LMFDB - Embedded newform 150.14.c.j.49.2

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,-2125764,0,8037120] 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} + 11557705x^{2} + 33395130437904 $ x^4 + 11557705*x^2 + 33395130437904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$2404.42i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.14.c.j.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-64.0000i q^{2} -729.000i q^{3} -4096.00 q^{4} -46656.0 q^{6} +170015. i q^{7} +262144. i q^{8} -531441. q^{9} -6.06791e6 q^{11} +2.98598e6i q^{12} -3.29464e7i q^{13} +1.08810e7 q^{14} +1.67772e7 q^{16} +5.09064e7i q^{17} +3.40122e7i q^{18} +3.38083e8 q^{19} +1.23941e8 q^{21} +3.88346e8i q^{22} +9.47034e8i q^{23} +1.91103e8 q^{24} -2.10857e9 q^{26} +3.87420e8i q^{27} -6.96381e8i q^{28} -5.81785e9 q^{29} +3.79039e9 q^{31} -1.07374e9i q^{32} +4.42350e9i q^{33} +3.25801e9 q^{34} +2.17678e9 q^{36} +2.84389e10i q^{37} -2.16373e10i q^{38} -2.40179e10 q^{39} +2.20260e10 q^{41} -7.93222e9i q^{42} -3.49140e10i q^{43} +2.48541e10 q^{44} +6.06102e10 q^{46} +5.50002e10i q^{47} -1.22306e10i q^{48} +6.79839e10 q^{49} +3.71108e10 q^{51} +1.34949e11i q^{52} +3.46323e9i q^{53} +2.47949e10 q^{54} -4.45684e10 q^{56} -2.46462e11i q^{57} +3.72342e11i q^{58} -2.80284e11 q^{59} +5.28916e11 q^{61} -2.42585e11i q^{62} -9.03529e10i q^{63} -6.87195e10 q^{64} +2.83104e11 q^{66} -7.51430e9i q^{67} -2.08513e11i q^{68} +6.90388e11 q^{69} +1.83209e11 q^{71} -1.39314e11i q^{72} -2.21482e12i q^{73} +1.82009e12 q^{74} -1.38479e12 q^{76} -1.03163e12i q^{77} +1.53715e12i q^{78} +6.58669e11 q^{79} +2.82430e11 q^{81} -1.40966e12i q^{82} +4.01969e12i q^{83} -5.07662e11 q^{84} -2.23450e12 q^{86} +4.24121e12i q^{87} -1.59067e12i q^{88} +2.09375e12 q^{89} +5.60138e12 q^{91} -3.87905e12i q^{92} -2.76319e12i q^{93} +3.52001e12 q^{94} -7.82758e11 q^{96} -8.64949e12i q^{97} -4.35097e12i q^{98} +3.22473e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16384 q^{4} - 186624 q^{6} - 2125764 q^{9} + 8037120 q^{11} - 30324736 q^{14} + 67108864 q^{16} + 181139296 q^{19} - 345417696 q^{21} + 764411904 q^{24} - 1714062848 q^{26} - 4144620456 q^{29} + 23456813552 q^{31}+ \cdots - 4271255089920 q^{99}+O(q^{100}) $ 4 * q - 16384 * q^4 - 186624 * q^6 - 2125764 * q^9 + 8037120 * q^11 - 30324736 * q^14 + 67108864 * q^16 + 181139296 * q^19 - 345417696 * q^21 + 764411904 * q^24 - 1714062848 * q^26 - 4144620456 * q^29 + 23456813552 * q^31 - 6094726656 * q^34 + 8707129344 * q^36 - 19524247128 * q^39 + 135743136456 * q^41 - 32920043520 * q^44 + 131298585600 * q^46 - 1433143716 * q^49 - 69422745816 * q^51 + 99179645184 * q^54 + 124210118656 * q^56 + 8668692480 * q^59 + 1774823369720 * q^61 - 274877906944 * q^64 - 374979870720 * q^66 + 1495572951600 * q^69 + 1872302664960 * q^71 + 6115692635648 * q^74 - 741946556416 * q^76 + 2497258829488 * q^79 + 1129718145924 * q^81 + 1414830882816 * q^84 - 9934644829184 * q^86 + 16032518338968 * q^89 + 27117915879808 * q^91 + 13683546024960 * q^94 - 3131031158784 * q^96 - 4271255089920 * 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
$7$	170015.i	0.546198i	0.961986	+	0.273099i	$0.0880486\pi$
$7$	170015.i	0.546198i	−0.961986	+	0.273099i	$0.911951\pi$
$8$	262144.i	0.353553i
$9$	−531441.	−0.333333
$10$	0	0
$11$	−6.06791e6	−1.03273	−0.516365	−	0.856369i	$-0.672715\pi$
$11$	−6.06791e6	−1.03273	−0.516365	+	0.856369i	$0.672715\pi$
$12$	2.98598e6i	0.288675i
$13$	− 3.29464e7i	− 1.89311i	−0.322539	−	0.946556i	$-0.604536\pi$
$13$	− 3.29464e7i	− 1.89311i	0.322539	−	0.946556i	$-0.395464\pi$
$14$	1.08810e7	0.386220
$15$	0	0
$16$	1.67772e7	0.250000
$17$	5.09064e7i	0.511511i	0.966742	+	0.255755i	$0.0823242\pi$
$17$	5.09064e7i	0.511511i	−0.966742	+	0.255755i	$0.917676\pi$
$18$	3.40122e7i	0.235702i
$19$	3.38083e8	1.64864	0.824318	−	0.566127i	$-0.191559\pi$
$19$	3.38083e8	1.64864	0.824318	+	0.566127i	$0.191559\pi$
$20$	0	0
$21$	1.23941e8	0.315347
$22$	3.88346e8i	0.730250i
$23$	9.47034e8i	1.33393i	0.745087	+	0.666967i	$0.232408\pi$
$23$	9.47034e8i	1.33393i	−0.745087	+	0.666967i	$0.767592\pi$
$24$	1.91103e8	0.204124
$25$	0	0
$26$	−2.10857e9	−1.33863
$27$	3.87420e8i	0.192450i
$28$	− 6.96381e8i	− 0.273099i
$29$	−5.81785e9	−1.81625	−0.908125	−	0.418700i	$-0.862486\pi$
$29$	−5.81785e9	−1.81625	−0.908125	+	0.418700i	$0.862486\pi$
$30$	0	0
$31$	3.79039e9	0.767065	0.383533	−	0.923527i	$-0.374707\pi$
$31$	3.79039e9	0.767065	0.383533	+	0.923527i	$0.374707\pi$
$32$	− 1.07374e9i	− 0.176777i
$33$	4.42350e9i	0.596246i
$34$	3.25801e9	0.361693
$35$	0	0
$36$	2.17678e9	0.166667
$37$	2.84389e10i	1.82222i	0.412160	+	0.911112i	$0.364775\pi$
$37$	2.84389e10i	1.82222i	−0.412160	+	0.911112i	$0.635225\pi$
$38$	− 2.16373e10i	− 1.16576i
$39$	−2.40179e10	−1.09299
$40$	0	0
$41$	2.20260e10	0.724169	0.362085	−	0.932145i	$-0.382065\pi$
$41$	2.20260e10	0.724169	0.362085	+	0.932145i	$0.382065\pi$
$42$	− 7.93222e9i	− 0.222984i
$43$	− 3.49140e10i	− 0.842276i	−0.906996	−	0.421138i	$-0.861631\pi$
$43$	− 3.49140e10i	− 0.842276i	0.906996	−	0.421138i	$-0.138369\pi$
$44$	2.48541e10	0.516365
$45$	0	0
$46$	6.06102e10	0.943234
$47$	5.50002e10i	0.744265i	0.928180	+	0.372133i	$0.121373\pi$
$47$	5.50002e10i	0.744265i	−0.928180	+	0.372133i	$0.878627\pi$
$48$	− 1.22306e10i	− 0.144338i
$49$	6.79839e10	0.701668
$50$	0	0
$51$	3.71108e10	0.295321
$52$	1.34949e11i	0.946556i
$53$	3.46323e9i	0.0214629i	0.999942	+	0.0107314i	$0.00341599\pi$
$53$	3.46323e9i	0.0214629i	−0.999942	+	0.0107314i	$0.996584\pi$
$54$	2.47949e10	0.136083
$55$	0	0
$56$	−4.45684e10	−0.193110
$57$	− 2.46462e11i	− 0.951840i
$58$	3.72342e11i	1.28428i
$59$	−2.80284e11	−0.865088	−0.432544	−	0.901613i	$-0.642384\pi$
$59$	−2.80284e11	−0.865088	−0.432544	+	0.901613i	$0.642384\pi$
$60$	0	0
$61$	5.28916e11	1.31445	0.657223	−	0.753696i	$-0.271731\pi$
$61$	5.28916e11	1.31445	0.657223	+	0.753696i	$0.271731\pi$
$62$	− 2.42585e11i	− 0.542397i
$63$	− 9.03529e10i	− 0.182066i
$64$	−6.87195e10	−0.125000
$65$	0	0
$66$	2.83104e11	0.421610
$67$	− 7.51430e9i	− 0.0101485i	−0.999987	−	0.00507426i	$-0.998385\pi$
$67$	− 7.51430e9i	− 0.0101485i	0.999987	−	0.00507426i	$-0.00161519\pi$
$68$	− 2.08513e11i	− 0.255755i
$69$	6.90388e11	0.770148
$70$	0	0
$71$	1.83209e11	0.169734	0.0848670	−	0.996392i	$-0.472953\pi$
$71$	1.83209e11	0.169734	0.0848670	+	0.996392i	$0.472953\pi$
$72$	− 1.39314e11i	− 0.117851i
$73$	− 2.21482e12i	− 1.71293i	−0.516202	−	0.856467i	$-0.672654\pi$
$73$	− 2.21482e12i	− 1.71293i	0.516202	−	0.856467i	$-0.327346\pi$
$74$	1.82009e12	1.28851
$75$	0	0
$76$	−1.38479e12	−0.824318
$77$	− 1.03163e12i	− 0.564074i
$78$	1.53715e12i	0.772860i
$79$	6.58669e11	0.304853	0.152427	−	0.988315i	$-0.451291\pi$
$79$	6.58669e11	0.304853	0.152427	+	0.988315i	$0.451291\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	− 1.40966e12i	− 0.512065i
$83$	4.01969e12i	1.34954i	0.738030	+	0.674768i	$0.235756\pi$
$83$	4.01969e12i	1.34954i	−0.738030	+	0.674768i	$0.764244\pi$
$84$	−5.07662e11	−0.157674
$85$	0	0
$86$	−2.23450e12	−0.595579
$87$	4.24121e12i	1.04861i
$88$	− 1.59067e12i	− 0.365125i
$89$	2.09375e12	0.446571	0.223285	−	0.974753i	$-0.428322\pi$
$89$	2.09375e12	0.446571	0.223285	+	0.974753i	$0.428322\pi$
$90$	0	0
$91$	5.60138e12	1.03401
$92$	− 3.87905e12i	− 0.666967i
$93$	− 2.76319e12i	− 0.442865i
$94$	3.52001e12	0.526275
$95$	0	0
$96$	−7.82758e11	−0.102062
$97$	− 8.64949e12i	− 1.05432i	−0.849765	−	0.527162i	$-0.823256\pi$
$97$	− 8.64949e12i	− 1.05432i	0.849765	−	0.527162i	$-0.176744\pi$
$98$	− 4.35097e12i	− 0.496154i
$99$	3.22473e12	0.344243
$100$	0	0
$101$	9.92703e12	0.930530	0.465265	−	0.885172i	$-0.345959\pi$
$101$	9.92703e12	0.930530	0.465265	+	0.885172i	$0.345959\pi$
$102$	− 2.37509e12i	− 0.208823i
$103$	− 9.95146e12i	− 0.821192i	−0.911817	−	0.410596i	$-0.865321\pi$
$103$	− 9.95146e12i	− 0.821192i	0.911817	−	0.410596i	$-0.134679\pi$
$104$	8.63670e12	0.669316
$105$	0	0
$106$	2.21646e11	0.0151765
$107$	− 1.03046e13i	− 0.663801i	−0.943314	−	0.331900i	$-0.892310\pi$
$107$	− 1.03046e13i	− 0.663801i	0.943314	−	0.331900i	$-0.107690\pi$
$108$	− 1.58687e12i	− 0.0962250i
$109$	−2.36639e13	−1.35149	−0.675747	−	0.737134i	$-0.736179\pi$
$109$	−2.36639e13	−1.35149	−0.675747	+	0.737134i	$0.736179\pi$
$110$	0	0
$111$	2.07320e13	1.05206
$112$	2.85238e12i	0.136549i
$113$	2.70737e12i	0.122331i	0.998128	+	0.0611656i	$0.0194818\pi$
$113$	2.70737e12i	0.122331i	−0.998128	+	0.0611656i	$0.980518\pi$
$114$	−1.57736e13	−0.673053
$115$	0	0
$116$	2.38299e13	0.908125
$117$	1.75091e13i	0.631037i
$118$	1.79382e13i	0.611709i
$119$	−8.65485e12	−0.279386
$120$	0	0
$121$	2.29677e12	0.0665292
$122$	− 3.38506e13i	− 0.929454i
$123$	− 1.60569e13i	− 0.418099i
$124$	−1.55254e13	−0.383533
$125$	0	0
$126$	−5.78259e12	−0.128740
$127$	6.46305e12i	0.136683i	0.997662	+	0.0683413i	$0.0217707\pi$
$127$	6.46305e12i	0.136683i	−0.997662	+	0.0683413i	$0.978229\pi$
$128$	4.39805e12i	0.0883883i
$129$	−2.54523e13	−0.486289
$130$	0	0
$131$	−8.36401e12	−0.144594	−0.0722972	−	0.997383i	$-0.523033\pi$
$131$	−8.36401e12	−0.144594	−0.0722972	+	0.997383i	$0.523033\pi$
$132$	− 1.81187e13i	− 0.298123i
$133$	5.74791e13i	0.900481i
$134$	−4.80915e11	−0.00717608
$135$	0	0
$136$	−1.33448e13	−0.180846
$137$	− 1.23769e14i	− 1.59930i	−0.600468	−	0.799649i	$-0.705019\pi$
$137$	− 1.23769e14i	− 1.59930i	0.600468	−	0.799649i	$-0.294981\pi$
$138$	− 4.41848e13i	− 0.544577i
$139$	1.98109e13	0.232975	0.116487	−	0.993192i	$-0.462837\pi$
$139$	1.98109e13	0.232975	0.116487	+	0.993192i	$0.462837\pi$
$140$	0	0
$141$	4.00951e13	0.429702
$142$	− 1.17254e13i	− 0.120020i
$143$	1.99916e14i	1.95507i
$144$	−8.91610e12	−0.0833333
$145$	0	0
$146$	−1.41749e14	−1.21123
$147$	− 4.95603e13i	− 0.405108i
$148$	− 1.16486e14i	− 0.911112i
$149$	1.36275e14	1.02024	0.510122	−	0.860102i	$-0.329600\pi$
$149$	1.36275e14	1.02024	0.510122	+	0.860102i	$0.329600\pi$
$150$	0	0
$151$	1.46787e14	1.00771	0.503856	−	0.863788i	$-0.331914\pi$
$151$	1.46787e14	1.00771	0.503856	+	0.863788i	$0.331914\pi$
$152$	8.86264e13i	0.582881i
$153$	− 2.70538e13i	− 0.170504i
$154$	−6.60246e13	−0.398861
$155$	0	0
$156$	9.83775e13	0.546494
$157$	− 2.46869e14i	− 1.31559i	−0.753199	−	0.657793i	$-0.771490\pi$
$157$	− 2.46869e14i	− 1.31559i	0.753199	−	0.657793i	$-0.228510\pi$
$158$	− 4.21548e13i	− 0.215564i
$159$	2.52469e12	0.0123916
$160$	0	0
$161$	−1.61010e14	−0.728592
$162$	− 1.80755e13i	− 0.0785674i
$163$	9.21834e13i	0.384976i	0.981299	+	0.192488i	$0.0616556\pi$
$163$	9.21834e13i	0.384976i	−0.981299	+	0.192488i	$0.938344\pi$
$164$	−9.02184e13	−0.362085
$165$	0	0
$166$	2.57260e14	0.954266
$167$	− 7.83286e13i	− 0.279424i	−0.990192	−	0.139712i	$-0.955382\pi$
$167$	− 7.83286e13i	− 0.279424i	0.990192	−	0.139712i	$-0.0446176\pi$
$168$	3.24904e13i	0.111492i
$169$	−7.82591e14	−2.58387
$170$	0	0
$171$	−1.79671e14	−0.549545
$172$	1.43008e14i	0.421138i
$173$	− 4.49950e14i	− 1.27604i	−0.770020	−	0.638020i	$-0.779754\pi$
$173$	− 4.49950e14i	− 1.27604i	0.770020	−	0.638020i	$-0.220246\pi$
$174$	2.71438e14	0.741481
$175$	0	0
$176$	−1.01803e14	−0.258182
$177$	2.04327e14i	0.499459i
$178$	− 1.34000e14i	− 0.315773i
$179$	1.39179e14	0.316249	0.158124	−	0.987419i	$-0.449455\pi$
$179$	1.39179e14	0.316249	0.158124	+	0.987419i	$0.449455\pi$
$180$	0	0
$181$	−5.20706e14	−1.10073	−0.550367	−	0.834923i	$-0.685512\pi$
$181$	−5.20706e14	−1.10073	−0.550367	+	0.834923i	$0.685512\pi$
$182$	− 3.58488e14i	− 0.731158i
$183$	− 3.85580e14i	− 0.758896i
$184$	−2.48259e14	−0.471617
$185$	0	0
$186$	−1.76844e14	−0.313153
$187$	− 3.08895e14i	− 0.528252i
$188$	− 2.25281e14i	− 0.372133i
$189$	−6.58673e13	−0.105116
$190$	0	0
$191$	1.09463e15	1.63136	0.815682	−	0.578501i	$-0.196362\pi$
$191$	1.09463e15	1.63136	0.815682	+	0.578501i	$0.196362\pi$
$192$	5.00965e13i	0.0721688i
$193$	− 6.26624e14i	− 0.872739i	−0.899767	−	0.436370i	$-0.856264\pi$
$193$	− 6.26624e14i	− 0.872739i	0.899767	−	0.436370i	$-0.143736\pi$
$194$	−5.53567e14	−0.745520
$195$	0	0
$196$	−2.78462e14	−0.350834
$197$	− 3.32275e14i	− 0.405012i	−0.979281	−	0.202506i	$-0.935091\pi$
$197$	− 3.32275e14i	− 0.405012i	0.979281	−	0.202506i	$-0.0649085\pi$
$198$	− 2.06383e14i	− 0.243417i
$199$	−5.22579e13	−0.0596495	−0.0298248	−	0.999555i	$-0.509495\pi$
$199$	−5.22579e13	−0.0596495	−0.0298248	+	0.999555i	$0.509495\pi$
$200$	0	0
$201$	−5.47793e12	−0.00585925
$202$	− 6.35330e14i	− 0.657984i
$203$	− 9.89121e14i	− 0.992031i
$204$	−1.52006e14	−0.147660
$205$	0	0
$206$	−6.36893e14	−0.580670
$207$	− 5.03293e14i	− 0.444645i
$208$	− 5.52749e14i	− 0.473278i
$209$	−2.05145e15	−1.70259
$210$	0	0
$211$	−1.36362e15	−1.06379	−0.531896	−	0.846810i	$-0.678520\pi$
$211$	−1.36362e15	−1.06379	−0.531896	+	0.846810i	$0.678520\pi$
$212$	− 1.41854e13i	− 0.0107314i
$213$	− 1.33560e14i	− 0.0979959i
$214$	−6.59496e14	−0.469378
$215$	0	0
$216$	−1.01560e14	−0.0680414
$217$	6.44422e14i	0.418969i
$218$	1.51449e15i	0.955650i
$219$	−1.61461e15	−0.988963
$220$	0	0
$221$	1.67718e15	0.968347
$222$	− 1.32685e15i	− 0.743920i
$223$	2.47259e15i	1.34639i	0.739464	+	0.673196i	$0.235079\pi$
$223$	2.47259e15i	1.34639i	−0.739464	+	0.673196i	$0.764921\pi$
$224$	1.82552e14	0.0965550
$225$	0	0
$226$	1.73271e14	0.0865012
$227$	− 1.16478e15i	− 0.565034i	−0.959262	−	0.282517i	$-0.908831\pi$
$227$	− 1.16478e15i	− 0.565034i	0.959262	−	0.282517i	$-0.0911693\pi$
$228$	1.00951e15i	0.475920i
$229$	2.63317e15	1.20656	0.603279	−	0.797530i	$-0.293860\pi$
$229$	2.63317e15	1.20656	0.603279	+	0.797530i	$0.293860\pi$
$230$	0	0
$231$	−7.52062e14	−0.325668
$232$	− 1.52511e15i	− 0.642141i
$233$	− 1.81315e15i	− 0.742369i	−0.928559	−	0.371185i	$-0.878952\pi$
$233$	− 1.81315e15i	− 0.742369i	0.928559	−	0.371185i	$-0.121048\pi$
$234$	1.12058e15	0.446211
$235$	0	0
$236$	1.14804e15	0.432544
$237$	− 4.80170e14i	− 0.176007i
$238$	5.53911e14i	0.197556i
$239$	−5.57074e15	−1.93342	−0.966710	−	0.255874i	$-0.917637\pi$
$239$	−5.57074e15	−1.93342	−0.966710	+	0.255874i	$0.917637\pi$
$240$	0	0
$241$	−6.85386e14	−0.225333	−0.112666	−	0.993633i	$-0.535939\pi$
$241$	−6.85386e14	−0.225333	−0.112666	+	0.993633i	$0.535939\pi$
$242$	− 1.46993e14i	− 0.0470433i
$243$	− 2.05891e14i	− 0.0641500i
$244$	−2.16644e15	−0.657223
$245$	0	0
$246$	−1.02764e15	−0.295641
$247$	− 1.11386e16i	− 3.12105i
$248$	9.93627e14i	0.271199i
$249$	2.93035e15	0.779155
$250$	0	0
$251$	7.27308e14	0.183586	0.0917929	−	0.995778i	$-0.470740\pi$
$251$	7.27308e14	0.183586	0.0917929	+	0.995778i	$0.470740\pi$
$252$	3.70085e14i	0.0910329i
$253$	− 5.74651e15i	− 1.37759i
$254$	4.13635e14	0.0966492
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	− 2.83845e14i	− 0.0614491i	−0.999528	−	0.0307245i	$-0.990219\pi$
$257$	− 2.83845e14i	− 0.0614491i	0.999528	−	0.0307245i	$-0.00978147\pi$
$258$	1.62895e15i	0.343858i
$259$	−4.83504e15	−0.995294
$260$	0	0
$261$	3.09184e15	0.605416
$262$	5.35297e14i	0.102244i
$263$	3.35049e15i	0.624303i	0.950032	+	0.312152i	$0.101050\pi$
$263$	3.35049e15i	0.624303i	−0.950032	+	0.312152i	$0.898950\pi$
$264$	−1.15959e15	−0.210805
$265$	0	0
$266$	3.67866e15	0.636736
$267$	− 1.52635e15i	− 0.257828i
$268$	3.07786e13i	0.00507426i
$269$	−7.65805e15	−1.23233	−0.616167	−	0.787615i	$-0.711315\pi$
$269$	−7.65805e15	−1.23233	−0.616167	+	0.787615i	$0.711315\pi$
$270$	0	0
$271$	4.60099e14	0.0705588	0.0352794	−	0.999377i	$-0.488768\pi$
$271$	4.60099e14	0.0705588	0.0352794	+	0.999377i	$0.488768\pi$
$272$	8.54068e14i	0.127878i
$273$	− 4.08341e15i	− 0.596988i
$274$	−7.92124e15	−1.13087
$275$	0	0
$276$	−2.82783e15	−0.385074
$277$	− 7.55123e15i	− 1.00438i	−0.864757	−	0.502191i	$-0.832527\pi$
$277$	− 7.55123e15i	− 1.00438i	0.864757	−	0.502191i	$-0.167473\pi$
$278$	− 1.26790e15i	− 0.164738i
$279$	−2.01437e15	−0.255688
$280$	0	0
$281$	5.96982e15	0.723386	0.361693	−	0.932297i	$-0.382199\pi$
$281$	5.96982e15	0.723386	0.361693	+	0.932297i	$0.382199\pi$
$282$	− 2.56609e15i	− 0.303845i
$283$	− 1.32479e16i	− 1.53297i	−0.642260	−	0.766486i	$-0.722003\pi$
$283$	− 1.32479e16i	− 1.53297i	0.642260	−	0.766486i	$-0.277997\pi$
$284$	−7.50426e14	−0.0848670
$285$	0	0
$286$	1.27946e16	1.38244
$287$	3.74474e15i	0.395539i
$288$	5.70630e14i	0.0589256i
$289$	7.31311e15	0.738357
$290$	0	0
$291$	−6.30548e15	−0.608714
$292$	9.07192e15i	0.856467i
$293$	4.74056e15i	0.437714i	0.975757	+	0.218857i	$0.0702327\pi$
$293$	4.74056e15i	0.437714i	−0.975757	+	0.218857i	$0.929767\pi$
$294$	−3.17186e15	−0.286455
$295$	0	0
$296$	−7.45509e15	−0.644253
$297$	− 2.35083e15i	− 0.198749i
$298$	− 8.72157e15i	− 0.721421i
$299$	3.12014e16	2.52529
$300$	0	0
$301$	5.93590e15	0.460049
$302$	− 9.39435e15i	− 0.712560i
$303$	− 7.23680e15i	− 0.537242i
$304$	5.67209e15	0.412159
$305$	0	0
$306$	−1.73144e15	−0.120564
$307$	− 3.78865e15i	− 0.258276i	−0.991627	−	0.129138i	$-0.958779\pi$
$307$	− 3.78865e15i	− 0.258276i	0.991627	−	0.129138i	$-0.0412211\pi$
$308$	4.22558e15i	0.282037i
$309$	−7.25461e15	−0.474115
$310$	0	0
$311$	1.46650e16	0.919050	0.459525	−	0.888165i	$-0.348020\pi$
$311$	1.46650e16	0.919050	0.459525	+	0.888165i	$0.348020\pi$
$312$	− 6.29616e15i	− 0.386430i
$313$	5.58982e15i	0.336016i	0.985786	+	0.168008i	$0.0537334\pi$
$313$	5.58982e15i	0.336016i	−0.985786	+	0.168008i	$0.946267\pi$
$314$	−1.57996e16	−0.930260
$315$	0	0
$316$	−2.69791e15	−0.152427
$317$	− 1.75354e16i	− 0.970578i	−0.874354	−	0.485289i	$-0.838714\pi$
$317$	− 1.75354e16i	− 0.970578i	0.874354	−	0.485289i	$-0.161286\pi$
$318$	− 1.61580e14i	− 0.00876218i
$319$	3.53022e16	1.87569
$320$	0	0
$321$	−7.51207e15	−0.383246
$322$	1.03046e16i	0.515192i
$323$	1.72106e16i	0.843295i
$324$	−1.15683e15	−0.0555556
$325$	0	0
$326$	5.89974e15	0.272219
$327$	1.72510e16i	0.780285i
$328$	5.77398e15i	0.256032i
$329$	−9.35085e15	−0.406516
$330$	0	0
$331$	−2.66488e16	−1.11377	−0.556886	−	0.830589i	$-0.688004\pi$
$331$	−2.66488e16	−1.11377	−0.556886	+	0.830589i	$0.688004\pi$
$332$	− 1.64646e16i	− 0.674768i
$333$	− 1.51136e16i	− 0.607408i
$334$	−5.01303e15	−0.197582
$335$	0	0
$336$	2.07938e15	0.0788368
$337$	2.82770e16i	1.05157i	0.850617	+	0.525786i	$0.176229\pi$
$337$	2.82770e16i	1.05157i	−0.850617	+	0.525786i	$0.823771\pi$
$338$	5.00858e16i	1.82707i
$339$	1.97367e15	0.0706279
$340$	0	0
$341$	−2.29997e16	−0.792171
$342$	1.14989e16i	0.388587i
$343$	2.80309e16i	0.929447i
$344$	9.15250e15	0.297790
$345$	0	0
$346$	−2.87968e16	−0.902297
$347$	4.37490e16i	1.34532i	0.739950	+	0.672662i	$0.234849\pi$
$347$	4.37490e16i	1.34532i	−0.739950	+	0.672662i	$0.765151\pi$
$348$	− 1.73720e16i	− 0.524306i
$349$	9.77276e15	0.289502	0.144751	−	0.989468i	$-0.453762\pi$
$349$	9.77276e15	0.289502	0.144751	+	0.989468i	$0.453762\pi$
$350$	0	0
$351$	1.27641e16	0.364330
$352$	6.51536e15i	0.182562i
$353$	− 3.36370e16i	− 0.925297i	−0.886542	−	0.462649i	$-0.846899\pi$
$353$	− 3.36370e16i	− 0.925297i	0.886542	−	0.462649i	$-0.153101\pi$
$354$	1.30769e16	0.353171
$355$	0	0
$356$	−8.57601e15	−0.223285
$357$	6.30939e15i	0.161304i
$358$	− 8.90746e15i	− 0.223622i
$359$	5.73427e16	1.41372	0.706861	−	0.707353i	$-0.250111\pi$
$359$	5.73427e16	1.41372	0.706861	+	0.707353i	$0.250111\pi$
$360$	0	0
$361$	7.22470e16	1.71800
$362$	3.33252e16i	0.778336i
$363$	− 1.67434e15i	− 0.0384107i
$364$	−2.29433e16	−0.517007
$365$	0	0
$366$	−2.46771e16	−0.536620
$367$	1.30762e15i	0.0279352i	0.999902	+	0.0139676i	$0.00444617\pi$
$367$	1.30762e15i	0.0279352i	−0.999902	+	0.0139676i	$0.995554\pi$
$368$	1.58886e16i	0.333484i
$369$	−1.17055e16	−0.241390
$370$	0	0
$371$	−5.88800e14	−0.0117230
$372$	1.13180e16i	0.221433i
$373$	− 5.05383e16i	− 0.971658i	−0.874054	−	0.485829i	$-0.838518\pi$
$373$	− 5.05383e16i	− 0.971658i	0.874054	−	0.485829i	$-0.161482\pi$
$374$	−1.97693e16	−0.373531
$375$	0	0
$376$	−1.44180e16	−0.263138
$377$	1.91677e17i	3.43836i
$378$	4.21550e15i	0.0743281i
$379$	−3.58137e16	−0.620719	−0.310359	−	0.950619i	$-0.600449\pi$
$379$	−3.58137e16	−0.620719	−0.310359	+	0.950619i	$0.600449\pi$
$380$	0	0
$381$	4.71156e15	0.0789137
$382$	− 7.00564e16i	− 1.15355i
$383$	1.16220e17i	1.88143i	0.339203	+	0.940713i	$0.389843\pi$
$383$	1.16220e17i	1.88143i	−0.339203	+	0.940713i	$0.610157\pi$
$384$	3.20618e15	0.0510310
$385$	0	0
$386$	−4.01039e16	−0.617120
$387$	1.85547e16i	0.280759i
$388$	3.54283e16i	0.527162i
$389$	−2.44732e16	−0.358112	−0.179056	−	0.983839i	$-0.557304\pi$
$389$	−2.44732e16	−0.358112	−0.179056	+	0.983839i	$0.557304\pi$
$390$	0	0
$391$	−4.82101e16	−0.682322
$392$	1.78216e16i	0.248077i
$393$	6.09736e15i	0.0834816i
$394$	−2.12656e16	−0.286386
$395$	0	0
$396$	−1.32085e16	−0.172122
$397$	7.19607e16i	0.922481i	0.887275	+	0.461240i	$0.152595\pi$
$397$	7.19607e16i	0.922481i	−0.887275	+	0.461240i	$0.847405\pi$
$398$	3.34451e15i	0.0421786i
$399$	4.19023e16	0.519893
$400$	0	0
$401$	2.77695e16	0.333526	0.166763	−	0.985997i	$-0.446669\pi$
$401$	2.77695e16	0.333526	0.166763	+	0.985997i	$0.446669\pi$
$402$	3.50587e14i	0.00414311i
$403$	− 1.24880e17i	− 1.45214i
$404$	−4.06611e16	−0.465265
$405$	0	0
$406$	−6.33038e16	−0.701472
$407$	− 1.72565e17i	− 1.88186i
$408$	9.72837e15i	0.104412i
$409$	1.50306e17	1.58772	0.793859	−	0.608102i	$-0.208069\pi$
$409$	1.50306e17	1.58772	0.793859	+	0.608102i	$0.208069\pi$
$410$	0	0
$411$	−9.02278e16	−0.923355
$412$	4.07612e16i	0.410596i
$413$	− 4.76525e16i	− 0.472509i
$414$	−3.22107e16	−0.314411
$415$	0	0
$416$	−3.53759e16	−0.334658
$417$	− 1.44422e16i	− 0.134508i
$418$	1.31293e17i	1.20392i
$419$	9.26732e16	0.836687	0.418343	−	0.908289i	$-0.362611\pi$
$419$	9.26732e16	0.836687	0.418343	+	0.908289i	$0.362611\pi$
$420$	0	0
$421$	4.68568e16	0.410146	0.205073	−	0.978747i	$-0.434257\pi$
$421$	4.68568e16	0.410146	0.205073	+	0.978747i	$0.434257\pi$
$422$	8.72715e16i	0.752214i
$423$	− 2.92293e16i	− 0.248088i
$424$	−9.07864e14	−0.00758827
$425$	0	0
$426$	−8.54782e15	−0.0692936
$427$	8.99236e16i	0.717947i
$428$	4.22078e16i	0.331900i
$429$	1.45739e17	1.12876
$430$	0	0
$431$	2.33764e17	1.75661	0.878304	−	0.478103i	$-0.158676\pi$
$431$	2.33764e17	1.75661	0.878304	+	0.478103i	$0.158676\pi$
$432$	6.49984e15i	0.0481125i
$433$	1.57411e17i	1.14779i	0.818927	+	0.573897i	$0.194569\pi$
$433$	1.57411e17i	1.14779i	−0.818927	+	0.573897i	$0.805431\pi$
$434$	4.12430e16	0.296256
$435$	0	0
$436$	9.69273e16	0.675747
$437$	3.20176e17i	2.19917i
$438$	1.03335e17i	0.699302i
$439$	2.21873e17	1.47940	0.739698	−	0.672939i	$-0.234968\pi$
$439$	2.21873e17	1.47940	0.739698	+	0.672939i	$0.234968\pi$
$440$	0	0
$441$	−3.61295e16	−0.233889
$442$	− 1.07340e17i	− 0.684725i
$443$	− 1.42772e17i	− 0.897470i	−0.893665	−	0.448735i	$-0.851875\pi$
$443$	− 1.42772e17i	− 0.897470i	0.893665	−	0.448735i	$-0.148125\pi$
$444$	−8.49181e16	−0.526031
$445$	0	0
$446$	1.58246e17	0.952042
$447$	− 9.93441e16i	− 0.589038i
$448$	− 1.16833e16i	− 0.0682747i
$449$	1.94696e17	1.12139	0.560693	−	0.828024i	$-0.310535\pi$
$449$	1.94696e17	1.12139	0.560693	+	0.828024i	$0.310535\pi$
$450$	0	0
$451$	−1.33652e17	−0.747871
$452$	− 1.10894e16i	− 0.0611656i
$453$	− 1.07007e17i	− 0.581803i
$454$	−7.45457e16	−0.399539
$455$	0	0
$456$	6.46086e16	0.336526
$457$	− 2.06061e17i	− 1.05813i	−0.848580	−	0.529067i	$-0.822542\pi$
$457$	− 2.06061e17i	− 1.05813i	0.848580	−	0.529067i	$-0.177458\pi$
$458$	− 1.68523e17i	− 0.853166i
$459$	−1.97222e16	−0.0984403
$460$	0	0
$461$	−3.50887e17	−1.70260	−0.851298	−	0.524682i	$-0.824184\pi$
$461$	−3.50887e17	−1.70260	−0.851298	+	0.524682i	$0.824184\pi$
$462$	4.81319e16i	0.230282i
$463$	− 3.11707e16i	− 0.147052i	−0.997293	−	0.0735259i	$-0.976575\pi$
$463$	− 3.11707e16i	− 0.147052i	0.997293	−	0.0735259i	$-0.0234252\pi$
$464$	−9.76073e16	−0.454062
$465$	0	0
$466$	−1.16042e17	−0.524934
$467$	− 3.16096e17i	− 1.41013i	−0.709141	−	0.705066i	$-0.750917\pi$
$467$	− 3.16096e17i	− 1.41013i	0.709141	−	0.705066i	$-0.249083\pi$
$468$	− 7.17172e16i	− 0.315519i
$469$	1.27754e15	0.00554309
$470$	0	0
$471$	−1.79968e17	−0.759554
$472$	− 7.34748e16i	− 0.305855i
$473$	2.11855e17i	0.869843i
$474$	−3.07309e16	−0.124456
$475$	0	0
$476$	3.54503e16	0.139693
$477$	− 1.84050e15i	− 0.00715429i
$478$	3.56527e17i	1.36713i
$479$	−7.59224e16	−0.287203	−0.143601	−	0.989636i	$-0.545868\pi$
$479$	−7.59224e16	−0.287203	−0.143601	+	0.989636i	$0.545868\pi$
$480$	0	0
$481$	9.36960e17	3.44967
$482$	4.38647e16i	0.159334i
$483$	1.17376e17i	0.420653i
$484$	−9.40756e15	−0.0332646
$485$	0	0
$486$	−1.31770e16	−0.0453609
$487$	− 3.20670e17i	− 1.08923i	−0.838686	−	0.544615i	$-0.816676\pi$
$487$	− 3.20670e17i	− 1.08923i	0.838686	−	0.544615i	$-0.183324\pi$
$488$	1.38652e17i	0.464727i
$489$	6.72017e16	0.222266
$490$	0	0
$491$	4.08390e17	1.31536	0.657681	−	0.753296i	$-0.271537\pi$
$491$	4.08390e17	1.31536	0.657681	+	0.753296i	$0.271537\pi$
$492$	6.57692e16i	0.209050i
$493$	− 2.96166e17i	− 0.929031i
$494$	−7.12871e17	−2.20692
$495$	0	0
$496$	6.35921e16	0.191766
$497$	3.11483e16i	0.0927083i
$498$	− 1.87542e17i	− 0.550946i
$499$	2.29462e17	0.665361	0.332680	−	0.943040i	$-0.392047\pi$
$499$	2.29462e17	0.665361	0.332680	+	0.943040i	$0.392047\pi$
$500$	0	0
$501$	−5.71015e16	−0.161325
$502$	− 4.65477e16i	− 0.129815i
$503$	− 6.88434e17i	− 1.89527i	−0.319361	−	0.947633i	$-0.603468\pi$
$503$	− 6.88434e17i	− 1.89527i	0.319361	−	0.947633i	$-0.396532\pi$
$504$	2.36855e16	0.0643700
$505$	0	0
$506$	−3.67777e17	−0.974105
$507$	5.70509e17i	1.49180i
$508$	− 2.64726e16i	− 0.0683413i
$509$	2.88019e17	0.734101	0.367051	−	0.930201i	$-0.380368\pi$
$509$	2.88019e17	0.734101	0.367051	+	0.930201i	$0.380368\pi$
$510$	0	0
$511$	3.76553e17	0.935601
$512$	− 1.80144e16i	− 0.0441942i
$513$	1.30980e17i	0.317280i
$514$	−1.81661e16	−0.0434511
$515$	0	0
$516$	1.04253e17	0.243144
$517$	− 3.33736e17i	− 0.768624i
$518$	3.09442e17i	0.703779i
$519$	−3.28013e17	−0.736722
$520$	0	0
$521$	−3.07194e17	−0.672926	−0.336463	−	0.941697i	$-0.609231\pi$
$521$	−3.07194e17	−0.672926	−0.336463	+	0.941697i	$0.609231\pi$
$522$	− 1.97878e17i	− 0.428094i
$523$	− 5.25192e17i	− 1.12217i	−0.827760	−	0.561083i	$-0.810385\pi$
$523$	− 5.25192e17i	− 1.12217i	0.827760	−	0.561083i	$-0.189615\pi$
$524$	3.42590e16	0.0722972
$525$	0	0
$526$	2.14431e17	0.441449
$527$	1.92955e17i	0.392362i
$528$	7.42141e16i	0.149062i
$529$	−3.92837e17	−0.779382
$530$	0	0
$531$	1.48954e17	0.288363
$532$	− 2.35434e17i	− 0.450240i
$533$	− 7.25677e17i	− 1.37093i
$534$	−9.76861e16	−0.182312
$535$	0	0
$536$	1.96983e15	0.00358804
$537$	− 1.01462e17i	− 0.182586i
$538$	4.90115e17i	0.871392i
$539$	−4.12520e17	−0.724633
$540$	0	0
$541$	−6.85158e16	−0.117492	−0.0587460	−	0.998273i	$-0.518710\pi$
$541$	−6.85158e16	−0.117492	−0.0587460	+	0.998273i	$0.518710\pi$
$542$	− 2.94463e16i	− 0.0498926i
$543$	3.79595e17i	0.635509i
$544$	5.46604e16	0.0904232
$545$	0	0
$546$	−2.61338e17	−0.422134
$547$	− 7.30717e17i	− 1.16636i	−0.812344	−	0.583179i	$-0.801809\pi$
$547$	− 7.30717e17i	− 1.16636i	0.812344	−	0.583179i	$-0.198191\pi$
$548$	5.06959e17i	0.799649i
$549$	−2.81088e17	−0.438149
$550$	0	0
$551$	−1.96691e18	−2.99433
$552$	1.80981e17i	0.272288i
$553$	1.11984e17i	0.166510i
$554$	−4.83279e17	−0.710206
$555$	0	0
$556$	−8.11456e16	−0.116487
$557$	− 1.23097e18i	− 1.74658i	−0.487199	−	0.873291i	$-0.661981\pi$
$557$	− 1.23097e18i	− 1.74658i	0.487199	−	0.873291i	$-0.338019\pi$
$558$	1.28919e17i	0.180799i
$559$	−1.15029e18	−1.59452
$560$	0	0
$561$	−2.25185e17	−0.304986
$562$	− 3.82069e17i	− 0.511511i
$563$	− 4.06336e16i	− 0.0537751i	−0.999638	−	0.0268876i	$-0.991440\pi$
$563$	− 4.06336e16i	− 0.0537751i	0.999638	−	0.0268876i	$-0.00855960\pi$
$564$	−1.64230e17	−0.214851
$565$	0	0
$566$	−8.47864e17	−1.08398
$567$	4.80172e16i	0.0606886i
$568$	4.80273e16i	0.0600100i
$569$	2.95112e17	0.364550	0.182275	−	0.983248i	$-0.441654\pi$
$569$	2.95112e17	0.364550	0.182275	+	0.983248i	$0.441654\pi$
$570$	0	0
$571$	1.05610e18	1.27518	0.637590	−	0.770376i	$-0.279932\pi$
$571$	1.05610e18	1.27518	0.637590	+	0.770376i	$0.279932\pi$
$572$	− 8.18855e17i	− 0.977536i
$573$	− 7.97986e17i	− 0.941868i
$574$	2.39664e17	0.279689
$575$	0	0
$576$	3.65203e16	0.0416667
$577$	5.39539e17i	0.608667i	0.952566	+	0.304334i	$0.0984338\pi$
$577$	5.39539e17i	0.608667i	−0.952566	+	0.304334i	$0.901566\pi$
$578$	− 4.68039e17i	− 0.522097i
$579$	−4.56809e17	−0.503876
$580$	0	0
$581$	−6.83406e17	−0.737113
$582$	4.03550e17i	0.430426i
$583$	− 2.10145e16i	− 0.0221653i
$584$	5.80603e17	0.605614
$585$	0	0
$586$	3.03396e17	0.309510
$587$	− 8.49866e16i	− 0.0857438i	−0.999081	−	0.0428719i	$-0.986349\pi$
$587$	− 8.49866e16i	− 0.0857438i	0.999081	−	0.0428719i	$-0.0136507\pi$
$588$	2.02999e17i	0.202554i
$589$	1.28146e18	1.26461
$590$	0	0
$591$	−2.42229e17	−0.233834
$592$	4.77126e17i	0.455556i
$593$	4.33934e17i	0.409796i	0.978783	+	0.204898i	$0.0656863\pi$
$593$	4.33934e17i	0.409796i	−0.978783	+	0.204898i	$0.934314\pi$
$594$	−1.50453e17	−0.140537
$595$	0	0
$596$	−5.58180e17	−0.510122
$597$	3.80960e16i	0.0344387i
$598$	− 1.99689e18i	− 1.78565i
$599$	−1.08180e18	−0.956909	−0.478455	−	0.878112i	$-0.658803\pi$
$599$	−1.08180e18	−0.956909	−0.478455	+	0.878112i	$0.658803\pi$
$600$	0	0
$601$	8.22862e17	0.712267	0.356134	−	0.934435i	$-0.384095\pi$
$601$	8.22862e17	0.712267	0.356134	+	0.934435i	$0.384095\pi$
$602$	− 3.79898e17i	− 0.325304i
$603$	3.99341e15i	0.00338284i
$604$	−6.01238e17	−0.503856
$605$	0	0
$606$	−4.63155e17	−0.379887
$607$	− 6.79810e17i	− 0.551647i	−0.961208	−	0.275823i	$-0.911049\pi$
$607$	− 6.79810e17i	− 0.551647i	0.961208	−	0.275823i	$-0.0889505\pi$
$608$	− 3.63014e17i	− 0.291440i
$609$	−7.21069e17	−0.572749
$610$	0	0
$611$	1.81206e18	1.40898
$612$	1.10812e17i	0.0852518i
$613$	9.66682e17i	0.735852i	0.929855	+	0.367926i	$0.119932\pi$
$613$	9.66682e17i	0.735852i	−0.929855	+	0.367926i	$0.880068\pi$
$614$	−2.42473e17	−0.182629
$615$	0	0
$616$	2.70437e17	0.199430
$617$	7.79322e17i	0.568674i	0.958724	+	0.284337i	$0.0917734\pi$
$617$	7.79322e17i	0.568674i	−0.958724	+	0.284337i	$0.908227\pi$
$618$	4.64295e17i	0.335250i
$619$	1.30527e18	0.932636	0.466318	−	0.884617i	$-0.345580\pi$
$619$	1.30527e18	0.932636	0.466318	+	0.884617i	$0.345580\pi$
$620$	0	0
$621$	−3.66900e17	−0.256716
$622$	− 9.38559e17i	− 0.649866i
$623$	3.55969e17i	0.243916i
$624$	−4.02954e17	−0.273247
$625$	0	0
$626$	3.57749e17	0.237599
$627$	1.49551e18i	0.982993i
$628$	1.01118e18i	0.657793i
$629$	−1.44772e18	−0.932087
$630$	0	0
$631$	2.48848e18	1.56944	0.784718	−	0.619853i	$-0.212808\pi$
$631$	2.48848e18	1.56944	0.784718	+	0.619853i	$0.212808\pi$
$632$	1.72666e17i	0.107782i
$633$	9.94077e17i	0.614180i
$634$	−1.12227e18	−0.686302
$635$	0	0
$636$	−1.03411e16	−0.00619579
$637$	− 2.23983e18i	− 1.32834i
$638$	− 2.25934e18i	− 1.32632i
$639$	−9.73650e16	−0.0565780
$640$	0	0
$641$	−1.11455e18	−0.634634	−0.317317	−	0.948320i	$-0.602782\pi$
$641$	−1.11455e18	−0.634634	−0.317317	+	0.948320i	$0.602782\pi$
$642$	4.80773e17i	0.270995i
$643$	− 1.21634e18i	− 0.678710i	−0.940658	−	0.339355i	$-0.889791\pi$
$643$	− 1.21634e18i	− 0.678710i	0.940658	−	0.339355i	$-0.110209\pi$
$644$	6.59496e17	0.364296
$645$	0	0
$646$	1.10148e18	0.596299
$647$	3.56728e18i	1.91188i	0.293567	+	0.955939i	$0.405158\pi$
$647$	3.56728e18i	1.91188i	−0.293567	+	0.955939i	$0.594842\pi$
$648$	7.40372e16i	0.0392837i
$649$	1.70074e18	0.893401
$650$	0	0
$651$	4.69784e17	0.241892
$652$	− 3.77583e17i	− 0.192488i
$653$	− 1.05284e18i	− 0.531408i	−0.964055	−	0.265704i	$-0.914396\pi$
$653$	− 1.05284e18i	− 0.531408i	0.964055	−	0.265704i	$-0.0856043\pi$
$654$	1.10406e18	0.551745
$655$	0	0
$656$	3.69535e17	0.181042
$657$	1.17705e18i	0.570978i
$658$	5.98454e17i	0.287450i
$659$	1.06619e18	0.507085	0.253542	−	0.967324i	$-0.418404\pi$
$659$	1.06619e18	0.507085	0.253542	+	0.967324i	$0.418404\pi$
$660$	0	0
$661$	−3.83025e17	−0.178615	−0.0893075	−	0.996004i	$-0.528465\pi$
$661$	−3.83025e17	−0.178615	−0.0893075	+	0.996004i	$0.528465\pi$
$662$	1.70553e18i	0.787556i
$663$	− 1.22267e18i	− 0.559076i
$664$	−1.05374e18	−0.477133
$665$	0	0
$666$	−9.67270e17	−0.429502
$667$	− 5.50970e18i	− 2.42276i
$668$	3.20834e17i	0.139712i
$669$	1.80252e18	0.777339
$670$	0	0
$671$	−3.20941e18	−1.35747
$672$	− 1.33081e17i	− 0.0557461i
$673$	3.12295e18i	1.29559i	0.761816	+	0.647793i	$0.224308\pi$
$673$	3.12295e18i	1.29559i	−0.761816	+	0.647793i	$0.775692\pi$
$674$	1.80973e18	0.743573
$675$	0	0
$676$	3.20549e18	1.29194
$677$	1.03569e18i	0.413431i	0.978401	+	0.206716i	$0.0662775\pi$
$677$	1.03569e18i	0.413431i	−0.978401	+	0.206716i	$0.933723\pi$
$678$	− 1.26315e17i	− 0.0499415i
$679$	1.47054e18	0.575869
$680$	0	0
$681$	−8.49122e17	−0.326222
$682$	1.47198e18i	0.560149i
$683$	− 2.86963e18i	− 1.08166i	−0.841131	−	0.540831i	$-0.818110\pi$
$683$	− 2.86963e18i	− 1.08166i	0.841131	−	0.540831i	$-0.181890\pi$
$684$	7.35933e17	0.274773
$685$	0	0
$686$	1.79398e18	0.657218
$687$	− 1.91958e18i	− 0.696607i
$688$	− 5.85760e17i	− 0.210569i
$689$	1.14101e17	0.0406316
$690$	0	0
$691$	1.70272e18	0.595026	0.297513	−	0.954718i	$-0.403843\pi$
$691$	1.70272e18	0.595026	0.297513	+	0.954718i	$0.403843\pi$
$692$	1.84299e18i	0.638020i
$693$	5.48253e17i	0.188025i
$694$	2.79994e18	0.951288
$695$	0	0
$696$	−1.11181e18	−0.370740
$697$	1.12126e18i	0.370420i
$698$	− 6.25457e17i	− 0.204709i
$699$	−1.32179e18	−0.428607
$700$	0	0
$701$	−1.89524e18	−0.603249	−0.301624	−	0.953427i	$-0.597529\pi$
$701$	−1.89524e18	−0.603249	−0.301624	+	0.953427i	$0.597529\pi$
$702$	− 8.16903e17i	− 0.257620i
$703$	9.61470e18i	3.00418i
$704$	4.16983e17	0.129091
$705$	0	0
$706$	−2.15277e18	−0.654284
$707$	1.68774e18i	0.508253i
$708$	− 8.36923e17i	− 0.249729i
$709$	1.81610e18	0.536957	0.268479	−	0.963286i	$-0.413479\pi$
$709$	1.81610e18	0.536957	0.268479	+	0.963286i	$0.413479\pi$
$710$	0	0
$711$	−3.50044e17	−0.101618
$712$	5.48864e17i	0.157887i
$713$	3.58962e18i	1.02322i
$714$	4.03801e17	0.114059
$715$	0	0
$716$	−5.70077e17	−0.158124
$717$	4.06107e18i	1.11626i
$718$	− 3.66993e18i	− 0.999652i
$719$	−4.07912e18	−1.10110	−0.550552	−	0.834801i	$-0.685583\pi$
$719$	−4.07912e18	−1.10110	−0.550552	+	0.834801i	$0.685583\pi$
$720$	0	0
$721$	1.69190e18	0.448533
$722$	− 4.62381e18i	− 1.21481i
$723$	4.99646e17i	0.130096i
$724$	2.13281e18	0.550367
$725$	0	0
$726$	−1.07158e17	−0.0271604
$727$	− 3.30463e18i	− 0.830136i	−0.909790	−	0.415068i	$-0.863758\pi$
$727$	− 3.30463e18i	− 0.830136i	0.909790	−	0.415068i	$-0.136242\pi$
$728$	1.46837e18i	0.365579i
$729$	−1.50095e17	−0.0370370
$730$	0	0
$731$	1.77735e18	0.430833
$732$	1.57934e18i	0.379448i
$733$	2.10951e18i	0.502350i	0.967942	+	0.251175i	$0.0808169\pi$
$733$	2.10951e18i	0.502350i	−0.967942	+	0.251175i	$0.919183\pi$
$734$	8.36876e16	0.0197532
$735$	0	0
$736$	1.01687e18	0.235809
$737$	4.55961e16i	0.0104807i
$738$	7.49152e17i	0.170688i
$739$	−3.64707e18	−0.823673	−0.411837	−	0.911258i	$-0.635113\pi$
$739$	−3.64707e18	−0.823673	−0.411837	+	0.911258i	$0.635113\pi$
$740$	0	0
$741$	−8.12005e18	−1.80194
$742$	3.76832e16i	0.00828939i
$743$	− 4.43149e18i	− 0.966324i	−0.875531	−	0.483162i	$-0.839488\pi$
$743$	− 4.43149e18i	− 0.966324i	0.875531	−	0.483162i	$-0.160512\pi$
$744$	7.24354e17	0.156577
$745$	0	0
$746$	−3.23445e18	−0.687066
$747$	− 2.13623e18i	− 0.449845i
$748$	1.26524e18i	0.264126i
$749$	1.75194e18	0.362566
$750$	0	0
$751$	4.80237e18	0.976779	0.488389	−	0.872626i	$-0.337585\pi$
$751$	4.80237e18	0.976779	0.488389	+	0.872626i	$0.337585\pi$
$752$	9.22749e17i	0.186066i
$753$	− 5.30207e17i	− 0.105993i
$754$	1.22673e19	2.43129
$755$	0	0
$756$	2.69792e17	0.0525579
$757$	5.04669e18i	0.974729i	0.873199	+	0.487364i	$0.162042\pi$
$757$	5.04669e18i	0.974729i	−0.873199	+	0.487364i	$0.837958\pi$
$758$	2.29208e18i	0.438914i
$759$	−4.18921e18	−0.795354
$760$	0	0
$761$	1.68626e18	0.314720	0.157360	−	0.987541i	$-0.449702\pi$
$761$	1.68626e18	0.314720	0.157360	+	0.987541i	$0.449702\pi$
$762$	− 3.01540e17i	− 0.0558004i
$763$	− 4.02322e18i	− 0.738183i
$764$	−4.48361e18	−0.815682
$765$	0	0
$766$	7.43805e18	1.33037
$767$	9.23435e18i	1.63771i
$768$	− 2.05195e17i	− 0.0360844i
$769$	−1.11315e18	−0.194104	−0.0970519	−	0.995279i	$-0.530941\pi$
$769$	−1.11315e18	−0.194104	−0.0970519	+	0.995279i	$0.530941\pi$
$770$	0	0
$771$	−2.06923e17	−0.0354777
$772$	2.56665e18i	0.436370i
$773$	9.65963e18i	1.62852i	0.580499	+	0.814261i	$0.302858\pi$
$773$	9.65963e18i	1.62852i	−0.580499	+	0.814261i	$0.697142\pi$
$774$	1.18750e18	0.198526
$775$	0	0
$776$	2.26741e18	0.372760
$777$	3.52474e18i	0.574633i
$778$	1.56629e18i	0.253223i
$779$	7.44660e18	1.19389
$780$	0	0
$781$	−1.11170e18	−0.175289
$782$	3.08545e18i	0.482474i
$783$	− 2.25395e18i	− 0.349537i
$784$	1.14058e18	0.175417
$785$	0	0
$786$	3.90231e17	0.0590304
$787$	1.40037e18i	0.210091i	0.994467	+	0.105045i	$0.0334988\pi$
$787$	1.40037e18i	0.210091i	−0.994467	+	0.105045i	$0.966501\pi$
$788$	1.36100e18i	0.202506i
$789$	2.44251e18	0.360442
$790$	0	0
$791$	−4.60293e17	−0.0668170
$792$	8.45345e17i	0.121708i
$793$	− 1.74259e19i	− 2.48839i
$794$	4.60549e18	0.652292
$795$	0	0
$796$	2.14048e17	0.0298248
$797$	9.30010e18i	1.28531i	0.766155	+	0.642656i	$0.222168\pi$
$797$	9.30010e18i	1.28531i	−0.766155	+	0.642656i	$0.777832\pi$
$798$	− 2.68175e18i	− 0.367620i
$799$	−2.79986e18	−0.380700
$800$	0	0
$801$	−1.11271e18	−0.148857
$802$	− 1.77725e18i	− 0.235838i
$803$	1.34393e19i	1.76900i
$804$	2.24376e16	0.00292962
$805$	0	0
$806$	−7.99230e18	−1.02682
$807$	5.58272e18i	0.711488i
$808$	2.60231e18i	0.328992i
$809$	−3.89357e18	−0.488296	−0.244148	−	0.969738i	$-0.578508\pi$
$809$	−3.89357e18	−0.488296	−0.244148	+	0.969738i	$0.578508\pi$
$810$	0	0
$811$	−1.53890e19	−1.89922	−0.949610	−	0.313434i	$-0.898521\pi$
$811$	−1.53890e19	−1.89922	−0.949610	+	0.313434i	$0.898521\pi$
$812$	4.05144e18i	0.496016i
$813$	− 3.35412e17i	− 0.0407371i
$814$	−1.10441e19	−1.33068
$815$	0	0
$816$	6.22616e17	0.0738302
$817$	− 1.18038e19i	− 1.38861i
$818$	− 9.61955e18i	− 1.12269i
$819$	−2.97680e18	−0.344671
$820$	0	0
$821$	3.58141e18	0.408153	0.204077	−	0.978955i	$-0.434581\pi$
$821$	3.58141e18	0.408153	0.204077	+	0.978955i	$0.434581\pi$
$822$	5.77458e18i	0.652911i
$823$	8.98746e18i	1.00818i	0.863651	+	0.504090i	$0.168172\pi$
$823$	8.98746e18i	1.00818i	−0.863651	+	0.504090i	$0.831828\pi$
$824$	2.60871e18	0.290335
$825$	0	0
$826$	−3.04976e18	−0.334114
$827$	1.73077e18i	0.188129i	0.995566	+	0.0940643i	$0.0299859\pi$
$827$	1.73077e18i	0.188129i	−0.995566	+	0.0940643i	$0.970014\pi$
$828$	2.06149e18i	0.222322i
$829$	−7.78822e18	−0.833362	−0.416681	−	0.909053i	$-0.636807\pi$
$829$	−7.78822e18	−0.833362	−0.416681	+	0.909053i	$0.636807\pi$
$830$	0	0
$831$	−5.50485e18	−0.579881
$832$	2.26406e18i	0.236639i
$833$	3.46082e18i	0.358911i
$834$	−9.24299e17	−0.0951116
$835$	0	0
$836$	8.40276e18	0.851297
$837$	1.46847e18i	0.147622i
$838$	− 5.93108e18i	− 0.591627i
$839$	3.26310e18	0.322981	0.161491	−	0.986874i	$-0.448370\pi$
$839$	3.26310e18	0.322981	0.161491	+	0.986874i	$0.448370\pi$
$840$	0	0
$841$	2.35867e19	2.29876
$842$	− 2.99883e18i	− 0.290017i
$843$	− 4.35200e18i	− 0.417647i
$844$	5.58538e18	0.531896
$845$	0	0
$846$	−1.87068e18	−0.175425
$847$	3.90485e17i	0.0363381i
$848$	5.81033e16i	0.00536571i
$849$	−9.65770e18	−0.885062
$850$	0	0
$851$	−2.69326e19	−2.43073
$852$	5.47061e17i	0.0489980i
$853$	− 5.82090e18i	− 0.517394i	−0.965958	−	0.258697i	$-0.916707\pi$
$853$	− 5.82090e18i	− 0.517394i	0.965958	−	0.258697i	$-0.0832932\pi$
$854$	5.75511e18	0.507666
$855$	0	0
$856$	2.70130e18	0.234689
$857$	− 9.30539e18i	− 0.802342i	−0.916003	−	0.401171i	$-0.868603\pi$
$857$	− 9.30539e18i	− 0.802342i	0.916003	−	0.401171i	$-0.131397\pi$
$858$	− 9.32727e18i	− 0.798155i
$859$	1.20727e19	1.02530	0.512649	−	0.858598i	$-0.328664\pi$
$859$	1.20727e19	1.02530	0.512649	+	0.858598i	$0.328664\pi$
$860$	0	0
$861$	2.72992e18	0.228365
$862$	− 1.49609e19i	− 1.24211i
$863$	6.75985e18i	0.557015i	0.960434	+	0.278508i	$0.0898397\pi$
$863$	6.75985e18i	0.557015i	−0.960434	+	0.278508i	$0.910160\pi$
$864$	4.15990e17	0.0340207
$865$	0	0
$866$	1.00743e19	0.811613
$867$	− 5.33126e18i	− 0.426290i
$868$	− 2.63955e18i	− 0.209485i
$869$	−3.99674e18	−0.314831
$870$	0	0
$871$	−2.47569e17	−0.0192123
$872$	− 6.20335e18i	− 0.477825i
$873$	4.59669e18i	0.351441i
$874$	2.04913e19	1.55505
$875$	0	0
$876$	6.61343e18	0.494482
$877$	− 6.38272e18i	− 0.473706i	−0.971546	−	0.236853i	$-0.923884\pi$
$877$	− 6.38272e18i	− 0.473706i	0.971546	−	0.236853i	$-0.0761159\pi$
$878$	− 1.41998e19i	− 1.04609i
$879$	3.45587e18	0.252714
$880$	0	0
$881$	−1.38731e19	−0.999609	−0.499804	−	0.866138i	$-0.666595\pi$
$881$	−1.38731e19	−0.999609	−0.499804	+	0.866138i	$0.666595\pi$
$882$	2.31228e18i	0.165385i
$883$	6.03335e18i	0.428365i	0.976794	+	0.214183i	$0.0687087\pi$
$883$	6.03335e18i	0.428365i	−0.976794	+	0.214183i	$0.931291\pi$
$884$	−6.86975e18	−0.484174
$885$	0	0
$886$	−9.13744e18	−0.634607
$887$	− 1.56332e19i	− 1.07781i	−0.842365	−	0.538907i	$-0.818838\pi$
$887$	− 1.56332e19i	− 1.07781i	0.842365	−	0.538907i	$-0.181162\pi$
$888$	5.43476e18i	0.371960i
$889$	−1.09881e18	−0.0746557
$890$	0	0
$891$	−1.71376e18	−0.114748
$892$	− 1.01277e19i	− 0.673196i
$893$	1.85946e19i	1.22702i
$894$	−6.35802e18	−0.416513
$895$	0	0
$896$	−7.47734e17	−0.0482775
$897$	− 2.27458e19i	− 1.45798i
$898$	− 1.24605e19i	− 0.792940i
$899$	−2.20519e19	−1.39318
$900$	0	0
$901$	−1.76300e17	−0.0109785
$902$	8.55370e18i	0.528824i
$903$	− 4.32727e18i	− 0.265610i
$904$	−7.09720e17	−0.0432506
$905$	0	0
$906$	−6.84848e18	−0.411397
$907$	− 1.67708e19i	− 1.00025i	−0.865954	−	0.500123i	$-0.833288\pi$
$907$	− 1.67708e19i	− 1.00025i	0.865954	−	0.500123i	$-0.166712\pi$
$908$	4.77092e18i	0.282517i
$909$	−5.27563e18	−0.310177
$910$	0	0
$911$	1.90416e19	1.10366	0.551828	−	0.833958i	$-0.313930\pi$
$911$	1.90416e19	1.10366	0.551828	+	0.833958i	$0.313930\pi$
$912$	− 4.13495e18i	− 0.237960i
$913$	− 2.43911e19i	− 1.39370i
$914$	−1.31879e19	−0.748213
$915$	0	0
$916$	−1.07855e19	−0.603279
$917$	− 1.42201e18i	− 0.0789771i
$918$	1.26222e18i	0.0696078i
$919$	1.55602e19	0.852050	0.426025	−	0.904711i	$-0.359914\pi$
$919$	1.55602e19	0.852050	0.426025	+	0.904711i	$0.359914\pi$
$920$	0	0
$921$	−2.76192e18	−0.149116
$922$	2.24568e19i	1.20392i
$923$	− 6.03609e18i	− 0.321325i
$924$	3.08044e18	0.162834
$925$	0	0
$926$	−1.99493e18	−0.103981
$927$	5.28861e18i	0.273731i
$928$	6.24687e18i	0.321071i
$929$	−2.03127e19	−1.03673	−0.518364	−	0.855160i	$-0.673459\pi$
$929$	−2.03127e19	−1.03673	−0.518364	+	0.855160i	$0.673459\pi$
$930$	0	0
$931$	2.29842e19	1.15680
$932$	7.42666e18i	0.371185i
$933$	− 1.06908e19i	− 0.530614i
$934$	−2.02302e19	−0.997114
$935$	0	0
$936$	−4.58990e18	−0.223105
$937$	3.27979e19i	1.58321i	0.611033	+	0.791605i	$0.290754\pi$
$937$	3.27979e19i	1.58321i	−0.611033	+	0.791605i	$0.709246\pi$
$938$	− 8.17628e16i	− 0.00391956i
$939$	4.07498e18	0.193999
$940$	0	0
$941$	2.39618e19	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$941$	2.39618e19	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$942$	1.15179e19i	0.537086i
$943$	2.08593e19i	0.965994i
$944$	−4.70238e18	−0.216272
$945$	0	0
$946$	1.35587e19	0.615072
$947$	− 1.88259e19i	− 0.848166i	−0.905623	−	0.424083i	$-0.860597\pi$
$947$	− 1.88259e19i	− 0.848166i	0.905623	−	0.424083i	$-0.139403\pi$
$948$	1.96678e18i	0.0880036i
$949$	−7.29705e19	−3.24278
$950$	0	0
$951$	−1.27833e19	−0.560363
$952$	− 2.26882e18i	− 0.0987778i
$953$	− 1.74009e19i	− 0.752431i	−0.926532	−	0.376215i	$-0.877225\pi$
$953$	− 1.74009e19i	− 0.752431i	0.926532	−	0.376215i	$-0.122775\pi$
$954$	−1.17792e17	−0.00505884
$955$	0	0
$956$	2.28177e19	0.966710
$957$	− 2.57353e19i	− 1.08293i
$958$	4.85903e18i	0.203083i
$959$	2.10426e19	0.873532
$960$	0	0
$961$	−1.00505e19	−0.411611
$962$	− 5.99654e19i	− 2.43929i
$963$	5.47630e18i	0.221267i
$964$	2.80734e18	0.112666
$965$	0	0
$966$	7.51208e18	0.297446
$967$	− 3.44802e19i	− 1.35612i	−0.735007	−	0.678059i	$-0.762821\pi$
$967$	− 3.44802e19i	− 1.35612i	0.735007	−	0.678059i	$-0.237179\pi$
$968$	6.02084e17i	0.0235216i
$969$	1.25465e19	0.486877
$970$	0	0
$971$	4.55517e19	1.74413	0.872067	−	0.489387i	$-0.162780\pi$
$971$	4.55517e19	1.74413	0.872067	+	0.489387i	$0.162780\pi$
$972$	8.43330e17i	0.0320750i
$973$	3.36816e18i	0.127250i
$974$	−2.05229e19	−0.770202
$975$	0	0
$976$	8.87374e18	0.328612
$977$	3.55127e19i	1.30638i	0.757194	+	0.653189i	$0.226569\pi$
$977$	3.55127e19i	1.30638i	−0.757194	+	0.653189i	$0.773431\pi$
$978$	− 4.30091e18i	− 0.157166i
$979$	−1.27047e19	−0.461186
$980$	0	0
$981$	1.25760e19	0.450498
$982$	− 2.61370e19i	− 0.930102i
$983$	− 5.22615e19i	− 1.84750i	−0.382998	−	0.923749i	$-0.625108\pi$
$983$	− 5.22615e19i	− 1.84750i	0.382998	−	0.923749i	$-0.374892\pi$
$984$	4.20923e18	0.147820
$985$	0	0
$986$	−1.89546e19	−0.656924
$987$	6.81677e18i	0.234702i
$988$	4.56238e19i	1.56053i
$989$	3.30647e19	1.12354
$990$	0	0
$991$	−2.90393e18	−0.0973885	−0.0486943	−	0.998814i	$-0.515506\pi$
$991$	−2.90393e18	−0.0973885	−0.0486943	+	0.998814i	$0.515506\pi$
$992$	− 4.06990e18i	− 0.135599i
$993$	1.94270e19i	0.643036i
$994$	1.99349e18	0.0655546
$995$	0	0
$996$	−1.20027e19	−0.389577
$997$	− 1.88720e19i	− 0.608555i	−0.952583	−	0.304278i	$-0.901585\pi$
$997$	− 1.88720e19i	− 0.608555i	0.952583	−	0.304278i	$-0.0984151\pi$
$998$	− 1.46856e19i	− 0.470481i
$999$	−1.10178e19	−0.350687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.14.c.j.49.2		4
5.2	odd	4		150.14.a.n.1.1		2
5.3	odd	4		30.14.a.g.1.2	✓	2
5.4	even	2	inner	150.14.c.j.49.3		4
15.8	even	4		90.14.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.14.a.g.1.2	✓	2	5.3	odd	4
90.14.a.m.1.2		2	15.8	even	4
150.14.a.n.1.1		2	5.2	odd	4
150.14.c.j.49.2		4	1.1	even	1	trivial
150.14.c.j.49.3		4	5.4	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-64.0000i q^{2} -729.000i q^{3} -4096.00 q^{4} -46656.0 q^{6} +170015. i q^{7} +262144. i q^{8} -531441. q^{9} -6.06791e6 q^{11} +2.98598e6i q^{12} -3.29464e7i q^{13} +1.08810e7 q^{14} +1.67772e7 q^{16} +5.09064e7i q^{17} +3.40122e7i q^{18} +3.38083e8 q^{19} +1.23941e8 q^{21} +3.88346e8i q^{22} +9.47034e8i q^{23} +1.91103e8 q^{24} -2.10857e9 q^{26} +3.87420e8i q^{27} -6.96381e8i q^{28} -5.81785e9 q^{29} +3.79039e9 q^{31} -1.07374e9i q^{32} +4.42350e9i q^{33} +3.25801e9 q^{34} +2.17678e9 q^{36} +2.84389e10i q^{37} -2.16373e10i q^{38} -2.40179e10 q^{39} +2.20260e10 q^{41} -7.93222e9i q^{42} -3.49140e10i q^{43} +2.48541e10 q^{44} +6.06102e10 q^{46} +5.50002e10i q^{47} -1.22306e10i q^{48} +6.79839e10 q^{49} +3.71108e10 q^{51} +1.34949e11i q^{52} +3.46323e9i q^{53} +2.47949e10 q^{54} -4.45684e10 q^{56} -2.46462e11i q^{57} +3.72342e11i q^{58} -2.80284e11 q^{59} +5.28916e11 q^{61} -2.42585e11i q^{62} -9.03529e10i q^{63} -6.87195e10 q^{64} +2.83104e11 q^{66} -7.51430e9i q^{67} -2.08513e11i q^{68} +6.90388e11 q^{69} +1.83209e11 q^{71} -1.39314e11i q^{72} -2.21482e12i q^{73} +1.82009e12 q^{74} -1.38479e12 q^{76} -1.03163e12i q^{77} +1.53715e12i q^{78} +6.58669e11 q^{79} +2.82430e11 q^{81} -1.40966e12i q^{82} +4.01969e12i q^{83} -5.07662e11 q^{84} -2.23450e12 q^{86} +4.24121e12i q^{87} -1.59067e12i q^{88} +2.09375e12 q^{89} +5.60138e12 q^{91} -3.87905e12i q^{92} -2.76319e12i q^{93} +3.52001e12 q^{94} -7.82758e11 q^{96} -8.64949e12i q^{97} -4.35097e12i q^{98} +3.22473e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16384 q^{4} - 186624 q^{6} - 2125764 q^{9} + 8037120 q^{11} - 30324736 q^{14} + 67108864 q^{16} + 181139296 q^{19} - 345417696 q^{21} + 764411904 q^{24} - 1714062848 q^{26} - 4144620456 q^{29} + 23456813552 q^{31}+ \cdots - 4271255089920 q^{99}+O(q^{100}) \) 4 * q - 16384 * q^4 - 186624 * q^6 - 2125764 * q^9 + 8037120 * q^11 - 30324736 * q^14 + 67108864 * q^16 + 181139296 * q^19 - 345417696 * q^21 + 764411904 * q^24 - 1714062848 * q^26 - 4144620456 * q^29 + 23456813552 * q^31 - 6094726656 * q^34 + 8707129344 * q^36 - 19524247128 * q^39 + 135743136456 * q^41 - 32920043520 * q^44 + 131298585600 * q^46 - 1433143716 * q^49 - 69422745816 * q^51 + 99179645184 * q^54 + 124210118656 * q^56 + 8668692480 * q^59 + 1774823369720 * q^61 - 274877906944 * q^64 - 374979870720 * q^66 + 1495572951600 * q^69 + 1872302664960 * q^71 + 6115692635648 * q^74 - 741946556416 * q^76 + 2497258829488 * q^79 + 1129718145924 * q^81 + 1414830882816 * q^84 - 9934644829184 * q^86 + 16032518338968 * q^89 + 27117915879808 * q^91 + 13683546024960 * q^94 - 3131031158784 * q^96 - 4271255089920 * q^99

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