479
$845$	0	0
$846$	1.07611e19	1.00913
$847$	− 3.31961e18i	− 0.308919i
$848$	− 5.74208e18i	− 0.530269i
$849$	1.01475e19	0.929952
$850$	0	0
$851$	1.47641e19	1.33249
$852$	3.29201e18i	0.294852i
$853$	2.07516e19i	1.84452i	0.386568	+	0.922261i	$0.373660\pi$
$853$	2.07516e19i	1.84452i	−0.386568	+	0.922261i	$0.626340\pi$
$854$	−8.43225e18	−0.743819
$855$	0	0
$856$	−1.12103e19	−0.973956
$857$	8.07408e18i	0.696174i	0.937462	+	0.348087i	$0.113169\pi$
$857$	8.07408e18i	0.696174i	−0.937462	+	0.348087i	$0.886831\pi$
$858$	− 1.94306e18i	− 0.166272i
$859$	−1.35586e19	−1.15149	−0.575743	−	0.817631i	$-0.695287\pi$
$859$	−1.35586e19	−1.15149	−0.575743	+	0.817631i	$0.695287\pi$
$860$	0	0
$861$	−1.77761e18	−0.148701
$862$	3.25964e19i	2.70627i
$863$	1.19838e19i	0.987469i	0.869613	+	0.493735i	$0.164369\pi$
$863$	1.19838e19i	0.987469i	−0.869613	+	0.493735i	$0.835631\pi$
$864$	1.14991e18	0.0940424
$865$	0	0
$866$	−2.77661e19	−2.23691
$867$	− 6.46426e18i	− 0.516886i
$868$	6.00467e19i	4.76553i
$869$	1.16091e18	0.0914474
$870$	0	0
$871$	3.70705e18	0.287681
$872$	3.04811e19i	2.34787i
$873$	1.66067e15i	0 0.000126967i
$874$	3.84023e18	0.291429
$875$	0	0
$876$	2.38371e19	1.78228
$877$	− 6.80753e18i	− 0.505234i	−0.967566	−	0.252617i	$-0.918709\pi$
$877$	− 6.80753e18i	− 0.505234i	0.967566	−	0.252617i	$-0.0812913\pi$
$878$	− 1.14474e19i	− 0.843322i
$879$	−1.10979e19	−0.811543
$880$	0	0
$881$	1.23865e19	0.892492	0.446246	−	0.894910i	$-0.352761\pi$
$881$	1.23865e19	0.892492	0.446246	+	0.894910i	$0.352761\pi$
$882$	− 8.95320e18i	− 0.640372i
$883$	− 1.00764e19i	− 0.715421i	−0.933832	−	0.357711i	$-0.883557\pi$
$883$	− 1.00764e19i	− 0.715421i	0.933832	−	0.357711i	$-0.116443\pi$
$884$	1.79546e18	0.126542
$885$	0	0
$886$	−3.35335e19	−2.32895
$887$	1.28943e17i	0.00888981i	0.999990	+	0.00444491i	$0.00141486\pi$
$887$	1.28943e17i	0.00888981i	−0.999990	+	0.00444491i	$0.998585\pi$
$888$	1.72984e19i	1.18392i
$889$	−1.46191e19	−0.993252
$890$	0	0
$891$	1.47131e18	0.0985141
$892$	3.54935e19i	2.35927i
$893$	3.28957e18i	0.217072i
$894$	1.90063e19	1.24510
$895$	0	0
$896$	3.23573e19	2.08916
$897$	− 2.14770e18i	− 0.137664i
$898$	7.40325e18i	0.471114i
$899$	−2.43258e19	−1.53684
$900$	0	0
$901$	1.96010e18	0.122058
$902$	4.52440e18i	0.279717i
$903$	− 1.17408e19i	− 0.720657i
$904$	−2.23162e19	−1.35996
$905$	0	0
$906$	−8.38263e18	−0.503555
$907$	− 1.98412e19i	− 1.18337i	−0.806169	−	0.591685i	$-0.798463\pi$
$907$	− 1.98412e19i	− 1.18337i	0.806169	−	0.591685i	$-0.201537\pi$
$908$	4.53940e19i	2.68807i
$909$	−7.19007e18	−0.422735
$910$	0	0
$911$	−9.94765e18	−0.576568	−0.288284	−	0.957545i	$-0.593085\pi$
$911$	−9.94765e18	−0.576568	−0.288284	+	0.957545i	$0.593085\pi$
$912$	1.78917e18i	0.102964i
$913$	1.08847e19i	0.621949i
$914$	5.25410e19	2.98090
$915$	0	0
$916$	1.24909e19	0.698671
$917$	− 1.90764e19i	− 1.05949i
$918$	1.99791e18i	0.110179i
$919$	−2.38402e19	−1.30544	−0.652722	−	0.757598i	$-0.726373\pi$
$919$	−2.38402e19	−1.30544	−0.652722	+	0.757598i	$0.726373\pi$
$920$	0	0
$921$	−6.18700e17	−0.0334035
$922$	− 1.26157e19i	− 0.676335i
$923$	8.27075e17i	0.0440285i
$924$	−2.97863e19	−1.57452
$925$	0	0
$926$	−1.01461e19	−0.528845
$927$	1.96423e18i	0.101666i
$928$	− 9.43091e18i	− 0.484721i
$929$	−1.47875e19	−0.754731	−0.377366	−	0.926064i	$-0.623170\pi$
$929$	−1.47875e19	−0.754731	−0.377366	+	0.926064i	$0.623170\pi$
$930$	0	0
$931$	2.73692e18	0.137749
$932$	4.23175e19i	2.11503i
$933$	1.81066e18i	0.0898684i
$934$	−3.71863e19	−1.83285
$935$	0	0
$936$	2.51636e18	0.122315
$937$	− 2.68119e19i	− 1.29425i	−0.762382	−	0.647127i	$-0.775970\pi$
$937$	− 2.68119e19i	− 1.29425i	0.762382	−	0.647127i	$-0.224030\pi$
$938$	− 8.35110e19i	− 4.00336i
$939$	−3.20696e18	−0.152675
$940$	0	0
$941$	−3.43324e19	−1.61202	−0.806011	−	0.591900i	$-0.798378\pi$
$941$	−3.43324e19	−1.61202	−0.806011	+	0.591900i	$0.798378\pi$
$942$	5.21188e18i	0.243032i
$943$	5.00089e18i	0.231591i
$944$	3.87753e19	1.78335
$945$	0	0
$946$	−2.98830e19	−1.35560
$947$	1.84464e19i	0.831067i	0.909578	+	0.415534i	$0.136405\pi$
$947$	1.84464e19i	0.831067i	−0.909578	+	0.415534i	$0.863595\pi$
$948$	2.83427e18i	0.126820i
$949$	5.98875e18	0.266137
$950$	0	0
$951$	1.60064e19	0.701652
$952$	− 2.14553e19i	− 0.934101i
$953$	− 1.31082e19i	− 0.566814i	−0.959000	−	0.283407i	$-0.908535\pi$
$953$	− 1.31082e19i	− 0.566814i	0.959000	−	0.283407i	$-0.0914648\pi$
$954$	5.17882e18	0.222416
$955$	0	0
$956$	−3.78941e19	−1.60544
$957$	− 1.20669e19i	− 0.507769i
$958$	− 7.67519e19i	− 3.20784i
$959$	6.21012e19	2.57798
$960$	0	0
$961$	3.41947e19	1.40041
$962$	8.19304e18i	0.333278i
$963$	− 4.02045e18i	− 0.162444i
$964$	8.07179e19	3.23943
$965$	0	0
$966$	−4.83824e19	−1.91574
$967$	2.99771e19i	1.17901i	0.807765	+	0.589505i	$0.200677\pi$
$967$	2.99771e19i	1.17901i	−0.807765	+	0.589505i	$0.799323\pi$
$968$	− 1.09420e19i	− 0.427473i
$969$	−6.10745e17	−0.0237004
$970$	0	0
$971$	−7.97793e18	−0.305468	−0.152734	−	0.988267i	$-0.548808\pi$
$971$	−7.97793e18	−0.305468	−0.152734	+	0.988267i	$0.548808\pi$
$972$	3.59208e18i	0.136620i
$973$	− 2.94605e19i	− 1.11303i
$974$	−4.68659e19	−1.75883
$975$	0	0
$976$	−1.10522e19	−0.409286
$977$	2.51869e19i	0.926530i	0.886220	+	0.463265i	$0.153322\pi$
$977$	2.51869e19i	0.926530i	−0.886220	+	0.463265i	$0.846678\pi$
$978$	− 8.51786e18i	− 0.311263i
$979$	6.98979e18	0.253733
$980$	0	0
$981$	−1.09317e19	−0.391596
$982$	− 1.10860e19i	− 0.394501i
$983$	2.17925e19i	0.770387i	0.922836	+	0.385193i	$0.125865\pi$
$983$	2.17925e19i	0.770387i	−0.922836	+	0.385193i	$0.874135\pi$
$984$	−5.85932e18	−0.205769
$985$	0	0
$986$	1.63858e19	0.567894
$987$	− 4.14447e19i	− 1.42694i
$988$	1.45015e18i	0.0496011i
$989$	−3.30302e19	−1.12237
$990$	0	0
$991$	−1.55987e18	−0.0523132	−0.0261566	−	0.999658i	$-0.508327\pi$
$991$	−1.55987e18	−0.0523132	−0.0261566	+	0.999658i	$0.508327\pi$
$992$	2.27235e19i	0.757092i
$993$	− 1.93531e19i	− 0.640589i
$994$	1.86320e19	0.612700
$995$	0	0
$996$	−2.65740e19	−0.862524
$997$	− 1.80157e19i	− 0.580942i	−0.956884	−	0.290471i	$-0.906188\pi$
$997$	− 1.80157e19i	− 0.580942i	0.956884	−	0.290471i	$-0.0938119\pi$
$998$	7.20908e19i	2.30957i
$999$	−6.20387e18	−0.197464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.14.b.c.49.1		4
5.2	odd	4		75.14.a.e.1.2		2
5.3	odd	4		3.14.a.b.1.1	✓	2
5.4	even	2	inner	75.14.b.c.49.4		4
15.8	even	4		9.14.a.c.1.2		2
20.3	even	4		48.14.a.g.1.1		2
35.13	even	4		147.14.a.b.1.1		2
40.3	even	4		192.14.a.o.1.2		2
40.13	odd	4		192.14.a.k.1.2		2
60.23	odd	4		144.14.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.14.a.b.1.1	✓	2	5.3	odd	4
9.14.a.c.1.2		2	15.8	even	4
48.14.a.g.1.1		2	20.3	even	4
75.14.a.e.1.2		2	5.2	odd	4
75.14.b.c.49.1		4	1.1	even	1	trivial
75.14.b.c.49.4		4	5.4	even	2	inner
144.14.a.m.1.2		2	60.23	odd	4
147.14.a.b.1.1		2	35.13	even	4
192.14.a.k.1.2		2	40.13	odd	4
192.14.a.o.1.2		2	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-160.120i q^{2} -729.000i q^{3} -17446.5 q^{4} -116728. q^{6} +449560. i q^{7} +1.48183e6i q^{8} -531441. q^{9} +O(q^{10})\)	\(q-160.120i q^{2} -729.000i q^{3} -17446.5 q^{4} -116728. q^{6} +449560. i q^{7} +1.48183e6i q^{8} -531441. q^{9} +5.20947e6 q^{11} +1.27185e7i q^{12} +3.19535e6i q^{13} +7.19836e7 q^{14} +9.43496e7 q^{16} +3.22068e7i q^{17} +8.50945e7i q^{18} -2.60127e7 q^{19} +3.27729e8 q^{21} -8.34142e8i q^{22} -9.21991e8i q^{23} +1.08026e9 q^{24} +5.11640e8 q^{26} +3.87420e8i q^{27} -7.84324e9i q^{28} +3.17741e9 q^{29} -7.65586e9 q^{31} -2.96811e9i q^{32} -3.79770e9i q^{33} +5.15697e9 q^{34} +9.27178e9 q^{36} +1.60133e10i q^{37} +4.16515e9i q^{38} +2.32941e9 q^{39} -5.42402e9 q^{41} -5.24760e10i q^{42} -3.58248e10i q^{43} -9.08870e10 q^{44} -1.47629e11 q^{46} -1.26460e11i q^{47} -6.87809e10i q^{48} -1.05215e11 q^{49} +2.34788e10 q^{51} -5.57477e10i q^{52} -6.08596e10i q^{53} +6.20339e10 q^{54} -6.66172e11 q^{56} +1.89632e10i q^{57} -5.08767e11i q^{58} +4.10975e11 q^{59} -1.17141e11 q^{61} +1.22586e12i q^{62} -2.38914e11i q^{63} +2.97657e11 q^{64} -6.08089e11 q^{66} -1.16014e12i q^{67} -5.61896e11i q^{68} -6.72131e11 q^{69} +2.58837e11 q^{71} -7.87506e11i q^{72} -1.87421e12i q^{73} +2.56405e12 q^{74} +4.53830e11 q^{76} +2.34197e12i q^{77} -3.72986e11i q^{78} +2.22847e11 q^{79} +2.82430e11 q^{81} +8.68495e11i q^{82} +2.08940e12i q^{83} -5.71772e12 q^{84} -5.73628e12 q^{86} -2.31633e12i q^{87} +7.71956e12i q^{88} +1.34175e12 q^{89} -1.43650e12 q^{91} +1.60855e13i q^{92} +5.58112e12i q^{93} -2.02488e13 q^{94} -2.16376e12 q^{96} -3.12485e9i q^{97} +1.68470e13i q^{98} -2.76853e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 41032 q^{4} - 78732 q^{6} - 2125764 q^{9}+O(q^{10}) \) 4 * q - 41032 * q^4 - 78732 * q^6 - 2125764 * q^9	\( 4 q - 41032 q^{4} - 78732 q^{6} - 2125764 q^{9} + 1344816 q^{11} + 243840672 q^{14} + 23034400 q^{16} - 512587088 q^{19} - 30629664 q^{21} + 2953079856 q^{24} + 5422592088 q^{26} + 9456950664 q^{29} - 11965103296 q^{31} - 644414184 q^{34} + 21806087112 q^{36} - 25562536632 q^{39} + 30517948584 q^{41} - 153920882016 q^{44} - 308504493216 q^{46} - 459519253860 q^{49} + 122236626312 q^{51} + 41841412812 q^{54} - 820741991040 q^{56} + 1855641648528 q^{59} + 358790922680 q^{61} + 158678840192 q^{64} - 1918167766416 q^{66} - 1253270462688 q^{69} - 1568917099872 q^{71} + 2708999602632 q^{74} + 2321356801952 q^{76} + 1428050940160 q^{79} + 1129718145924 q^{81} - 9329490850752 q^{84} - 21477442268304 q^{86} - 6540357403368 q^{89} - 22380807889856 q^{91} - 52685591533632 q^{94} - 10650886375104 q^{96} - 714690359856 q^{99}+O(q^{100}) \) 4 * q - 41032 * q^4 - 78732 * q^6 - 2125764 * q^9 + 1344816 * q^11 + 243840672 * q^14 + 23034400 * q^16 - 512587088 * q^19 - 30629664 * q^21 + 2953079856 * q^24 + 5422592088 * q^26 + 9456950664 * q^29 - 11965103296 * q^31 - 644414184 * q^34 + 21806087112 * q^36 - 25562536632 * q^39 + 30517948584 * q^41 - 153920882016 * q^44 - 308504493216 * q^46 - 459519253860 * q^49 + 122236626312 * q^51 + 41841412812 * q^54 - 820741991040 * q^56 + 1855641648528 * q^59 + 358790922680 * q^61 + 158678840192 * q^64 - 1918167766416 * q^66 - 1253270462688 * q^69 - 1568917099872 * q^71 + 2708999602632 * q^74 + 2321356801952 * q^76 + 1428050940160 * q^79 + 1129718145924 * q^81 - 9329490850752 * q^84 - 21477442268304 * q^86 - 6540357403368 * q^89 - 22380807889856 * q^91 - 52685591533632 * q^94 - 10650886375104 * q^96 - 714690359856 * q^99

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