LMFDB - Embedded newform 150.14.c.m.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,14,Mod(49,150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("150.49"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	150.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-16384,0,186624,0,0,-2125764,0,11958408] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$160.846393428$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 10129455x^{2} + 25651469713984 $ x^4 - 10129455*x^2 + 25651469713984
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.4
Root			$2250.50 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.14.c.m.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+64.0000i q^{2} -729.000i q^{3} -4096.00 q^{4} +46656.0 q^{6} +277006. i q^{7} -262144. i q^{8} -531441. q^{9} +18948.6 q^{11} +2.98598e6i q^{12} +6.01018e6i q^{13} -1.77284e7 q^{14} +1.67772e7 q^{16} +9.37569e7i q^{17} -3.40122e7i q^{18} +5.41067e7 q^{19} +2.01938e8 q^{21} +1.21271e6i q^{22} +2.03954e8i q^{23} -1.91103e8 q^{24} -3.84651e8 q^{26} +3.87420e8i q^{27} -1.13462e9i q^{28} -3.05609e9 q^{29} +4.34655e9 q^{31} +1.07374e9i q^{32} -1.38135e7i q^{33} -6.00044e9 q^{34} +2.17678e9 q^{36} +9.81444e9i q^{37} +3.46283e9i q^{38} +4.38142e9 q^{39} -7.81935e9 q^{41} +1.29240e10i q^{42} -2.58184e10i q^{43} -7.76135e7 q^{44} -1.30531e10 q^{46} -4.89513e9i q^{47} -1.22306e10i q^{48} +2.01565e10 q^{49} +6.83488e10 q^{51} -2.46177e10i q^{52} +4.29788e10i q^{53} -2.47949e10 q^{54} +7.26156e10 q^{56} -3.94437e10i q^{57} -1.95590e11i q^{58} +2.79921e11 q^{59} +2.71521e11 q^{61} +2.78179e11i q^{62} -1.47213e11i q^{63} -6.87195e10 q^{64} +8.84066e8 q^{66} -2.60849e11i q^{67} -3.84028e11i q^{68} +1.48683e11 q^{69} +1.75686e12 q^{71} +1.39314e11i q^{72} +1.00814e12i q^{73} -6.28124e11 q^{74} -2.21621e11 q^{76} +5.24888e9i q^{77} +2.80411e11i q^{78} -3.96314e12 q^{79} +2.82430e11 q^{81} -5.00438e11i q^{82} +6.14648e11i q^{83} -8.27137e11 q^{84} +1.65238e12 q^{86} +2.22789e12i q^{87} -4.96726e9i q^{88} -4.36298e12 q^{89} -1.66486e12 q^{91} -8.35396e11i q^{92} -3.16863e12i q^{93} +3.13288e11 q^{94} +7.82758e11 q^{96} -4.72628e12i q^{97} +1.29001e12i q^{98} -1.00701e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16384 q^{4} + 186624 q^{6} - 2125764 q^{9} + 11958408 q^{11} - 1778432 q^{14} + 67108864 q^{16} - 471684740 q^{19} + 20257452 q^{21} - 764411904 q^{24} + 3162588416 q^{26} + 3965146440 q^{29} - 7190293012 q^{31}+ \cdots - 6355188305928 q^{99}+O(q^{100}) $ 4 * q - 16384 * q^4 + 186624 * q^6 - 2125764 * q^9 + 11958408 * q^11 - 1778432 * q^14 + 67108864 * q^16 - 471684740 * q^19 + 20257452 * q^21 - 764411904 * q^24 + 3162588416 * q^26 + 3965146440 * q^29 - 7190293012 * q^31 + 6210329088 * q^34 + 8707129344 * q^36 - 36023858676 * q^39 + 21588341808 * q^41 - 48981639168 * q^44 + 100092581376 * q^46 + 95634679992 * q^49 - 70739529768 * q^51 - 99179645184 * q^54 + 7284457472 * q^56 + 657254281560 * q^59 + 1978324726508 * q^61 - 274877906944 * q^64 + 557931483648 * q^66 - 1140117059736 * q^69 + 5259349361328 * q^71 + 482026198528 * q^74 + 1932020695040 * q^76 - 10219104462560 * q^79 + 1129718145924 * q^81 - 82974523392 * q^84 - 966250226944 * q^86 - 21799732071360 * q^89 - 19494236561732 * q^91 - 7777010652672 * q^94 + 3131031158784 * q^96 - 6355188305928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	64.0000i	0.707107i
$2$	64.0000i	0.707107i
$3$	− 729.000i	− 0.577350i
$3$	− 729.000i	− 0.577350i
$4$	−4096.00	−0.500000
$5$	0	0
$5$	0	0
$6$	46656.0	0.408248
$7$	277006.i	0.889923i	0.895550	+	0.444962i	$0.146783\pi$
$7$	277006.i	0.889923i	−0.895550	+	0.444962i	$0.853217\pi$
$8$	− 262144.i	− 0.353553i
$9$	−531441.	−0.333333
$10$	0	0
$11$	18948.6	0.00322496	0.00161248	−	0.999999i	$-0.499487\pi$
$11$	18948.6	0.00322496	0.00161248	+	0.999999i	$0.499487\pi$
$12$	2.98598e6i	0.288675i
$13$	6.01018e6i	0.345347i	0.984979	+	0.172673i	$0.0552405\pi$
$13$	6.01018e6i	0.345347i	−0.984979	+	0.172673i	$0.944759\pi$
$14$	−1.77284e7	−0.629271
$15$	0	0
$16$	1.67772e7	0.250000
$17$	9.37569e7i	0.942074i	0.882113	+	0.471037i	$0.156120\pi$
$17$	9.37569e7i	0.942074i	−0.882113	+	0.471037i	$0.843880\pi$
$18$	− 3.40122e7i	− 0.235702i
$19$	5.41067e7	0.263847	0.131924	−	0.991260i	$-0.457885\pi$
$19$	5.41067e7	0.263847	0.131924	+	0.991260i	$0.457885\pi$
$20$	0	0
$21$	2.01938e8	0.513797
$22$	1.21271e6i	0.00228039i
$23$	2.03954e8i	0.287278i	0.989630	+	0.143639i	$0.0458803\pi$
$23$	2.03954e8i	0.287278i	−0.989630	+	0.143639i	$0.954120\pi$
$24$	−1.91103e8	−0.204124
$25$	0	0
$26$	−3.84651e8	−0.244197
$27$	3.87420e8i	0.192450i
$28$	− 1.13462e9i	− 0.444962i
$29$	−3.05609e9	−0.954069	−0.477034	−	0.878885i	$-0.658288\pi$
$29$	−3.05609e9	−0.954069	−0.477034	+	0.878885i	$0.658288\pi$
$30$	0	0
$31$	4.34655e9	0.879617	0.439808	−	0.898092i	$-0.355046\pi$
$31$	4.34655e9	0.879617	0.439808	+	0.898092i	$0.355046\pi$
$32$	1.07374e9i	0.176777i
$33$	− 1.38135e7i	− 0.00186193i
$34$	−6.00044e9	−0.666147
$35$	0	0
$36$	2.17678e9	0.166667
$37$	9.81444e9i	0.628860i	0.949281	+	0.314430i	$0.101813\pi$
$37$	9.81444e9i	0.628860i	−0.949281	+	0.314430i	$0.898187\pi$
$38$	3.46283e9i	0.186568i
$39$	4.38142e9	0.199386
$40$	0	0
$41$	−7.81935e9	−0.257084	−0.128542	−	0.991704i	$-0.541030\pi$
$41$	−7.81935e9	−0.257084	−0.128542	+	0.991704i	$0.541030\pi$
$42$	1.29240e10i	0.363310i
$43$	− 2.58184e10i	− 0.622852i	−0.950270	−	0.311426i	$-0.899193\pi$
$43$	− 2.58184e10i	− 0.622852i	0.950270	−	0.311426i	$-0.100807\pi$
$44$	−7.76135e7	−0.00161248
$45$	0	0
$46$	−1.30531e10	−0.203136
$47$	− 4.89513e9i	− 0.0662412i	−0.999451	−	0.0331206i	$-0.989455\pi$
$47$	− 4.89513e9i	− 0.0662412i	0.999451	−	0.0331206i	$-0.0105445\pi$
$48$	− 1.22306e10i	− 0.144338i
$49$	2.01565e10	0.208037
$50$	0	0
$51$	6.83488e10	0.543907
$52$	− 2.46177e10i	− 0.172673i
$53$	4.29788e10i	0.266355i	0.991092	+	0.133178i	$0.0425181\pi$
$53$	4.29788e10i	0.266355i	−0.991092	+	0.133178i	$0.957482\pi$
$54$	−2.47949e10	−0.136083
$55$	0	0
$56$	7.26156e10	0.314635
$57$	− 3.94437e10i	− 0.152332i
$58$	− 1.95590e11i	− 0.674628i
$59$	2.79921e11	0.863966	0.431983	−	0.901882i	$-0.357814\pi$
$59$	2.79921e11	0.863966	0.431983	+	0.901882i	$0.357814\pi$
$60$	0	0
$61$	2.71521e11	0.674777	0.337388	−	0.941366i	$-0.390456\pi$
$61$	2.71521e11	0.674777	0.337388	+	0.941366i	$0.390456\pi$
$62$	2.78179e11i	0.621983i
$63$	− 1.47213e11i	− 0.296641i
$64$	−6.87195e10	−0.125000
$65$	0	0
$66$	8.84066e8	0.00131659
$67$	− 2.60849e11i	− 0.352292i	−0.984364	−	0.176146i	$-0.943637\pi$
$67$	− 2.60849e11i	− 0.352292i	0.984364	−	0.176146i	$-0.0563631\pi$
$68$	− 3.84028e11i	− 0.471037i
$69$	1.48683e11	0.165860
$70$	0	0
$71$	1.75686e12	1.62764	0.813818	−	0.581120i	$-0.197385\pi$
$71$	1.75686e12	1.62764	0.813818	+	0.581120i	$0.197385\pi$
$72$	1.39314e11i	0.117851i
$73$	1.00814e12i	0.779687i	0.920881	+	0.389844i	$0.127471\pi$
$73$	1.00814e12i	0.779687i	−0.920881	+	0.389844i	$0.872529\pi$
$74$	−6.28124e11	−0.444671
$75$	0	0
$76$	−2.21621e11	−0.131924
$77$	5.24888e9i	0.00286997i
$78$	2.80411e11i	0.140987i
$79$	−3.96314e12	−1.83427	−0.917136	−	0.398574i	$-0.869505\pi$
$79$	−3.96314e12	−1.83427	−0.917136	+	0.398574i	$0.869505\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	− 5.00438e11i	− 0.181786i
$83$	6.14648e11i	0.206357i	0.994663	+	0.103178i	$0.0329013\pi$
$83$	6.14648e11i	0.206357i	−0.994663	+	0.103178i	$0.967099\pi$
$84$	−8.27137e11	−0.256899
$85$	0	0
$86$	1.65238e12	0.440423
$87$	2.22789e12i	0.550832i
$88$	− 4.96726e9i	− 0.00114020i
$89$	−4.36298e12	−0.930569	−0.465284	−	0.885161i	$-0.654048\pi$
$89$	−4.36298e12	−0.930569	−0.465284	+	0.885161i	$0.654048\pi$
$90$	0	0
$91$	−1.66486e12	−0.307332
$92$	− 8.35396e11i	− 0.143639i
$93$	− 3.16863e12i	− 0.507847i
$94$	3.13288e11	0.0468396
$95$	0	0
$96$	7.82758e11	0.102062
$97$	− 4.72628e12i	− 0.576107i	−0.957614	−	0.288054i	$-0.906992\pi$
$97$	− 4.72628e12i	− 0.576107i	0.957614	−	0.288054i	$-0.0930082\pi$
$98$	1.29001e12i	0.147104i
$99$	−1.00701e10	−0.00107499
$100$	0	0
$101$	−3.99477e12	−0.374457	−0.187229	−	0.982316i	$-0.559951\pi$
$101$	−3.99477e12	−0.374457	−0.187229	+	0.982316i	$0.559951\pi$
$102$	4.37432e12i	0.384600i
$103$	3.72247e12i	0.307177i	0.988135	+	0.153589i	$0.0490831\pi$
$103$	3.72247e12i	0.307177i	−0.988135	+	0.153589i	$0.950917\pi$
$104$	1.57553e12	0.122099
$105$	0	0
$106$	−2.75065e12	−0.188342
$107$	7.95158e12i	0.512223i	0.966647	+	0.256111i	$0.0824414\pi$
$107$	7.95158e12i	0.512223i	−0.966647	+	0.256111i	$0.917559\pi$
$108$	− 1.58687e12i	− 0.0962250i
$109$	−1.82409e13	−1.04177	−0.520887	−	0.853625i	$-0.674399\pi$
$109$	−1.82409e13	−1.04177	−0.520887	+	0.853625i	$0.674399\pi$
$110$	0	0
$111$	7.15473e12	0.363073
$112$	4.64740e12i	0.222481i
$113$	6.77016e12i	0.305907i	0.988233	+	0.152953i	$0.0488784\pi$
$113$	6.77016e12i	0.305907i	−0.988233	+	0.152953i	$0.951122\pi$
$114$	2.52440e12	0.107715
$115$	0	0
$116$	1.25178e13	0.477034
$117$	− 3.19406e12i	− 0.115116i
$118$	1.79149e13i	0.610916i
$119$	−2.59713e13	−0.838374
$120$	0	0
$121$	−3.45224e13	−0.999990
$122$	1.73774e13i	0.477139i
$123$	5.70031e12i	0.148428i
$124$	−1.78035e13	−0.439808
$125$	0	0
$126$	9.42160e12	0.209757
$127$	2.77305e13i	0.586454i	0.956043	+	0.293227i	$0.0947292\pi$
$127$	2.77305e13i	0.586454i	−0.956043	+	0.293227i	$0.905271\pi$
$128$	− 4.39805e12i	− 0.0883883i
$129$	−1.88216e13	−0.359604
$130$	0	0
$131$	−6.44782e12	−0.111468	−0.0557339	−	0.998446i	$-0.517750\pi$
$131$	−6.44782e12	−0.111468	−0.0557339	+	0.998446i	$0.517750\pi$
$132$	5.65802e10i	0 0.000930966i
$133$	1.49879e13i	0.234804i
$134$	1.66943e13	0.249108
$135$	0	0
$136$	2.45778e13	0.333073
$137$	8.56757e13i	1.10707i	0.832827	+	0.553534i	$0.186721\pi$
$137$	8.56757e13i	1.10707i	−0.832827	+	0.553534i	$0.813279\pi$
$138$	9.51569e12i	0.117281i
$139$	3.77579e10	0.000444029 0	0.000222014	−	1.00000i	$-0.499929\pi$
$139$	3.77579e10	0.000444029 0	0.000222014		1.00000i	$0.499929\pi$
$140$	0	0
$141$	−3.56855e12	−0.0382444
$142$	1.12439e14i	1.15091i
$143$	1.13884e11i	0.00111373i
$144$	−8.91610e12	−0.0833333
$145$	0	0
$146$	−6.45207e13	−0.551322
$147$	− 1.46941e13i	− 0.120110i
$148$	− 4.01999e13i	− 0.314430i
$149$	−1.52859e14	−1.14441	−0.572204	−	0.820111i	$-0.693912\pi$
$149$	−1.52859e14	−1.14441	−0.572204	+	0.820111i	$0.693912\pi$
$150$	0	0
$151$	−1.12168e14	−0.770052	−0.385026	−	0.922906i	$-0.625808\pi$
$151$	−1.12168e14	−0.770052	−0.385026	+	0.922906i	$0.625808\pi$
$152$	− 1.41837e13i	− 0.0932840i
$153$	− 4.98262e13i	− 0.314025i
$154$	−3.35929e11	−0.00202937
$155$	0	0
$156$	−1.79463e13	−0.0996931
$157$	1.16442e14i	0.620528i	0.950650	+	0.310264i	$0.100417\pi$
$157$	1.16442e14i	0.620528i	−0.950650	+	0.310264i	$0.899583\pi$
$158$	− 2.53641e14i	− 1.29703i
$159$	3.13316e13	0.153780
$160$	0	0
$161$	−5.64966e13	−0.255655
$162$	1.80755e13i	0.0785674i
$163$	− 1.74797e14i	− 0.729988i	−0.931010	−	0.364994i	$-0.881071\pi$
$163$	− 1.74797e14i	− 0.729988i	0.931010	−	0.364994i	$-0.118929\pi$
$164$	3.20281e13	0.128542
$165$	0	0
$166$	−3.93375e13	−0.145916
$167$	− 4.74353e14i	− 1.69217i	−0.533046	−	0.846086i	$-0.678953\pi$
$167$	− 4.74353e14i	− 1.69217i	0.533046	−	0.846086i	$-0.321047\pi$
$168$	− 5.29367e13i	− 0.181655i
$169$	2.66753e14	0.880736
$170$	0	0
$171$	−2.87545e13	−0.0879490
$172$	1.05752e14i	0.311426i
$173$	− 3.98898e14i	− 1.13126i	−0.824659	−	0.565630i	$-0.808633\pi$
$173$	− 3.98898e14i	− 1.13126i	0.824659	−	0.565630i	$-0.191367\pi$
$174$	−1.42585e14	−0.389497
$175$	0	0
$176$	3.17905e11	0.000806241 0
$177$	− 2.04062e14i	− 0.498811i
$178$	− 2.79231e14i	− 0.658011i
$179$	−5.98063e14	−1.35895	−0.679473	−	0.733700i	$-0.737792\pi$
$179$	−5.98063e14	−1.35895	−0.679473	+	0.733700i	$0.737792\pi$
$180$	0	0
$181$	−2.92373e14	−0.618054	−0.309027	−	0.951053i	$-0.600003\pi$
$181$	−2.92373e14	−0.618054	−0.309027	+	0.951053i	$0.600003\pi$
$182$	− 1.06551e14i	− 0.217317i
$183$	− 1.97939e14i	− 0.389582i
$184$	5.34654e13	0.101568
$185$	0	0
$186$	2.02793e14	0.359102
$187$	1.77656e12i	0.00303815i
$188$	2.00505e13i	0.0331206i
$189$	−1.07318e14	−0.171266
$190$	0	0
$191$	−5.95959e14	−0.888178	−0.444089	−	0.895983i	$-0.646473\pi$
$191$	−5.95959e14	−0.888178	−0.444089	+	0.895983i	$0.646473\pi$
$192$	5.00965e13i	0.0721688i
$193$	− 8.68685e14i	− 1.20987i	−0.796274	−	0.604937i	$-0.793198\pi$
$193$	− 8.68685e14i	− 1.20987i	0.796274	−	0.604937i	$-0.206802\pi$
$194$	3.02482e14	0.407370
$195$	0	0
$196$	−8.25609e13	−0.104018
$197$	3.44315e14i	0.419687i	0.977735	+	0.209843i	$0.0672954\pi$
$197$	3.44315e14i	0.419687i	−0.977735	+	0.209843i	$0.932705\pi$
$198$	− 6.44484e11i	0 0.000760131i
$199$	−7.86343e14	−0.897567	−0.448784	−	0.893640i	$-0.648143\pi$
$199$	−7.86343e14	−0.897567	−0.448784	+	0.893640i	$0.648143\pi$
$200$	0	0
$201$	−1.90159e14	−0.203396
$202$	− 2.55665e14i	− 0.264781i
$203$	− 8.46557e14i	− 0.849048i
$204$	−2.79956e14	−0.271953
$205$	0	0
$206$	−2.38238e14	−0.217207
$207$	− 1.08390e14i	− 0.0957592i
$208$	1.00834e14i	0.0863367i
$209$	1.02525e12	0.000850897 0
$210$	0	0
$211$	−1.52192e15	−1.18729	−0.593645	−	0.804727i	$-0.702312\pi$
$211$	−1.52192e15	−1.18729	−0.593645	+	0.804727i	$0.702312\pi$
$212$	− 1.76041e14i	− 0.133178i
$213$	− 1.28075e15i	− 0.939716i
$214$	−5.08901e14	−0.362196
$215$	0	0
$216$	1.01560e14	0.0680414
$217$	1.20402e15i	0.782791i
$218$	− 1.16742e15i	− 0.736646i
$219$	7.34931e14	0.450153
$220$	0	0
$221$	−5.63495e14	−0.325342
$222$	4.57902e14i	0.256731i
$223$	− 3.14165e15i	− 1.71071i	−0.518044	−	0.855354i	$-0.673340\pi$
$223$	− 3.14165e15i	− 1.71071i	0.518044	−	0.855354i	$-0.326660\pi$
$224$	−2.97433e14	−0.157318
$225$	0	0
$226$	−4.33290e14	−0.216309
$227$	1.18781e15i	0.576206i	0.957599	+	0.288103i	$0.0930245\pi$
$227$	1.18781e15i	0.576206i	−0.957599	+	0.288103i	$0.906975\pi$
$228$	1.61562e14i	0.0761661i
$229$	3.53988e14	0.162203	0.0811014	−	0.996706i	$-0.474156\pi$
$229$	3.53988e14	0.162203	0.0811014	+	0.996706i	$0.474156\pi$
$230$	0	0
$231$	3.82644e12	0.00165698
$232$	8.01137e14i	0.337314i
$233$	− 1.94804e15i	− 0.797600i	−0.917038	−	0.398800i	$-0.869427\pi$
$233$	− 1.94804e15i	− 0.797600i	0.917038	−	0.398800i	$-0.130573\pi$
$234$	2.04420e14	0.0813990
$235$	0	0
$236$	−1.14655e15	−0.431983
$237$	2.88913e15i	1.05902i
$238$	− 1.66216e15i	− 0.592820i
$239$	−2.68201e15	−0.930839	−0.465419	−	0.885090i	$-0.654097\pi$
$239$	−2.68201e15	−0.930839	−0.465419	+	0.885090i	$0.654097\pi$
$240$	0	0
$241$	−3.64825e15	−1.19943	−0.599713	−	0.800215i	$-0.704719\pi$
$241$	−3.64825e15	−1.19943	−0.599713	+	0.800215i	$0.704719\pi$
$242$	− 2.20943e15i	− 0.707099i
$243$	− 2.05891e14i	− 0.0641500i
$244$	−1.11215e15	−0.337388
$245$	0	0
$246$	−3.64820e14	−0.104954
$247$	3.25191e14i	0.0911188i
$248$	− 1.13942e15i	− 0.310991i
$249$	4.48078e14	0.119140
$250$	0	0
$251$	−5.03958e15	−1.27208	−0.636041	−	0.771655i	$-0.719429\pi$
$251$	−5.03958e15	−1.27208	−0.636041	+	0.771655i	$0.719429\pi$
$252$	6.02983e14i	0.148321i
$253$	3.86465e12i	0 0.000926459i
$254$	−1.77475e15	−0.414686
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	3.98091e15i	0.861821i	0.902395	+	0.430911i	$0.141808\pi$
$257$	3.98091e15i	0.861821i	−0.902395	+	0.430911i	$0.858192\pi$
$258$	− 1.20458e15i	− 0.254278i
$259$	−2.71866e15	−0.559637
$260$	0	0
$261$	1.62413e15	0.318023
$262$	− 4.12661e14i	− 0.0788197i
$263$	1.19256e15i	0.222213i	0.993809	+	0.111106i	$0.0354394\pi$
$263$	1.19256e15i	0.222213i	−0.993809	+	0.111106i	$0.964561\pi$
$264$	−3.62113e12	−0.000658293 0
$265$	0	0
$266$	−9.59225e14	−0.166031
$267$	3.18061e15i	0.537264i
$268$	1.06844e15i	0.176146i
$269$	−7.56846e15	−1.21792	−0.608958	−	0.793202i	$-0.708412\pi$
$269$	−7.56846e15	−1.21792	−0.608958	+	0.793202i	$0.708412\pi$
$270$	0	0
$271$	5.62339e15	0.862378	0.431189	−	0.902262i	$-0.358094\pi$
$271$	5.62339e15	0.862378	0.431189	+	0.902262i	$0.358094\pi$
$272$	1.57298e15i	0.235519i
$273$	1.21368e15i	0.177438i
$274$	−5.48325e15	−0.782815
$275$	0	0
$276$	−6.09004e14	−0.0829299
$277$	8.86600e15i	1.17926i	0.807674	+	0.589629i	$0.200726\pi$
$277$	8.86600e15i	1.17926i	−0.807674	+	0.589629i	$0.799274\pi$
$278$	2.41650e12i	0 0.000313976i
$279$	−2.30993e15	−0.293206
$280$	0	0
$281$	−3.47521e15	−0.421104	−0.210552	−	0.977583i	$-0.567526\pi$
$281$	−3.47521e15	−0.421104	−0.210552	+	0.977583i	$0.567526\pi$
$282$	− 2.28387e14i	− 0.0270429i
$283$	4.91812e14i	0.0569098i	0.999595	+	0.0284549i	$0.00905869\pi$
$283$	4.91812e14i	0.0569098i	−0.999595	+	0.0284549i	$0.990941\pi$
$284$	−7.19609e15	−0.813818
$285$	0	0
$286$	−7.28861e12	−0.000787527 0
$287$	− 2.16601e15i	− 0.228785i
$288$	− 5.70630e14i	− 0.0589256i
$289$	1.11423e15	0.112496
$290$	0	0
$291$	−3.44546e15	−0.332616
$292$	− 4.12932e15i	− 0.389844i
$293$	5.30726e15i	0.490039i	0.969518	+	0.245019i	$0.0787943\pi$
$293$	5.30726e15i	0.490039i	−0.969518	+	0.245019i	$0.921206\pi$
$294$	9.40420e14	0.0849306
$295$	0	0
$296$	2.57280e15	0.222336
$297$	7.34108e12i	0 0.000620644i
$298$	− 9.78299e15i	− 0.809219i
$299$	−1.22580e15	−0.0992104
$300$	0	0
$301$	7.15187e15	0.554290
$302$	− 7.17877e15i	− 0.544509i
$303$	2.91218e15i	0.216193i
$304$	9.07759e14	0.0659618
$305$	0	0
$306$	3.18888e15	0.222049
$307$	− 1.38973e15i	− 0.0947397i	−0.998877	−	0.0473698i	$-0.984916\pi$
$307$	− 1.38973e15i	− 0.0947397i	0.998877	−	0.0473698i	$-0.0150839\pi$
$308$	− 2.14994e13i	− 0.00143498i
$309$	2.71368e15	0.177349
$310$	0	0
$311$	−2.27450e16	−1.42542	−0.712710	−	0.701459i	$-0.752532\pi$
$311$	−2.27450e16	−1.42542	−0.712710	+	0.701459i	$0.752532\pi$
$312$	− 1.14856e15i	− 0.0704936i
$313$	− 2.24753e16i	− 1.35104i	−0.737342	−	0.675520i	$-0.763919\pi$
$313$	− 2.24753e16i	− 1.35104i	0.737342	−	0.675520i	$-0.236081\pi$
$314$	−7.45228e15	−0.438780
$315$	0	0
$316$	1.62330e16	0.917136
$317$	− 2.41947e16i	− 1.33917i	−0.742737	−	0.669583i	$-0.766473\pi$
$317$	− 2.41947e16i	− 1.33917i	0.742737	−	0.669583i	$-0.233527\pi$
$318$	2.00522e15i	0.108739i
$319$	−5.79087e13	−0.00307684
$320$	0	0
$321$	5.79670e15	0.295732
$322$	− 3.61578e15i	− 0.180775i
$323$	5.07287e15i	0.248563i
$324$	−1.15683e15	−0.0555556
$325$	0	0
$326$	1.11870e16	0.516179
$327$	1.32976e16i	0.601469i
$328$	2.04980e15i	0.0908930i
$329$	1.35598e15	0.0589496
$330$	0	0
$331$	8.02999e15	0.335609	0.167804	−	0.985820i	$-0.446332\pi$
$331$	8.02999e15	0.335609	0.167804	+	0.985820i	$0.446332\pi$
$332$	− 2.51760e15i	− 0.103178i
$333$	− 5.21579e15i	− 0.209620i
$334$	3.03586e16	1.19655
$335$	0	0
$336$	3.38795e15	0.128449
$337$	3.38160e16i	1.25756i	0.777585	+	0.628778i	$0.216445\pi$
$337$	3.38160e16i	1.25756i	−0.777585	+	0.628778i	$0.783555\pi$
$338$	1.70722e16i	0.622774i
$339$	4.93544e15	0.176615
$340$	0	0
$341$	8.23610e13	0.00283673
$342$	− 1.84029e15i	− 0.0621893i
$343$	3.24223e16i	1.07506i
$344$	−6.76814e15	−0.220211
$345$	0	0
$346$	2.55295e16	0.799921
$347$	− 3.33636e16i	− 1.02596i	−0.858400	−	0.512981i	$-0.828541\pi$
$347$	− 3.33636e16i	− 1.02596i	0.858400	−	0.512981i	$-0.171459\pi$
$348$	− 9.12545e15i	− 0.275416i
$349$	4.09490e16	1.21305	0.606524	−	0.795065i	$-0.292564\pi$
$349$	4.09490e16	1.21305	0.606524	+	0.795065i	$0.292564\pi$
$350$	0	0
$351$	−2.32847e15	−0.0664620
$352$	2.03459e13i	0 0.000570098i
$353$	3.12548e16i	0.859766i	0.902884	+	0.429883i	$0.141445\pi$
$353$	3.12548e16i	0.859766i	−0.902884	+	0.429883i	$0.858555\pi$
$354$	1.30600e16	0.352713
$355$	0	0
$356$	1.78708e16	0.465284
$357$	1.89330e16i	0.484035i
$358$	− 3.82760e16i	− 0.960920i
$359$	3.19306e16	0.787216	0.393608	−	0.919278i	$-0.371227\pi$
$359$	3.19306e16	0.787216	0.393608	+	0.919278i	$0.371227\pi$
$360$	0	0
$361$	−3.91255e16	−0.930385
$362$	− 1.87119e16i	− 0.437030i
$363$	2.51668e16i	0.577344i
$364$	6.81926e15	0.153666
$365$	0	0
$366$	1.26681e16	0.275476
$367$	− 1.99266e16i	− 0.425701i	−0.977085	−	0.212850i	$-0.931725\pi$
$367$	− 1.99266e16i	− 0.425701i	0.977085	−	0.212850i	$-0.0682747\pi$
$368$	3.42178e15i	0.0718194i
$369$	4.15552e15	0.0856948
$370$	0	0
$371$	−1.19054e16	−0.237036
$372$	1.29787e16i	0.253923i
$373$	8.04217e16i	1.54620i	0.634283	+	0.773101i	$0.281295\pi$
$373$	8.04217e16i	1.54620i	−0.634283	+	0.773101i	$0.718705\pi$
$374$	−1.13700e14	−0.00214830
$375$	0	0
$376$	−1.28323e15	−0.0234198
$377$	− 1.83677e16i	− 0.329485i
$378$	− 6.86835e15i	− 0.121103i
$379$	1.03786e17	1.79880	0.899401	−	0.437124i	$-0.144003\pi$
$379$	1.03786e17	1.79880	0.899401	+	0.437124i	$0.144003\pi$
$380$	0	0
$381$	2.02156e16	0.338589
$382$	− 3.81414e16i	− 0.628036i
$383$	1.04417e17i	1.69036i	0.534479	+	0.845182i	$0.320508\pi$
$383$	1.04417e17i	1.69036i	−0.534479	+	0.845182i	$0.679492\pi$
$384$	−3.20618e15	−0.0510310
$385$	0	0
$386$	5.55959e16	0.855510
$387$	1.37210e16i	0.207617i
$388$	1.93589e16i	0.288054i
$389$	3.90559e16	0.571497	0.285749	−	0.958305i	$-0.407758\pi$
$389$	3.90559e16	0.571497	0.285749	+	0.958305i	$0.407758\pi$
$390$	0	0
$391$	−1.91221e16	−0.270637
$392$	− 5.28390e15i	− 0.0735521i
$393$	4.70046e15i	0.0643560i
$394$	−2.20362e16	−0.296763
$395$	0	0
$396$	4.12470e13	0.000537494 0
$397$	− 1.04950e17i	− 1.34537i	−0.739928	−	0.672686i	$-0.765141\pi$
$397$	− 1.04950e17i	− 1.34537i	0.739928	−	0.672686i	$-0.234859\pi$
$398$	− 5.03259e16i	− 0.634676i
$399$	1.09262e16	0.135564
$400$	0	0
$401$	−7.38952e16	−0.887519	−0.443760	−	0.896146i	$-0.646356\pi$
$401$	−7.38952e16	−0.887519	−0.443760	+	0.896146i	$0.646356\pi$
$402$	− 1.21702e16i	− 0.143823i
$403$	2.61235e16i	0.303773i
$404$	1.63626e16	0.187229
$405$	0	0
$406$	5.41797e16	0.600368
$407$	1.85970e14i	0.00202805i
$408$	− 1.79172e16i	− 0.192300i
$409$	6.25131e16	0.660343	0.330171	−	0.943921i	$-0.392893\pi$
$409$	6.25131e16	0.660343	0.330171	+	0.943921i	$0.392893\pi$
$410$	0	0
$411$	6.24576e16	0.639166
$412$	− 1.52472e16i	− 0.153589i
$413$	7.75398e16i	0.768864i
$414$	6.93694e15	0.0677120
$415$	0	0
$416$	−6.45338e15	−0.0610493
$417$	− 2.75255e13i	0 0.000256360i
$418$	6.56157e13i	0 0.000601675i
$419$	1.52359e16	0.137556	0.0687778	−	0.997632i	$-0.478090\pi$
$419$	1.52359e16	0.137556	0.0687778	+	0.997632i	$0.478090\pi$
$420$	0	0
$421$	−1.23261e17	−1.07892	−0.539461	−	0.842010i	$-0.681372\pi$
$421$	−1.23261e17	−1.07892	−0.539461	+	0.842010i	$0.681372\pi$
$422$	− 9.74032e16i	− 0.839541i
$423$	2.60147e15i	0.0220804i
$424$	1.12666e16	0.0941708
$425$	0	0
$426$	8.19679e16	0.664479
$427$	7.52131e16i	0.600499i
$428$	− 3.25697e16i	− 0.256111i
$429$	8.30218e13	0.000643013 0
$430$	0	0
$431$	5.11634e15	0.0384465	0.0192233	−	0.999815i	$-0.493881\pi$
$431$	5.11634e15	0.0384465	0.0192233	+	0.999815i	$0.493881\pi$
$432$	6.49984e15i	0.0481125i
$433$	9.71820e16i	0.708622i	0.935128	+	0.354311i	$0.115285\pi$
$433$	9.71820e16i	0.708622i	−0.935128	+	0.354311i	$0.884715\pi$
$434$	−7.70574e16	−0.553517
$435$	0	0
$436$	7.47147e16	0.520887
$437$	1.10353e16i	0.0757973i
$438$	4.70356e16i	0.318306i
$439$	1.31064e17	0.873903	0.436951	−	0.899485i	$-0.356058\pi$
$439$	1.31064e17	0.873903	0.436951	+	0.899485i	$0.356058\pi$
$440$	0	0
$441$	−1.07120e16	−0.0693455
$442$	− 3.60637e16i	− 0.230052i
$443$	1.74771e17i	1.09861i	0.835621	+	0.549306i	$0.185108\pi$
$443$	1.74771e17i	1.09861i	−0.835621	+	0.549306i	$0.814892\pi$
$444$	−2.93058e16	−0.181536
$445$	0	0
$446$	2.01065e17	1.20965
$447$	1.11434e17i	0.660724i
$448$	− 1.90357e16i	− 0.111240i
$449$	−2.94238e17	−1.69472	−0.847358	−	0.531021i	$-0.821808\pi$
$449$	−2.94238e17	−1.69472	−0.847358	+	0.531021i	$0.821808\pi$
$450$	0	0
$451$	−1.48166e14	−0.000829087 0
$452$	− 2.77306e16i	− 0.152953i
$453$	8.17707e16i	0.444590i
$454$	−7.60196e16	−0.407439
$455$	0	0
$456$	−1.03399e16	−0.0538576
$457$	8.34052e16i	0.428290i	0.976802	+	0.214145i	$0.0686964\pi$
$457$	8.34052e16i	0.428290i	−0.976802	+	0.214145i	$0.931304\pi$
$458$	2.26552e16i	0.114695i
$459$	−3.63233e16	−0.181302
$460$	0	0
$461$	1.16806e17	0.566773	0.283387	−	0.959006i	$-0.408542\pi$
$461$	1.16806e17	0.566773	0.283387	+	0.959006i	$0.408542\pi$
$462$	2.44892e14i	0.00117166i
$463$	− 4.15144e16i	− 0.195849i	−0.995194	−	0.0979247i	$-0.968780\pi$
$463$	− 4.15144e16i	− 0.195849i	0.995194	−	0.0979247i	$-0.0312204\pi$
$464$	−5.12727e16	−0.238517
$465$	0	0
$466$	1.24675e17	0.563988
$467$	2.61415e17i	1.16619i	0.812403	+	0.583096i	$0.198159\pi$
$467$	2.61415e17i	1.16619i	−0.812403	+	0.583096i	$0.801841\pi$
$468$	1.30828e16i	0.0575578i
$469$	7.22568e16	0.313513
$470$	0	0
$471$	8.48861e16	0.358262
$472$	− 7.33795e16i	− 0.305458i
$473$	− 4.89223e14i	− 0.00200867i
$474$	−1.84904e17	−0.748839
$475$	0	0
$476$	1.06378e17	0.419187
$477$	− 2.28407e16i	− 0.0887851i
$478$	− 1.71649e17i	− 0.658203i
$479$	1.56831e15	0.00593270	0.00296635	−	0.999996i	$-0.499056\pi$
$479$	1.56831e15	0.00593270	0.00296635	+	0.999996i	$0.499056\pi$
$480$	0	0
$481$	−5.89865e16	−0.217175
$482$	− 2.33488e17i	− 0.848122i
$483$	4.11860e16i	0.147602i
$484$	1.41404e17	0.499995
$485$	0	0
$486$	1.31770e16	0.0453609
$487$	1.68831e17i	0.573474i	0.958009	+	0.286737i	$0.0925706\pi$
$487$	1.68831e17i	0.573474i	−0.958009	+	0.286737i	$0.907429\pi$
$488$	− 7.11777e16i	− 0.238570i
$489$	−1.27427e17	−0.421459
$490$	0	0
$491$	−2.10028e16	−0.0676469	−0.0338234	−	0.999428i	$-0.510768\pi$
$491$	−2.10028e16	−0.0676469	−0.0338234	+	0.999428i	$0.510768\pi$
$492$	− 2.33485e16i	− 0.0742139i
$493$	− 2.86530e17i	− 0.898803i
$494$	−2.08122e16	−0.0644307
$495$	0	0
$496$	7.29230e16	0.219904
$497$	4.86661e17i	1.44847i
$498$	2.86770e16i	0.0842448i
$499$	2.04183e17	0.592060	0.296030	−	0.955179i	$-0.404337\pi$
$499$	2.04183e17	0.592060	0.296030	+	0.955179i	$0.404337\pi$
$500$	0	0
$501$	−3.45803e17	−0.976976
$502$	− 3.22533e17i	− 0.899498i
$503$	− 1.02017e17i	− 0.280854i	−0.990091	−	0.140427i	$-0.955153\pi$
$503$	− 1.02017e17i	− 0.280854i	0.990091	−	0.140427i	$-0.0448475\pi$
$504$	−3.85909e16	−0.104878
$505$	0	0
$506$	−2.47337e14	−0.000655106 0
$507$	− 1.94463e17i	− 0.508493i
$508$	− 1.13584e17i	− 0.293227i
$509$	−1.49904e17	−0.382074	−0.191037	−	0.981583i	$-0.561185\pi$
$509$	−1.49904e17	−0.382074	−0.191037	+	0.981583i	$0.561185\pi$
$510$	0	0
$511$	−2.79260e17	−0.693862
$512$	1.80144e16i	0.0441942i
$513$	2.09620e16i	0.0507774i
$514$	−2.54778e17	−0.609400
$515$	0	0
$516$	7.70934e16	0.179802
$517$	− 9.27559e13i	0 0.000213625i
$518$	− 1.73994e17i	− 0.395723i
$519$	−2.90797e17	−0.653133
$520$	0	0
$521$	−5.29322e17	−1.15951	−0.579755	−	0.814791i	$-0.696852\pi$
$521$	−5.29322e17	−1.15951	−0.579755	+	0.814791i	$0.696852\pi$
$522$	1.03945e17i	0.224876i
$523$	− 2.76315e17i	− 0.590396i	−0.955436	−	0.295198i	$-0.904614\pi$
$523$	− 2.76315e17i	− 0.590396i	0.955436	−	0.295198i	$-0.0953856\pi$
$524$	2.64103e16	0.0557339
$525$	0	0
$526$	−7.63240e16	−0.157128
$527$	4.07519e17i	0.828664i
$528$	− 2.31753e14i	0 0.000465483i
$529$	4.62439e17	0.917472
$530$	0	0
$531$	−1.48761e17	−0.287989
$532$	− 6.13904e16i	− 0.117402i
$533$	− 4.69957e16i	− 0.0887833i
$534$	−2.03559e17	−0.379903
$535$	0	0
$536$	−6.83800e16	−0.124554
$537$	4.35988e17i	0.784588i
$538$	− 4.84381e17i	− 0.861197i
$539$	3.81937e14	0.000670910 0
$540$	0	0
$541$	−9.07438e17	−1.55609	−0.778045	−	0.628209i	$-0.783788\pi$
$541$	−9.07438e17	−1.55609	−0.778045	+	0.628209i	$0.783788\pi$
$542$	3.59897e17i	0.609793i
$543$	2.13140e17i	0.356834i
$544$	−1.00671e17	−0.166537
$545$	0	0
$546$	−7.76756e16	−0.125468
$547$	− 6.24262e17i	− 0.996436i	−0.867052	−	0.498218i	$-0.833988\pi$
$547$	− 6.24262e17i	− 0.996436i	0.867052	−	0.498218i	$-0.166012\pi$
$548$	− 3.50928e17i	− 0.553534i
$549$	−1.44298e17	−0.224926
$550$	0	0
$551$	−1.65355e17	−0.251728
$552$	− 3.89763e16i	− 0.0586403i
$553$	− 1.09782e18i	− 1.63236i
$554$	−5.67424e17	−0.833862
$555$	0	0
$556$	−1.54656e14	−0.000222014 0
$557$	5.70849e17i	0.809958i	0.914326	+	0.404979i	$0.132721\pi$
$557$	5.70849e17i	0.809958i	−0.914326	+	0.404979i	$0.867279\pi$
$558$	− 1.47836e17i	− 0.207328i
$559$	1.55173e17	0.215100
$560$	0	0
$561$	1.29511e15	0.00175408
$562$	− 2.22413e17i	− 0.297766i
$563$	5.41359e17i	0.716442i	0.933637	+	0.358221i	$0.116617\pi$
$563$	5.41359e17i	0.716442i	−0.933637	+	0.358221i	$0.883383\pi$
$564$	1.46168e16	0.0191222
$565$	0	0
$566$	−3.14759e16	−0.0402413
$567$	7.82348e16i	0.0988804i
$568$	− 4.60549e17i	− 0.575456i
$569$	−1.74017e17	−0.214962	−0.107481	−	0.994207i	$-0.534279\pi$
$569$	−1.74017e17	−0.214962	−0.107481	+	0.994207i	$0.534279\pi$
$570$	0	0
$571$	−1.05427e18	−1.27297	−0.636485	−	0.771289i	$-0.719612\pi$
$571$	−1.05427e18	−1.27297	−0.636485	+	0.771289i	$0.719612\pi$
$572$	− 4.66471e14i	0 0.000556865i
$573$	4.34454e17i	0.512790i
$574$	1.38625e17	0.161776
$575$	0	0
$576$	3.65203e16	0.0416667
$577$	− 1.01793e18i	− 1.14835i	−0.818732	−	0.574176i	$-0.805323\pi$
$577$	− 1.01793e18i	− 1.14835i	0.818732	−	0.574176i	$-0.194677\pi$
$578$	7.13107e16i	0.0795470i
$579$	−6.33272e17	−0.698521
$580$	0	0
$581$	−1.70261e17	−0.183642
$582$	− 2.20509e17i	− 0.235195i
$583$	8.14389e14i	0 0.000858986i
$584$	2.64277e17	0.275661
$585$	0	0
$586$	−3.39664e17	−0.346510
$587$	6.05137e17i	0.610529i	0.952268	+	0.305265i	$0.0987449\pi$
$587$	6.05137e17i	0.610529i	−0.952268	+	0.305265i	$0.901255\pi$
$588$	6.01869e16i	0.0600550i
$589$	2.35177e17	0.232084
$590$	0	0
$591$	2.51006e17	0.242306
$592$	1.64659e17i	0.157215i
$593$	− 1.97380e18i	− 1.86401i	−0.362445	−	0.932005i	$-0.618058\pi$
$593$	− 1.97380e18i	− 1.86401i	0.362445	−	0.932005i	$-0.381942\pi$
$594$	−4.69829e14	−0.000438862 0
$595$	0	0
$596$	6.26112e17	0.572204
$597$	5.73244e17i	0.518211i
$598$	− 7.84513e16i	− 0.0701524i
$599$	3.53981e17	0.313116	0.156558	−	0.987669i	$-0.449960\pi$
$599$	3.53981e17	0.313116	0.156558	+	0.987669i	$0.449960\pi$
$600$	0	0
$601$	−5.26298e17	−0.455562	−0.227781	−	0.973712i	$-0.573147\pi$
$601$	−5.26298e17	−0.455562	−0.227781	+	0.973712i	$0.573147\pi$
$602$	4.57720e17i	0.391942i
$603$	1.38626e17i	0.117431i
$604$	4.59441e17	0.385026
$605$	0	0
$606$	−1.86380e17	−0.152872
$607$	− 2.29959e18i	− 1.86605i	−0.359809	−	0.933026i	$-0.617158\pi$
$607$	− 2.29959e18i	− 1.86605i	0.359809	−	0.933026i	$-0.382842\pi$
$608$	5.80966e16i	0.0466420i
$609$	−6.17140e17	−0.490198
$610$	0	0
$611$	2.94206e16	0.0228762
$612$	2.04088e17i	0.157012i
$613$	− 2.10907e18i	− 1.60545i	−0.596348	−	0.802726i	$-0.703382\pi$
$613$	− 2.10907e18i	− 1.60545i	0.596348	−	0.802726i	$-0.296618\pi$
$614$	8.89429e16	0.0669911
$615$	0	0
$616$	1.37596e15	0.00101469
$617$	1.28616e18i	0.938517i	0.883061	+	0.469259i	$0.155479\pi$
$617$	1.28616e18i	0.938517i	−0.883061	+	0.469259i	$0.844521\pi$
$618$	1.73675e17i	0.125405i
$619$	1.69276e18	1.20950	0.604750	−	0.796415i	$-0.293273\pi$
$619$	1.69276e18	1.20950	0.604750	+	0.796415i	$0.293273\pi$
$620$	0	0
$621$	−7.90160e16	−0.0552866
$622$	− 1.45568e18i	− 1.00792i
$623$	− 1.20857e18i	− 0.828135i
$624$	7.35080e16	0.0498465
$625$	0	0
$626$	1.43842e18	0.955329
$627$	− 7.47404e14i	0 0.000491266i
$628$	− 4.76946e17i	− 0.310264i
$629$	−9.20171e17	−0.592433
$630$	0	0
$631$	−3.34107e17	−0.210715	−0.105357	−	0.994434i	$-0.533599\pi$
$631$	−3.34107e17	−0.210715	−0.105357	+	0.994434i	$0.533599\pi$
$632$	1.03891e18i	0.648513i
$633$	1.10948e18i	0.685483i
$634$	1.54846e18	0.946933
$635$	0	0
$636$	−1.28334e17	−0.0768902
$637$	1.21144e17i	0.0718448i
$638$	− 3.70616e15i	− 0.00217565i
$639$	−9.33666e17	−0.542545
$640$	0	0
$641$	2.16392e18	1.23215	0.616075	−	0.787688i	$-0.288722\pi$
$641$	2.16392e18	1.23215	0.616075	+	0.787688i	$0.288722\pi$
$642$	3.70989e17i	0.209114i
$643$	− 3.69069e16i	− 0.0205938i	−0.999947	−	0.0102969i	$-0.996722\pi$
$643$	− 3.69069e16i	− 0.0205938i	0.999947	−	0.0102969i	$-0.00327766\pi$
$644$	2.31410e17	0.127827
$645$	0	0
$646$	−3.24664e17	−0.175761
$647$	1.03998e18i	0.557372i	0.960382	+	0.278686i	$0.0898989\pi$
$647$	1.03998e18i	0.557372i	−0.960382	+	0.278686i	$0.910101\pi$
$648$	− 7.40372e16i	− 0.0392837i
$649$	5.30410e15	0.00278626
$650$	0	0
$651$	8.77732e17	0.451945
$652$	7.15970e17i	0.364994i
$653$	8.43682e17i	0.425837i	0.977070	+	0.212918i	$0.0682968\pi$
$653$	8.43682e17i	0.425837i	−0.977070	+	0.212918i	$0.931703\pi$
$654$	−8.51047e17	−0.425303
$655$	0	0
$656$	−1.31187e17	−0.0642711
$657$	− 5.35765e17i	− 0.259896i
$658$	8.67829e16i	0.0416837i
$659$	−1.97563e18	−0.939614	−0.469807	−	0.882769i	$-0.655677\pi$
$659$	−1.97563e18	−0.939614	−0.469807	+	0.882769i	$0.655677\pi$
$660$	0	0
$661$	−2.83369e17	−0.132143	−0.0660713	−	0.997815i	$-0.521046\pi$
$661$	−2.83369e17	−0.132143	−0.0660713	+	0.997815i	$0.521046\pi$
$662$	5.13920e17i	0.237311i
$663$	4.10788e17i	0.187837i
$664$	1.61126e17	0.0729582
$665$	0	0
$666$	3.33811e17	0.148224
$667$	− 6.23303e17i	− 0.274083i
$668$	1.94295e18i	0.846086i
$669$	−2.29026e18	−0.987678
$670$	0	0
$671$	5.14495e15	0.00217613
$672$	2.16829e17i	0.0908274i
$673$	1.27613e18i	0.529415i	0.964329	+	0.264708i	$0.0852754\pi$
$673$	1.27613e18i	0.529415i	−0.964329	+	0.264708i	$0.914725\pi$
$674$	−2.16422e18	−0.889227
$675$	0	0
$676$	−1.09262e18	−0.440368
$677$	− 2.37398e18i	− 0.947658i	−0.880617	−	0.473829i	$-0.842872\pi$
$677$	− 2.37398e18i	− 0.947658i	0.880617	−	0.473829i	$-0.157128\pi$
$678$	3.15868e17i	0.124886i
$679$	1.30921e18	0.512691
$680$	0	0
$681$	8.65911e17	0.332673
$682$	5.27110e15i	0.00200587i
$683$	4.49062e18i	1.69267i	0.532652	+	0.846335i	$0.321196\pi$
$683$	4.49062e18i	1.69267i	−0.532652	+	0.846335i	$0.678804\pi$
$684$	1.17778e17	0.0439745
$685$	0	0
$686$	−2.07503e18	−0.760182
$687$	− 2.58057e17i	− 0.0936478i
$688$	− 4.33161e17i	− 0.155713i
$689$	−2.58310e17	−0.0919850
$690$	0	0
$691$	3.71159e18	1.29704	0.648519	−	0.761198i	$-0.275389\pi$
$691$	3.71159e18	1.29704	0.648519	+	0.761198i	$0.275389\pi$
$692$	1.63389e18i	0.565630i
$693$	− 2.78947e15i	0 0.000956656i
$694$	2.13527e18	0.725465
$695$	0	0
$696$	5.84029e17	0.194748
$697$	− 7.33118e17i	− 0.242193i
$698$	2.62073e18i	0.857754i
$699$	−1.42012e18	−0.460495
$700$	0	0
$701$	2.99557e18	0.953483	0.476741	−	0.879044i	$-0.341818\pi$
$701$	2.99557e18	0.953483	0.476741	+	0.879044i	$0.341818\pi$
$702$	− 1.49022e17i	− 0.0469958i
$703$	5.31026e17i	0.165923i
$704$	−1.30214e15	−0.000403120 0
$705$	0	0
$706$	−2.00030e18	−0.607947
$707$	− 1.10658e18i	− 0.333238i
$708$	8.35838e17i	0.249406i
$709$	5.18607e18	1.53334	0.766668	−	0.642043i	$-0.221913\pi$
$709$	5.18607e18	1.53334	0.766668	+	0.642043i	$0.221913\pi$
$710$	0	0
$711$	2.10618e18	0.611424
$712$	1.14373e18i	0.329006i
$713$	8.86497e17i	0.252694i
$714$	−1.21171e18	−0.342265
$715$	0	0
$716$	2.44967e18	0.679473
$717$	1.95519e18i	0.537420i
$718$	2.04356e18i	0.556645i
$719$	−1.81508e18	−0.489957	−0.244979	−	0.969529i	$-0.578781\pi$
$719$	−1.81508e18	−0.489957	−0.244979	+	0.969529i	$0.578781\pi$
$720$	0	0
$721$	−1.03115e18	−0.273364
$722$	− 2.50403e18i	− 0.657881i
$723$	2.65957e18i	0.692489i
$724$	1.19756e18	0.309027
$725$	0	0
$726$	−1.61067e18	−0.408244
$727$	− 2.62578e18i	− 0.659606i	−0.944050	−	0.329803i	$-0.893018\pi$
$727$	− 2.62578e18i	− 0.659606i	0.944050	−	0.329803i	$-0.106982\pi$
$728$	4.36432e17i	0.108658i
$729$	−1.50095e17	−0.0370370
$730$	0	0
$731$	2.42065e18	0.586773
$732$	8.10758e17i	0.194791i
$733$	− 8.57217e16i	− 0.0204134i	−0.999948	−	0.0102067i	$-0.996751\pi$
$733$	− 8.57217e16i	− 0.0204134i	0.999948	−	0.0102067i	$-0.00324895\pi$
$734$	1.27530e18	0.301016
$735$	0	0
$736$	−2.18994e17	−0.0507840
$737$	− 4.94272e15i	− 0.00113613i
$738$	2.65954e17i	0.0605954i
$739$	7.04373e18	1.59079	0.795396	−	0.606089i	$-0.207263\pi$
$739$	7.04373e18	1.59079	0.795396	+	0.606089i	$0.207263\pi$
$740$	0	0
$741$	2.37064e17	0.0526074
$742$	− 7.61946e17i	− 0.167610i
$743$	7.27567e18i	1.58652i	0.608882	+	0.793261i	$0.291618\pi$
$743$	7.27567e18i	1.58652i	−0.608882	+	0.793261i	$0.708382\pi$
$744$	−8.30638e17	−0.179551
$745$	0	0
$746$	−5.14699e18	−1.09333
$747$	− 3.26649e17i	− 0.0687856i
$748$	− 7.27679e15i	− 0.00151908i
$749$	−2.20264e18	−0.455839
$750$	0	0
$751$	2.46146e17	0.0500649	0.0250325	−	0.999687i	$-0.492031\pi$
$751$	2.46146e17	0.0500649	0.0250325	+	0.999687i	$0.492031\pi$
$752$	− 8.21267e16i	− 0.0165603i
$753$	3.67385e18i	0.734437i
$754$	1.17553e18	0.232981
$755$	0	0
$756$	4.39574e17	0.0856329
$757$	− 3.88745e18i	− 0.750829i	−0.926857	−	0.375415i	$-0.877500\pi$
$757$	− 3.88745e18i	− 0.750829i	0.926857	−	0.375415i	$-0.122500\pi$
$758$	6.64230e18i	1.27195i
$759$	2.81733e15	0.000534892 0
$760$	0	0
$761$	8.38833e18	1.56558	0.782790	−	0.622285i	$-0.213796\pi$
$761$	8.38833e18	1.56558	0.782790	+	0.622285i	$0.213796\pi$
$762$	1.29380e18i	0.239419i
$763$	− 5.05284e18i	− 0.927100i
$764$	2.44105e18	0.444089
$765$	0	0
$766$	−6.68270e18	−1.19527
$767$	1.68237e18i	0.298368i
$768$	− 2.05195e17i	− 0.0360844i
$769$	1.00207e19	1.74735	0.873673	−	0.486513i	$-0.161732\pi$
$769$	1.00207e19	1.74735	0.873673	+	0.486513i	$0.161732\pi$
$770$	0	0
$771$	2.90208e18	0.497573
$772$	3.55813e18i	0.604937i
$773$	− 6.82020e18i	− 1.14982i	−0.818216	−	0.574911i	$-0.805037\pi$
$773$	− 6.82020e18i	− 1.14982i	0.818216	−	0.574911i	$-0.194963\pi$
$774$	−8.78142e17	−0.146808
$775$	0	0
$776$	−1.23897e18	−0.203685
$777$	1.98190e18i	0.323107i
$778$	2.49958e18i	0.404110i
$779$	−4.23079e17	−0.0678310
$780$	0	0
$781$	3.32900e16	0.00524906
$782$	− 1.22381e18i	− 0.191369i
$783$	− 1.18399e18i	− 0.183611i
$784$	3.38169e17	0.0520092
$785$	0	0
$786$	−3.00830e17	−0.0455065
$787$	− 6.89127e18i	− 1.03386i	−0.856026	−	0.516932i	$-0.827074\pi$
$787$	− 6.89127e18i	− 1.03386i	0.856026	−	0.516932i	$-0.172926\pi$
$788$	− 1.41031e18i	− 0.209843i
$789$	8.69378e17	0.128294
$790$	0	0
$791$	−1.87538e18	−0.272233
$792$	2.63981e15i	0 0.000380065i
$793$	1.63189e18i	0.233032i
$794$	6.71677e18	0.951321
$795$	0	0
$796$	3.22086e18	0.448784
$797$	− 3.64788e18i	− 0.504152i	−0.967707	−	0.252076i	$-0.918887\pi$
$797$	− 3.64788e18i	− 0.504152i	0.967707	−	0.252076i	$-0.0811133\pi$
$798$	6.99275e17i	0.0958582i
$799$	4.58952e17	0.0624041
$800$	0	0
$801$	2.31867e18	0.310190
$802$	− 4.72929e18i	− 0.627571i
$803$	1.91028e16i	0.00251446i
$804$	7.78891e17	0.101698
$805$	0	0
$806$	−1.67191e18	−0.214800
$807$	5.51741e18i	0.703165i
$808$	1.04720e18i	0.132391i
$809$	−1.34730e19	−1.68966	−0.844828	−	0.535037i	$-0.820298\pi$
$809$	−1.34730e19	−1.68966	−0.844828	+	0.535037i	$0.820298\pi$
$810$	0	0
$811$	1.21919e19	1.50465	0.752326	−	0.658791i	$-0.228932\pi$
$811$	1.21919e19	1.50465	0.752326	+	0.658791i	$0.228932\pi$
$812$	3.46750e18i	0.424524i
$813$	− 4.09945e18i	− 0.497894i
$814$	−1.19021e16	−0.00143405
$815$	0	0
$816$	1.14670e18	0.135977
$817$	− 1.39695e18i	− 0.164338i
$818$	4.00084e18i	0.466933i
$819$	8.84774e17	0.102444
$820$	0	0
$821$	−1.93186e18	−0.220164	−0.110082	−	0.993923i	$-0.535111\pi$
$821$	−1.93186e18	−0.220164	−0.110082	+	0.993923i	$0.535111\pi$
$822$	3.99729e18i	0.451958i
$823$	− 1.38748e19i	− 1.55642i	−0.628002	−	0.778212i	$-0.716127\pi$
$823$	− 1.38748e19i	− 1.55642i	0.628002	−	0.778212i	$-0.283873\pi$
$824$	9.75823e17	0.108604
$825$	0	0
$826$	−4.96255e18	−0.543669
$827$	1.16839e18i	0.127000i	0.997982	+	0.0635000i	$0.0202263\pi$
$827$	1.16839e18i	0.127000i	−0.997982	+	0.0635000i	$0.979774\pi$
$828$	4.43964e17i	0.0478796i
$829$	2.37776e18	0.254427	0.127214	−	0.991875i	$-0.459397\pi$
$829$	2.37776e18	0.254427	0.127214	+	0.991875i	$0.459397\pi$
$830$	0	0
$831$	6.46331e18	0.680845
$832$	− 4.13016e17i	− 0.0431684i
$833$	1.88981e18i	0.195986i
$834$	1.76163e15	0.000181274 0
$835$	0	0
$836$	−4.19940e15	−0.000425448 0
$837$	1.68394e18i	0.169282i
$838$	9.75100e17i	0.0972665i
$839$	−2.46136e18	−0.243625	−0.121812	−	0.992553i	$-0.538871\pi$
$839$	−2.46136e18	−0.243625	−0.121812	+	0.992553i	$0.538871\pi$
$840$	0	0
$841$	−9.20921e17	−0.0897528
$842$	− 7.88867e18i	− 0.762914i
$843$	2.53343e18i	0.243125i
$844$	6.23380e18	0.593645
$845$	0	0
$846$	−1.66494e17	−0.0156132
$847$	− 9.56291e18i	− 0.889914i
$848$	7.21065e17i	0.0665888i
$849$	3.58531e17	0.0328569
$850$	0	0
$851$	−2.00170e18	−0.180657
$852$	5.24595e18i	0.469858i
$853$	− 1.09322e19i	− 0.971711i	−0.874039	−	0.485856i	$-0.838508\pi$
$853$	− 1.09322e19i	− 0.971711i	0.874039	−	0.485856i	$-0.161492\pi$
$854$	−4.81364e18	−0.424617
$855$	0	0
$856$	2.08446e18	0.181098
$857$	− 1.59094e19i	− 1.37177i	−0.727712	−	0.685883i	$-0.759416\pi$
$857$	− 1.59094e19i	− 1.37177i	0.727712	−	0.685883i	$-0.240584\pi$
$858$	5.31339e15i	0 0.000454679i
$859$	9.02568e18	0.766521	0.383261	−	0.923640i	$-0.374801\pi$
$859$	9.02568e18	0.766521	0.383261	+	0.923640i	$0.374801\pi$
$860$	0	0
$861$	−1.57902e18	−0.132089
$862$	3.27446e17i	0.0271858i
$863$	− 1.73210e19i	− 1.42726i	−0.700523	−	0.713630i	$-0.747050\pi$
$863$	− 1.73210e19i	− 1.42726i	0.700523	−	0.713630i	$-0.252950\pi$
$864$	−4.15990e17	−0.0340207
$865$	0	0
$866$	−6.21965e18	−0.501071
$867$	− 8.12273e17i	− 0.0649498i
$868$	− 4.93167e18i	− 0.391396i
$869$	−7.50960e16	−0.00591546
$870$	0	0
$871$	1.56775e18	0.121663
$872$	4.78174e18i	0.368323i
$873$	2.51174e18i	0.192036i
$874$	−7.06258e17	−0.0535968
$875$	0	0
$876$	−3.01028e18	−0.225076
$877$	− 1.06065e19i	− 0.787182i	−0.919286	−	0.393591i	$-0.871233\pi$
$877$	− 1.06065e19i	− 0.787182i	0.919286	−	0.393591i	$-0.128767\pi$
$878$	8.38808e18i	0.617942i
$879$	3.86899e18	0.282924
$880$	0	0
$881$	−1.56065e19	−1.12451	−0.562254	−	0.826965i	$-0.690066\pi$
$881$	−1.56065e19	−1.12451	−0.562254	+	0.826965i	$0.690066\pi$
$882$	− 6.85566e17i	− 0.0490347i
$883$	2.60968e17i	0.0185286i	0.999957	+	0.00926431i	$0.00294896\pi$
$883$	2.60968e17i	0.0185286i	−0.999957	+	0.00926431i	$0.997051\pi$
$884$	2.30808e18	0.162671
$885$	0	0
$886$	−1.11853e19	−0.776836
$887$	1.04619e19i	0.721288i	0.932704	+	0.360644i	$0.117443\pi$
$887$	1.04619e19i	0.721288i	−0.932704	+	0.360644i	$0.882557\pi$
$888$	− 1.87557e18i	− 0.128366i
$889$	−7.68153e18	−0.521899
$890$	0	0
$891$	5.35164e15	0.000358329 0
$892$	1.28682e19i	0.855354i
$893$	− 2.64859e17i	− 0.0174775i
$894$	−7.13180e18	−0.467203
$895$	0	0
$896$	1.21829e18	0.0786588
$897$	8.93609e17i	0.0572792i
$898$	− 1.88312e19i	− 1.19835i
$899$	−1.32835e19	−0.839215
$900$	0	0
$901$	−4.02956e18	−0.250926
$902$	− 9.48261e15i	0 0.000586253i
$903$	− 5.21371e18i	− 0.320020i
$904$	1.77476e18	0.108154
$905$	0	0
$906$	−5.23332e18	−0.314372
$907$	1.25229e19i	0.746894i	0.927651	+	0.373447i	$0.121824\pi$
$907$	1.25229e19i	0.746894i	−0.927651	+	0.373447i	$0.878176\pi$
$908$	− 4.86525e18i	− 0.288103i
$909$	2.12298e18	0.124819
$910$	0	0
$911$	−8.44025e18	−0.489200	−0.244600	−	0.969624i	$-0.578657\pi$
$911$	−8.44025e18	−0.489200	−0.244600	+	0.969624i	$0.578657\pi$
$912$	− 6.61756e17i	− 0.0380830i
$913$	1.16467e16i	0 0.000665493i
$914$	−5.33793e18	−0.302847
$915$	0	0
$916$	−1.44994e18	−0.0811014
$917$	− 1.78609e18i	− 0.0991978i
$918$	− 2.32469e18i	− 0.128200i
$919$	−2.80678e19	−1.53694	−0.768472	−	0.639884i	$-0.778982\pi$
$919$	−2.80678e19	−1.53694	−0.768472	+	0.639884i	$0.778982\pi$
$920$	0	0
$921$	−1.01312e18	−0.0546980
$922$	7.47559e18i	0.400769i
$923$	1.05590e19i	0.562099i
$924$	−1.56731e16	−0.000828489 0
$925$	0	0
$926$	2.65692e18	0.138486
$927$	− 1.97827e18i	− 0.102392i
$928$	− 3.28146e18i	− 0.168657i
$929$	−1.44237e19	−0.736164	−0.368082	−	0.929793i	$-0.619986\pi$
$929$	−1.44237e19	−0.736164	−0.368082	+	0.929793i	$0.619986\pi$
$930$	0	0
$931$	1.09060e18	0.0548899
$932$	7.97919e18i	0.398800i
$933$	1.65811e19i	0.822967i
$934$	−1.67305e19	−0.824622
$935$	0	0
$936$	−8.37302e17	−0.0406995
$937$	1.50662e19i	0.727272i	0.931541	+	0.363636i	$0.118465\pi$
$937$	1.50662e19i	0.727272i	−0.931541	+	0.363636i	$0.881535\pi$
$938$	4.62444e18i	0.221687i
$939$	−1.63845e19	−0.780023
$940$	0	0
$941$	−2.74730e18	−0.128995	−0.0644977	−	0.997918i	$-0.520545\pi$
$941$	−2.74730e18	−0.128995	−0.0644977	+	0.997918i	$0.520545\pi$
$942$	5.43271e18i	0.253329i
$943$	− 1.59479e18i	− 0.0738546i
$944$	4.69629e18	0.215992
$945$	0	0
$946$	3.13103e16	0.00142035
$947$	7.30852e18i	0.329272i	0.986354	+	0.164636i	$0.0526449\pi$
$947$	7.30852e18i	0.329272i	−0.986354	+	0.164636i	$0.947355\pi$
$948$	− 1.18339e19i	− 0.529509i
$949$	−6.05908e18	−0.269263
$950$	0	0
$951$	−1.76379e19	−0.773168
$952$	6.80821e18i	0.296410i
$953$	− 3.28674e19i	− 1.42122i	−0.703586	−	0.710610i	$-0.748419\pi$
$953$	− 3.28674e19i	− 1.42122i	0.703586	−	0.710610i	$-0.251581\pi$
$954$	1.46181e18	0.0627806
$955$	0	0
$956$	1.09855e19	0.465419
$957$	4.22154e16i	0.00177641i
$958$	1.00372e17i	0.00419505i
$959$	−2.37327e19	−0.985205
$960$	0	0
$961$	−5.52507e18	−0.226274
$962$	− 3.77514e18i	− 0.153566i
$963$	− 4.22579e18i	− 0.170741i
$964$	1.49432e19	0.599713
$965$	0	0
$966$	−2.63591e18	−0.104371
$967$	4.81990e19i	1.89568i	0.318739	+	0.947842i	$0.396741\pi$
$967$	4.81990e19i	1.89568i	−0.318739	+	0.947842i	$0.603259\pi$
$968$	9.04983e18i	0.353550i
$969$	3.69812e18	0.143508
$970$	0	0
$971$	−3.34021e19	−1.27893	−0.639467	−	0.768819i	$-0.720845\pi$
$971$	−3.34021e19	−1.27893	−0.639467	+	0.768819i	$0.720845\pi$
$972$	8.43330e17i	0.0320750i
$973$	1.04592e16i	0 0.000395152i
$974$	−1.08052e19	−0.405507
$975$	0	0
$976$	4.55537e18	0.168694
$977$	9.58022e18i	0.352420i	0.984353	+	0.176210i	$0.0563838\pi$
$977$	9.58022e18i	0.352420i	−0.984353	+	0.176210i	$0.943616\pi$
$978$	− 8.15535e18i	− 0.298016i
$979$	−8.26724e16	−0.00300105
$980$	0	0
$981$	9.69396e18	0.347258
$982$	− 1.34418e18i	− 0.0478336i
$983$	− 2.89457e19i	− 1.02326i	−0.859206	−	0.511629i	$-0.829042\pi$
$983$	− 2.89457e19i	− 1.02326i	0.859206	−	0.511629i	$-0.170958\pi$
$984$	1.49430e18	0.0524771
$985$	0	0
$986$	1.83379e19	0.635550
$987$	− 9.88511e17i	− 0.0340346i
$988$	− 1.33198e18i	− 0.0455594i
$989$	5.26578e18	0.178931
$990$	0	0
$991$	−1.69539e19	−0.568580	−0.284290	−	0.958738i	$-0.591758\pi$
$991$	−1.69539e19	−0.568580	−0.284290	+	0.958738i	$0.591758\pi$
$992$	4.66707e18i	0.155496i
$993$	− 5.85387e18i	− 0.193764i
$994$	−3.11463e19	−1.02422
$995$	0	0
$996$	−1.83533e18	−0.0595701
$997$	1.70090e19i	0.548480i	0.961661	+	0.274240i	$0.0884263\pi$
$997$	1.70090e19i	0.548480i	−0.961661	+	0.274240i	$0.911574\pi$
$998$	1.30677e19i	0.418650i
$999$	−3.80231e18	−0.121024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.14.c.m.49.4		4
5.2	odd	4		150.14.a.j.1.1	✓	2
5.3	odd	4		150.14.a.p.1.2	yes	2
5.4	even	2	inner	150.14.c.m.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.14.a.j.1.1	✓	2	5.2	odd	4
150.14.a.p.1.2	yes	2	5.3	odd	4
150.14.c.m.49.1		4	5.4	even	2	inner
150.14.c.m.49.4		4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+64.0000i q^{2} -729.000i q^{3} -4096.00 q^{4} +46656.0 q^{6} +277006. i q^{7} -262144. i q^{8} -531441. q^{9} +18948.6 q^{11} +2.98598e6i q^{12} +6.01018e6i q^{13} -1.77284e7 q^{14} +1.67772e7 q^{16} +9.37569e7i q^{17} -3.40122e7i q^{18} +5.41067e7 q^{19} +2.01938e8 q^{21} +1.21271e6i q^{22} +2.03954e8i q^{23} -1.91103e8 q^{24} -3.84651e8 q^{26} +3.87420e8i q^{27} -1.13462e9i q^{28} -3.05609e9 q^{29} +4.34655e9 q^{31} +1.07374e9i q^{32} -1.38135e7i q^{33} -6.00044e9 q^{34} +2.17678e9 q^{36} +9.81444e9i q^{37} +3.46283e9i q^{38} +4.38142e9 q^{39} -7.81935e9 q^{41} +1.29240e10i q^{42} -2.58184e10i q^{43} -7.76135e7 q^{44} -1.30531e10 q^{46} -4.89513e9i q^{47} -1.22306e10i q^{48} +2.01565e10 q^{49} +6.83488e10 q^{51} -2.46177e10i q^{52} +4.29788e10i q^{53} -2.47949e10 q^{54} +7.26156e10 q^{56} -3.94437e10i q^{57} -1.95590e11i q^{58} +2.79921e11 q^{59} +2.71521e11 q^{61} +2.78179e11i q^{62} -1.47213e11i q^{63} -6.87195e10 q^{64} +8.84066e8 q^{66} -2.60849e11i q^{67} -3.84028e11i q^{68} +1.48683e11 q^{69} +1.75686e12 q^{71} +1.39314e11i q^{72} +1.00814e12i q^{73} -6.28124e11 q^{74} -2.21621e11 q^{76} +5.24888e9i q^{77} +2.80411e11i q^{78} -3.96314e12 q^{79} +2.82430e11 q^{81} -5.00438e11i q^{82} +6.14648e11i q^{83} -8.27137e11 q^{84} +1.65238e12 q^{86} +2.22789e12i q^{87} -4.96726e9i q^{88} -4.36298e12 q^{89} -1.66486e12 q^{91} -8.35396e11i q^{92} -3.16863e12i q^{93} +3.13288e11 q^{94} +7.82758e11 q^{96} -4.72628e12i q^{97} +1.29001e12i q^{98} -1.00701e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16384 q^{4} + 186624 q^{6} - 2125764 q^{9} + 11958408 q^{11} - 1778432 q^{14} + 67108864 q^{16} - 471684740 q^{19} + 20257452 q^{21} - 764411904 q^{24} + 3162588416 q^{26} + 3965146440 q^{29} - 7190293012 q^{31}+ \cdots - 6355188305928 q^{99}+O(q^{100}) \) 4 * q - 16384 * q^4 + 186624 * q^6 - 2125764 * q^9 + 11958408 * q^11 - 1778432 * q^14 + 67108864 * q^16 - 471684740 * q^19 + 20257452 * q^21 - 764411904 * q^24 + 3162588416 * q^26 + 3965146440 * q^29 - 7190293012 * q^31 + 6210329088 * q^34 + 8707129344 * q^36 - 36023858676 * q^39 + 21588341808 * q^41 - 48981639168 * q^44 + 100092581376 * q^46 + 95634679992 * q^49 - 70739529768 * q^51 - 99179645184 * q^54 + 7284457472 * q^56 + 657254281560 * q^59 + 1978324726508 * q^61 - 274877906944 * q^64 + 557931483648 * q^66 - 1140117059736 * q^69 + 5259349361328 * q^71 + 482026198528 * q^74 + 1932020695040 * q^76 - 10219104462560 * q^79 + 1129718145924 * q^81 - 82974523392 * q^84 - 966250226944 * q^86 - 21799732071360 * q^89 - 19494236561732 * q^91 - 7777010652672 * q^94 + 3131031158784 * q^96 - 6355188305928 * q^99

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