LMFDB - Embedded newform 150.14.c.d.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 = [2,0,0,-8192,0,-93312,0,0,-1062882,0,13224840] 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:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.14.c.d.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+64.0000i q^{2} +729.000i q^{3} -4096.00 q^{4} -46656.0 q^{6} +176336. i q^{7} -262144. i q^{8} -531441. q^{9} +6.61242e6 q^{11} -2.98598e6i q^{12} +2.40290e7i q^{13} -1.12855e7 q^{14} +1.67772e7 q^{16} -1.54665e8i q^{17} -3.40122e7i q^{18} -1.90035e8 q^{19} -1.28549e8 q^{21} +4.23195e8i q^{22} +3.52958e8i q^{23} +1.91103e8 q^{24} -1.53785e9 q^{26} -3.87420e8i q^{27} -7.22272e8i q^{28} +2.80409e9 q^{29} +2.76366e9 q^{31} +1.07374e9i q^{32} +4.82045e9i q^{33} +9.89856e9 q^{34} +2.17678e9 q^{36} +2.00303e10i q^{37} -1.21622e10i q^{38} -1.75171e10 q^{39} -3.96245e10 q^{41} -8.22713e9i q^{42} +8.14862e10i q^{43} -2.70845e10 q^{44} -2.25893e10 q^{46} -3.41360e10i q^{47} +1.22306e10i q^{48} +6.57946e10 q^{49} +1.12751e11 q^{51} -9.84227e10i q^{52} +2.18108e10i q^{53} +2.47949e10 q^{54} +4.62254e10 q^{56} -1.38535e11i q^{57} +1.79462e11i q^{58} -2.29220e11 q^{59} +9.79974e9 q^{61} +1.76874e11i q^{62} -9.37122e10i q^{63} -6.87195e10 q^{64} -3.08509e11 q^{66} +7.89043e11i q^{67} +6.33508e11i q^{68} -2.57306e11 q^{69} -3.69505e11 q^{71} +1.39314e11i q^{72} +6.93078e11i q^{73} -1.28194e12 q^{74} +7.78383e11 q^{76} +1.16601e12i q^{77} -1.12110e12i q^{78} -2.23131e12 q^{79} +2.82430e11 q^{81} -2.53597e12i q^{82} -2.08433e12i q^{83} +5.26536e11 q^{84} -5.21512e12 q^{86} +2.04418e12i q^{87} -1.73341e12i q^{88} -2.22196e12 q^{89} -4.23717e12 q^{91} -1.44572e12i q^{92} +2.01471e12i q^{93} +2.18471e12 q^{94} -7.82758e11 q^{96} +1.02684e13i q^{97} +4.21086e12i q^{98} -3.51411e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8192 q^{4} - 93312 q^{6} - 1062882 q^{9} + 13224840 q^{11} - 22571008 q^{14} + 33554432 q^{16} - 380069752 q^{19} - 257097888 q^{21} + 382205952 q^{24} - 3075709184 q^{26} + 5608172532 q^{29} + 5527322416 q^{31}+ \cdots - 7028222194440 q^{99}+O(q^{100}) $ 2 * q - 8192 * q^4 - 93312 * q^6 - 1062882 * q^9 + 13224840 * q^11 - 22571008 * q^14 + 33554432 * q^16 - 380069752 * q^19 - 257097888 * q^21 + 382205952 * q^24 - 3075709184 * q^26 + 5608172532 * q^29 + 5527322416 * q^31 + 19797126912 * q^34 + 4353564672 * q^36 - 35034249924 * q^39 - 79249094412 * q^41 - 54168944640 * q^44 - 45178598400 * q^46 + 131589251022 * q^49 + 225501648732 * q^51 + 49589822592 * q^54 + 92450848768 * q^56 - 458439322440 * q^59 + 19599473500 * q^61 - 137438953472 * q^64 - 617018135040 * q^66 - 514612472400 * q^69 - 739009410480 * q^71 - 2563872975616 * q^74 + 1556765704192 * q^76 - 4462619990416 * q^79 + 564859072962 * q^81 + 1053072949248 * q^84 - 10430230380032 * q^86 - 4443922193076 * q^89 - 8474347729216 * q^91 + 4369410232320 * q^94 - 1565515579392 * q^96 - 7028222194440 * 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
$7$	176336.i	0.566505i	0.959045	+	0.283252i	$0.0914134\pi$
$7$	176336.i	0.566505i	−0.959045	+	0.283252i	$0.908587\pi$
$8$	− 262144.i	− 0.353553i
$9$	−531441.	−0.333333
$10$	0	0
$11$	6.61242e6	1.12540	0.562701	−	0.826660i	$-0.309762\pi$
$11$	6.61242e6	1.12540	0.562701	+	0.826660i	$0.309762\pi$
$12$	− 2.98598e6i	− 0.288675i
$13$	2.40290e7i	1.38071i	0.723469	+	0.690357i	$0.242546\pi$
$13$	2.40290e7i	1.38071i	−0.723469	+	0.690357i	$0.757454\pi$
$14$	−1.12855e7	−0.400580
$15$	0	0
$16$	1.67772e7	0.250000
$17$	− 1.54665e8i	− 1.55408i	−0.629449	−	0.777041i	$-0.716719\pi$
$17$	− 1.54665e8i	− 1.55408i	0.629449	−	0.777041i	$-0.283281\pi$
$18$	− 3.40122e7i	− 0.235702i
$19$	−1.90035e8	−0.926691	−0.463345	−	0.886178i	$-0.653351\pi$
$19$	−1.90035e8	−0.926691	−0.463345	+	0.886178i	$0.653351\pi$
$20$	0	0
$21$	−1.28549e8	−0.327072
$22$	4.23195e8i	0.795780i
$23$	3.52958e8i	0.497155i	0.968612	+	0.248578i	$0.0799631\pi$
$23$	3.52958e8i	0.497155i	−0.968612	+	0.248578i	$0.920037\pi$
$24$	1.91103e8	0.204124
$25$	0	0
$26$	−1.53785e9	−0.976312
$27$	− 3.87420e8i	− 0.192450i
$28$	− 7.22272e8i	− 0.283252i
$29$	2.80409e9	0.875396	0.437698	−	0.899122i	$-0.355794\pi$
$29$	2.80409e9	0.875396	0.437698	+	0.899122i	$0.355794\pi$
$30$	0	0
$31$	2.76366e9	0.559286	0.279643	−	0.960104i	$-0.409784\pi$
$31$	2.76366e9	0.559286	0.279643	+	0.960104i	$0.409784\pi$
$32$	1.07374e9i	0.176777i
$33$	4.82045e9i	0.649752i
$34$	9.89856e9	1.09890
$35$	0	0
$36$	2.17678e9	0.166667
$37$	2.00303e10i	1.28344i	0.766939	+	0.641720i	$0.221779\pi$
$37$	2.00303e10i	1.28344i	−0.766939	+	0.641720i	$0.778221\pi$
$38$	− 1.21622e10i	− 0.655269i
$39$	−1.75171e10	−0.797155
$40$	0	0
$41$	−3.96245e10	−1.30277	−0.651387	−	0.758745i	$-0.725813\pi$
$41$	−3.96245e10	−1.30277	−0.651387	+	0.758745i	$0.725813\pi$
$42$	− 8.22713e9i	− 0.231275i
$43$	8.14862e10i	1.96580i	0.184144	+	0.982899i	$0.441049\pi$
$43$	8.14862e10i	1.96580i	−0.184144	+	0.982899i	$0.558951\pi$
$44$	−2.70845e10	−0.562701
$45$	0	0
$46$	−2.25893e10	−0.351542
$47$	− 3.41360e10i	− 0.461931i	−0.972962	−	0.230965i	$-0.925812\pi$
$47$	− 3.41360e10i	− 0.461931i	0.972962	−	0.230965i	$-0.0741884\pi$
$48$	1.22306e10i	0.144338i
$49$	6.57946e10	0.679072
$50$	0	0
$51$	1.12751e11	0.897250
$52$	− 9.84227e10i	− 0.690357i
$53$	2.18108e10i	0.135170i	0.997714	+	0.0675848i	$0.0215293\pi$
$53$	2.18108e10i	0.135170i	−0.997714	+	0.0675848i	$0.978471\pi$
$54$	2.47949e10	0.136083
$55$	0	0
$56$	4.62254e10	0.200290
$57$	− 1.38535e11i	− 0.535025i
$58$	1.79462e11i	0.618998i
$59$	−2.29220e11	−0.707479	−0.353740	−	0.935344i	$-0.615090\pi$
$59$	−2.29220e11	−0.707479	−0.353740	+	0.935344i	$0.615090\pi$
$60$	0	0
$61$	9.79974e9	0.0243540	0.0121770	−	0.999926i	$-0.496124\pi$
$61$	9.79974e9	0.0243540	0.0121770	+	0.999926i	$0.496124\pi$
$62$	1.76874e11i	0.395475i
$63$	− 9.37122e10i	− 0.188835i
$64$	−6.87195e10	−0.125000
$65$	0	0
$66$	−3.08509e11	−0.459444
$67$	7.89043e11i	1.06565i	0.846226	+	0.532825i	$0.178869\pi$
$67$	7.89043e11i	1.06565i	−0.846226	+	0.532825i	$0.821131\pi$
$68$	6.33508e11i	0.777041i
$69$	−2.57306e11	−0.287033
$70$	0	0
$71$	−3.69505e11	−0.342327	−0.171163	−	0.985243i	$-0.554753\pi$
$71$	−3.69505e11	−0.342327	−0.171163	+	0.985243i	$0.554753\pi$
$72$	1.39314e11i	0.117851i
$73$	6.93078e11i	0.536023i	0.963416	+	0.268011i	$0.0863665\pi$
$73$	6.93078e11i	0.536023i	−0.963416	+	0.268011i	$0.913633\pi$
$74$	−1.28194e12	−0.907529
$75$	0	0
$76$	7.78383e11	0.463345
$77$	1.16601e12i	0.637546i
$78$	− 1.12110e12i	− 0.563674i
$79$	−2.23131e12	−1.03272	−0.516361	−	0.856371i	$-0.672714\pi$
$79$	−2.23131e12	−1.03272	−0.516361	+	0.856371i	$0.672714\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	− 2.53597e12i	− 0.921201i
$83$	− 2.08433e12i	− 0.699775i	−0.936792	−	0.349888i	$-0.886220\pi$
$83$	− 2.08433e12i	− 0.699775i	0.936792	−	0.349888i	$-0.113780\pi$
$84$	5.26536e11	0.163536
$85$	0	0
$86$	−5.21512e12	−1.39003
$87$	2.04418e12i	0.505410i
$88$	− 1.73341e12i	− 0.397890i
$89$	−2.22196e12	−0.473916	−0.236958	−	0.971520i	$-0.576150\pi$
$89$	−2.22196e12	−0.473916	−0.236958	+	0.971520i	$0.576150\pi$
$90$	0	0
$91$	−4.23717e12	−0.782181
$92$	− 1.44572e12i	− 0.248578i
$93$	2.01471e12i	0.322904i
$94$	2.18471e12	0.326634
$95$	0	0
$96$	−7.82758e11	−0.102062
$97$	1.02684e13i	1.25166i	0.779960	+	0.625829i	$0.215239\pi$
$97$	1.02684e13i	1.25166i	−0.779960	+	0.625829i	$0.784761\pi$
$98$	4.21086e12i	0.480176i
$99$	−3.51411e12	−0.375134
$100$	0	0
$101$	−2.74433e12	−0.257245	−0.128623	−	0.991694i	$-0.541056\pi$
$101$	−2.74433e12	−0.257245	−0.128623	+	0.991694i	$0.541056\pi$
$102$	7.21605e12i	0.634452i
$103$	2.67772e12i	0.220964i	0.993878	+	0.110482i	$0.0352395\pi$
$103$	2.67772e12i	0.220964i	−0.993878	+	0.110482i	$0.964760\pi$
$104$	6.29905e12	0.488156
$105$	0	0
$106$	−1.39589e12	−0.0955793
$107$	− 1.87398e13i	− 1.20718i	−0.797297	−	0.603588i	$-0.793737\pi$
$107$	− 1.87398e13i	− 1.20718i	0.797297	−	0.603588i	$-0.206263\pi$
$108$	1.58687e12i	0.0962250i
$109$	−1.36996e13	−0.782410	−0.391205	−	0.920304i	$-0.627942\pi$
$109$	−1.36996e13	−0.782410	−0.391205	+	0.920304i	$0.627942\pi$
$110$	0	0
$111$	−1.46021e13	−0.740994
$112$	2.95843e12i	0.141626i
$113$	− 7.96199e12i	− 0.359759i	−0.983689	−	0.179880i	$-0.942429\pi$
$113$	− 7.96199e12i	− 0.359759i	0.983689	−	0.179880i	$-0.0575708\pi$
$114$	8.86627e12	0.378320
$115$	0	0
$116$	−1.14855e13	−0.437698
$117$	− 1.27700e13i	− 0.460238i
$118$	− 1.46701e13i	− 0.500263i
$119$	2.72730e13	0.880396
$120$	0	0
$121$	9.20139e12	0.266531
$122$	6.27183e11i	0.0172209i
$123$	− 2.88863e13i	− 0.752157i
$124$	−1.13200e13	−0.279643
$125$	0	0
$126$	5.99758e12	0.133527
$127$	4.46432e13i	0.944129i	0.881564	+	0.472064i	$0.156491\pi$
$127$	4.46432e13i	0.944129i	−0.881564	+	0.472064i	$0.843509\pi$
$128$	− 4.39805e12i	− 0.0883883i
$129$	−5.94034e13	−1.13495
$130$	0	0
$131$	−1.87106e13	−0.323463	−0.161732	−	0.986835i	$-0.551708\pi$
$131$	−1.87106e13	−0.323463	−0.161732	+	0.986835i	$0.551708\pi$
$132$	− 1.97446e13i	− 0.324876i
$133$	− 3.35100e13i	− 0.524975i
$134$	−5.04987e13	−0.753528
$135$	0	0
$136$	−4.05445e13	−0.549451
$137$	1.36578e13i	0.176481i	0.996099	+	0.0882405i	$0.0281244\pi$
$137$	1.36578e13i	0.176481i	−0.996099	+	0.0882405i	$0.971876\pi$
$138$	− 1.64676e13i	− 0.202963i
$139$	9.46162e13	1.11268	0.556339	−	0.830956i	$-0.312206\pi$
$139$	9.46162e13	1.11268	0.556339	+	0.830956i	$0.312206\pi$
$140$	0	0
$141$	2.48852e13	0.266696
$142$	− 2.36483e13i	− 0.242061i
$143$	1.58890e14i	1.55386i
$144$	−8.91610e12	−0.0833333
$145$	0	0
$146$	−4.43570e13	−0.379025
$147$	4.79643e13i	0.392062i
$148$	− 8.20439e13i	− 0.641720i
$149$	−1.22018e14	−0.913506	−0.456753	−	0.889593i	$-0.650988\pi$
$149$	−1.22018e14	−0.913506	−0.456753	+	0.889593i	$0.650988\pi$
$150$	0	0
$151$	1.65699e14	1.13755	0.568775	−	0.822493i	$-0.307418\pi$
$151$	1.65699e14	1.13755	0.568775	+	0.822493i	$0.307418\pi$
$152$	4.98165e13i	0.327635i
$153$	8.21954e13i	0.518028i
$154$	−7.46245e13	−0.450813
$155$	0	0
$156$	7.17501e13	0.398578
$157$	− 1.38407e14i	− 0.737581i	−0.929512	−	0.368791i	$-0.879772\pi$
$157$	− 1.38407e14i	− 0.737581i	0.929512	−	0.368791i	$-0.120228\pi$
$158$	− 1.42804e14i	− 0.730245i
$159$	−1.59001e13	−0.0780402
$160$	0	0
$161$	−6.22392e13	−0.281641
$162$	1.80755e13i	0.0785674i
$163$	− 2.12316e14i	− 0.886672i	−0.896356	−	0.443336i	$-0.853795\pi$
$163$	− 2.12316e14i	− 0.886672i	0.896356	−	0.443336i	$-0.146205\pi$
$164$	1.62302e14	0.651387
$165$	0	0
$166$	1.33397e14	0.494816
$167$	− 3.19109e14i	− 1.13837i	−0.822210	−	0.569184i	$-0.807259\pi$
$167$	− 3.19109e14i	− 1.13837i	0.822210	−	0.569184i	$-0.192741\pi$
$168$	3.36983e13i	0.115637i
$169$	−2.74517e14	−0.906369
$170$	0	0
$171$	1.00992e14	0.308897
$172$	− 3.33767e14i	− 0.982899i
$173$	4.29507e13i	0.121806i	0.998144	+	0.0609032i	$0.0193981\pi$
$173$	4.29507e13i	0.121806i	−0.998144	+	0.0609032i	$0.980602\pi$
$174$	−1.30827e14	−0.357379
$175$	0	0
$176$	1.10938e14	0.281351
$177$	− 1.67101e14i	− 0.408463i
$178$	− 1.42206e14i	− 0.335109i
$179$	−2.87102e14	−0.652367	−0.326183	−	0.945307i	$-0.605763\pi$
$179$	−2.87102e14	−0.652367	−0.326183	+	0.945307i	$0.605763\pi$
$180$	0	0
$181$	−4.39276e14	−0.928597	−0.464298	−	0.885679i	$-0.653693\pi$
$181$	−4.39276e14	−0.928597	−0.464298	+	0.885679i	$0.653693\pi$
$182$	− 2.71179e14i	− 0.553085i
$183$	7.14401e12i	0.0140608i
$184$	9.25258e13	0.175771
$185$	0	0
$186$	−1.28941e14	−0.228327
$187$	− 1.02271e15i	− 1.74897i
$188$	1.39821e14i	0.230965i
$189$	6.83162e13	0.109024
$190$	0	0
$191$	6.39238e14	0.952677	0.476338	−	0.879262i	$-0.341964\pi$
$191$	6.39238e14	0.952677	0.476338	+	0.879262i	$0.341964\pi$
$192$	− 5.00965e13i	− 0.0721688i
$193$	− 2.70674e13i	− 0.0376984i	−0.999822	−	0.0188492i	$-0.994000\pi$
$193$	− 2.70674e13i	− 0.0376984i	0.999822	−	0.0188492i	$-0.00600025\pi$
$194$	−6.57176e14	−0.885056
$195$	0	0
$196$	−2.69495e14	−0.339536
$197$	− 1.34873e15i	− 1.64397i	−0.569509	−	0.821985i	$-0.692866\pi$
$197$	− 1.34873e15i	− 1.64397i	0.569509	−	0.821985i	$-0.307134\pi$
$198$	− 2.24903e14i	− 0.265260i
$199$	−5.78234e14	−0.660022	−0.330011	−	0.943977i	$-0.607053\pi$
$199$	−5.78234e14	−0.660022	−0.330011	+	0.943977i	$0.607053\pi$
$200$	0	0
$201$	−5.75212e14	−0.615253
$202$	− 1.75637e14i	− 0.181900i
$203$	4.94461e14i	0.495916i
$204$	−4.61827e14	−0.448625
$205$	0	0
$206$	−1.71374e14	−0.156245
$207$	− 1.87576e14i	− 0.165718i
$208$	4.03139e14i	0.345178i
$209$	−1.25659e15	−1.04290
$210$	0	0
$211$	1.24126e15	0.968334	0.484167	−	0.874976i	$-0.339123\pi$
$211$	1.24126e15	0.968334	0.484167	+	0.874976i	$0.339123\pi$
$212$	− 8.93372e13i	− 0.0675848i
$213$	− 2.69369e14i	− 0.197642i
$214$	1.19935e15	0.853602
$215$	0	0
$216$	−1.01560e14	−0.0680414
$217$	4.87333e14i	0.316838i
$218$	− 8.76772e14i	− 0.553247i
$219$	−5.05254e14	−0.309473
$220$	0	0
$221$	3.71644e15	2.14574
$222$	− 9.34532e14i	− 0.523962i
$223$	− 3.28010e15i	− 1.78610i	−0.449959	−	0.893049i	$-0.648561\pi$
$223$	− 3.28010e15i	− 1.78610i	0.449959	−	0.893049i	$-0.351439\pi$
$224$	−1.89339e14	−0.100145
$225$	0	0
$226$	5.09567e14	0.254388
$227$	− 2.83811e15i	− 1.37677i	−0.725346	−	0.688384i	$-0.758320\pi$
$227$	− 2.83811e15i	− 1.37677i	0.725346	−	0.688384i	$-0.241680\pi$
$228$	5.67441e14i	0.267513i
$229$	−2.51453e15	−1.15220	−0.576099	−	0.817380i	$-0.695426\pi$
$229$	−2.51453e15	−1.15220	−0.576099	+	0.817380i	$0.695426\pi$
$230$	0	0
$231$	−8.50020e14	−0.368088
$232$	− 7.35074e14i	− 0.309499i
$233$	− 1.37233e15i	− 0.561882i	−0.959725	−	0.280941i	$-0.909354\pi$
$233$	− 1.37233e15i	− 0.561882i	0.959725	−	0.280941i	$-0.0906464\pi$
$234$	8.17279e14	0.325437
$235$	0	0
$236$	9.38884e14	0.353740
$237$	− 1.62662e15i	− 0.596243i
$238$	1.74547e15i	0.622534i
$239$	−2.19281e15	−0.761051	−0.380525	−	0.924770i	$-0.624257\pi$
$239$	−2.19281e15	−0.761051	−0.380525	+	0.924770i	$0.624257\pi$
$240$	0	0
$241$	8.93064e14	0.293611	0.146805	−	0.989165i	$-0.453101\pi$
$241$	8.93064e14	0.293611	0.146805	+	0.989165i	$0.453101\pi$
$242$	5.88889e14i	0.188466i
$243$	2.05891e14i	0.0641500i
$244$	−4.01397e13	−0.0121770
$245$	0	0
$246$	1.84872e15	0.531855
$247$	− 4.56634e15i	− 1.27949i
$248$	− 7.24477e14i	− 0.197737i
$249$	1.51948e15	0.404015
$250$	0	0
$251$	−7.33069e15	−1.85040	−0.925200	−	0.379479i	$-0.876103\pi$
$251$	−7.33069e15	−1.85040	−0.925200	+	0.379479i	$0.876103\pi$
$252$	3.83845e14i	0.0944175i
$253$	2.33391e15i	0.559500i
$254$	−2.85717e15	−0.667600
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	7.57064e15i	1.63896i	0.573110	+	0.819478i	$0.305737\pi$
$257$	7.57064e15i	1.63896i	−0.573110	+	0.819478i	$0.694263\pi$
$258$	− 3.80182e15i	− 0.802534i
$259$	−3.53206e15	−0.727075
$260$	0	0
$261$	−1.49021e15	−0.291799
$262$	− 1.19748e15i	− 0.228723i
$263$	− 4.17154e15i	− 0.777292i	−0.921387	−	0.388646i	$-0.872943\pi$
$263$	− 4.17154e15i	− 0.777292i	0.921387	−	0.388646i	$-0.127057\pi$
$264$	1.26365e15	0.229722
$265$	0	0
$266$	2.14464e15	0.371213
$267$	− 1.61981e15i	− 0.273616i
$268$	− 3.23192e15i	− 0.532825i
$269$	1.18525e15	0.190731	0.0953654	−	0.995442i	$-0.469598\pi$
$269$	1.18525e15	0.190731	0.0953654	+	0.995442i	$0.469598\pi$
$270$	0	0
$271$	−7.38509e15	−1.13254	−0.566272	−	0.824218i	$-0.691615\pi$
$271$	−7.38509e15	−1.13254	−0.566272	+	0.824218i	$0.691615\pi$
$272$	− 2.59485e15i	− 0.388521i
$273$	− 3.08890e15i	− 0.451592i
$274$	−8.74101e14	−0.124791
$275$	0	0
$276$	1.05393e15	0.143516
$277$	− 8.90718e15i	− 1.18474i	−0.805668	−	0.592368i	$-0.798193\pi$
$277$	− 8.90718e15i	− 1.18474i	0.805668	−	0.592368i	$-0.201807\pi$
$278$	6.05544e15i	0.786782i
$279$	−1.46872e15	−0.186429
$280$	0	0
$281$	7.28107e15	0.882275	0.441137	−	0.897440i	$-0.354575\pi$
$281$	7.28107e15	0.882275	0.441137	+	0.897440i	$0.354575\pi$
$282$	1.59265e15i	0.188582i
$283$	− 2.25119e15i	− 0.260495i	−0.991482	−	0.130248i	$-0.958423\pi$
$283$	− 2.25119e15i	− 0.260495i	0.991482	−	0.130248i	$-0.0415772\pi$
$284$	1.51349e15	0.171163
$285$	0	0
$286$	−1.01689e16	−1.09874
$287$	− 6.98723e15i	− 0.738028i
$288$	− 5.70630e14i	− 0.0589256i
$289$	−1.40167e16	−1.41517
$290$	0	0
$291$	−7.48565e15	−0.722645
$292$	− 2.83885e15i	− 0.268011i
$293$	1.47912e16i	1.36572i	0.730548	+	0.682862i	$0.239265\pi$
$293$	1.47912e16i	1.36572i	−0.730548	+	0.682862i	$0.760735\pi$
$294$	−3.06971e15	−0.277230
$295$	0	0
$296$	5.25081e15	0.453764
$297$	− 2.56179e15i	− 0.216584i
$298$	− 7.80912e15i	− 0.645947i
$299$	−8.48122e15	−0.686429
$300$	0	0
$301$	−1.43689e16	−1.11363
$302$	1.06048e16i	0.804369i
$303$	− 2.00062e15i	− 0.148521i
$304$	−3.18826e15	−0.231673
$305$	0	0
$306$	−5.26050e15	−0.366301
$307$	2.48209e16i	1.69207i	0.533129	+	0.846034i	$0.321016\pi$
$307$	2.48209e16i	1.69207i	−0.533129	+	0.846034i	$0.678984\pi$
$308$	− 4.77597e15i	− 0.318773i
$309$	−1.95205e15	−0.127574
$310$	0	0
$311$	−3.32199e15	−0.208188	−0.104094	−	0.994567i	$-0.533194\pi$
$311$	−3.32199e15	−0.208188	−0.104094	+	0.994567i	$0.533194\pi$
$312$	4.59201e15i	0.281837i
$313$	− 9.51146e15i	− 0.571754i	−0.958266	−	0.285877i	$-0.907715\pi$
$313$	− 9.51146e15i	− 0.571754i	0.958266	−	0.285877i	$-0.0922848\pi$
$314$	8.85804e15	0.521549
$315$	0	0
$316$	9.13945e15	0.516361
$317$	− 1.51151e16i	− 0.836614i	−0.908306	−	0.418307i	$-0.862624\pi$
$317$	− 1.51151e16i	− 0.836614i	0.908306	−	0.418307i	$-0.137376\pi$
$318$	− 1.01761e15i	− 0.0551828i
$319$	1.85418e16	0.985173
$320$	0	0
$321$	1.36613e16	0.696963
$322$	− 3.98331e15i	− 0.199150i
$323$	2.93918e16i	1.44015i
$324$	−1.15683e15	−0.0555556
$325$	0	0
$326$	1.35882e16	0.626972
$327$	− 9.98698e15i	− 0.451725i
$328$	1.03873e16i	0.460600i
$329$	6.01941e15	0.261686
$330$	0	0
$331$	3.67739e15	0.153694	0.0768472	−	0.997043i	$-0.475515\pi$
$331$	3.67739e15	0.153694	0.0768472	+	0.997043i	$0.475515\pi$
$332$	8.53741e15i	0.349888i
$333$	− 1.06449e16i	− 0.427813i
$334$	2.04230e16	0.804947
$335$	0	0
$336$	−2.15669e15	−0.0817679
$337$	2.85819e16i	1.06291i	0.847087	+	0.531454i	$0.178354\pi$
$337$	2.85819e16i	1.06291i	−0.847087	+	0.531454i	$0.821646\pi$
$338$	− 1.75691e16i	− 0.640900i
$339$	5.80429e15	0.207707
$340$	0	0
$341$	1.82745e16	0.629422
$342$	6.46351e15i	0.218423i
$343$	2.86870e16i	0.951203i
$344$	2.13611e16	0.695015
$345$	0	0
$346$	−2.74884e15	−0.0861302
$347$	1.94892e16i	0.599311i	0.954047	+	0.299655i	$0.0968717\pi$
$347$	1.94892e16i	0.599311i	−0.954047	+	0.299655i	$0.903128\pi$
$348$	− 8.37296e15i	− 0.252705i
$349$	−5.84726e16	−1.73216	−0.866079	−	0.499908i	$-0.833367\pi$
$349$	−5.84726e16	−1.73216	−0.866079	+	0.499908i	$0.833367\pi$
$350$	0	0
$351$	9.30932e15	0.265718
$352$	7.10003e15i	0.198945i
$353$	4.93208e16i	1.35673i	0.734724	+	0.678366i	$0.237312\pi$
$353$	4.93208e16i	1.35673i	−0.734724	+	0.678366i	$0.762688\pi$
$354$	1.06945e16	0.288827
$355$	0	0
$356$	9.10115e15	0.236958
$357$	1.98820e16i	0.508297i
$358$	− 1.83745e16i	− 0.461293i
$359$	−2.83880e16	−0.699875	−0.349937	−	0.936773i	$-0.613797\pi$
$359$	−2.83880e16	−0.699875	−0.349937	+	0.936773i	$0.613797\pi$
$360$	0	0
$361$	−5.93973e15	−0.141244
$362$	− 2.81137e16i	− 0.656617i
$363$	6.70781e15i	0.153882i
$364$	1.73555e16	0.391090
$365$	0	0
$366$	−4.57217e14	−0.00994248
$367$	− 3.05678e16i	− 0.653032i	−0.945192	−	0.326516i	$-0.894125\pi$
$367$	− 3.05678e16i	− 0.653032i	0.945192	−	0.326516i	$-0.105875\pi$
$368$	5.92165e15i	0.124289i
$369$	2.10581e16	0.434258
$370$	0	0
$371$	−3.84603e15	−0.0765743
$372$	− 8.25225e15i	− 0.161452i
$373$	− 4.67482e16i	− 0.898789i	−0.893333	−	0.449394i	$-0.851640\pi$
$373$	− 4.67482e16i	− 0.898789i	0.893333	−	0.449394i	$-0.148360\pi$
$374$	6.54535e16	1.23671
$375$	0	0
$376$	−8.94855e15	−0.163317
$377$	6.73793e16i	1.20867i
$378$	4.37224e15i	0.0770916i
$379$	7.93540e16	1.37535	0.687677	−	0.726017i	$-0.258631\pi$
$379$	7.93540e16	1.37535	0.687677	+	0.726017i	$0.258631\pi$
$380$	0	0
$381$	−3.25449e16	−0.545093
$382$	4.09112e16i	0.673644i
$383$	1.12647e17i	1.82360i	0.410640	+	0.911798i	$0.365305\pi$
$383$	1.12647e17i	1.82360i	−0.410640	+	0.911798i	$0.634695\pi$
$384$	3.20618e15	0.0510310
$385$	0	0
$386$	1.73231e15	0.0266568
$387$	− 4.33051e16i	− 0.655266i
$388$	− 4.20593e16i	− 0.625829i
$389$	7.86645e16	1.15108	0.575541	−	0.817773i	$-0.304791\pi$
$389$	7.86645e16	1.15108	0.575541	+	0.817773i	$0.304791\pi$
$390$	0	0
$391$	5.45902e16	0.772620
$392$	− 1.72477e16i	− 0.240088i
$393$	− 1.36400e16i	− 0.186751i
$394$	8.63186e16	1.16246
$395$	0	0
$396$	1.43938e16	0.187567
$397$	4.32882e16i	0.554921i	0.960737	+	0.277461i	$0.0894928\pi$
$397$	4.32882e16i	0.554921i	−0.960737	+	0.277461i	$0.910507\pi$
$398$	− 3.70070e16i	− 0.466706i
$399$	2.44288e16	0.303094
$400$	0	0
$401$	1.01567e17	1.21987	0.609936	−	0.792451i	$-0.291195\pi$
$401$	1.01567e17	1.21987	0.609936	+	0.792451i	$0.291195\pi$
$402$	− 3.68136e16i	− 0.435049i
$403$	6.64080e16i	0.772213i
$404$	1.12408e16	0.128623
$405$	0	0
$406$	−3.16455e16	−0.350666
$407$	1.32448e17i	1.44439i
$408$	− 2.95570e16i	− 0.317226i
$409$	9.64582e16	1.01891	0.509457	−	0.860496i	$-0.329846\pi$
$409$	9.64582e16	1.01891	0.509457	+	0.860496i	$0.329846\pi$
$410$	0	0
$411$	−9.95656e15	−0.101891
$412$	− 1.09679e16i	− 0.110482i
$413$	− 4.04197e16i	− 0.400791i
$414$	1.20049e16	0.117181
$415$	0	0
$416$	−2.58009e16	−0.244078
$417$	6.89752e16i	0.642405i
$418$	− 8.04218e16i	− 0.737442i
$419$	−2.92985e16	−0.264517	−0.132259	−	0.991215i	$-0.542223\pi$
$419$	−2.92985e16	−0.264517	−0.132259	+	0.991215i	$0.542223\pi$
$420$	0	0
$421$	−1.81553e17	−1.58917	−0.794584	−	0.607154i	$-0.792311\pi$
$421$	−1.81553e17	−1.58917	−0.794584	+	0.607154i	$0.792311\pi$
$422$	7.94404e16i	0.684716i
$423$	1.81413e16i	0.153977i
$424$	5.71758e15	0.0477897
$425$	0	0
$426$	1.72396e16	0.139754
$427$	1.72805e15i	0.0137967i
$428$	7.67582e16i	0.603588i
$429$	−1.15831e17	−0.897121
$430$	0	0
$431$	−5.10999e16	−0.383988	−0.191994	−	0.981396i	$-0.561495\pi$
$431$	−5.10999e16	−0.383988	−0.191994	+	0.981396i	$0.561495\pi$
$432$	− 6.49984e15i	− 0.0481125i
$433$	2.04438e17i	1.49070i	0.666675	+	0.745348i	$0.267717\pi$
$433$	2.04438e17i	1.49070i	−0.666675	+	0.745348i	$0.732283\pi$
$434$	−3.11893e16	−0.224038
$435$	0	0
$436$	5.61134e16	0.391205
$437$	− 6.70743e16i	− 0.460709i
$438$	− 3.23362e16i	− 0.218830i
$439$	−2.41391e17	−1.60954	−0.804770	−	0.593586i	$-0.797712\pi$
$439$	−2.41391e17	−1.60954	−0.804770	+	0.593586i	$0.797712\pi$
$440$	0	0
$441$	−3.49660e16	−0.226357
$442$	2.37852e17i	1.51727i
$443$	− 1.69539e17i	− 1.06573i	−0.846201	−	0.532864i	$-0.821116\pi$
$443$	− 1.69539e17i	− 1.06573i	0.846201	−	0.532864i	$-0.178884\pi$
$444$	5.98100e16	0.370497
$445$	0	0
$446$	2.09926e17	1.26296
$447$	− 8.89508e16i	− 0.527413i
$448$	− 1.21177e16i	− 0.0708131i
$449$	−1.46735e17	−0.845149	−0.422575	−	0.906328i	$-0.638874\pi$
$449$	−1.46735e17	−0.845149	−0.422575	+	0.906328i	$0.638874\pi$
$450$	0	0
$451$	−2.62014e17	−1.46615
$452$	3.26123e16i	0.179880i
$453$	1.20795e17i	0.656765i
$454$	1.81639e17	0.973522
$455$	0	0
$456$	−3.63162e16	−0.189160
$457$	3.53190e17i	1.81365i	0.421508	+	0.906825i	$0.361501\pi$
$457$	3.53190e17i	1.81365i	−0.421508	+	0.906825i	$0.638499\pi$
$458$	− 1.60930e17i	− 0.814726i
$459$	−5.99204e16	−0.299083
$460$	0	0
$461$	8.13033e15	0.0394505	0.0197252	−	0.999805i	$-0.493721\pi$
$461$	8.13033e15	0.0394505	0.0197252	+	0.999805i	$0.493721\pi$
$462$	− 5.44013e16i	− 0.260277i
$463$	4.12513e16i	0.194608i	0.995255	+	0.0973040i	$0.0310219\pi$
$463$	4.12513e16i	0.194608i	−0.995255	+	0.0973040i	$0.968978\pi$
$464$	4.70448e16	0.218849
$465$	0	0
$466$	8.78291e16	0.397310
$467$	− 1.76637e17i	− 0.787991i	−0.919112	−	0.393995i	$-0.871093\pi$
$467$	− 1.76637e17i	− 0.787991i	0.919112	−	0.393995i	$-0.128907\pi$
$468$	5.23059e16i	0.230119i
$469$	−1.39137e17	−0.603696
$470$	0	0
$471$	1.00899e17	0.425843
$472$	6.00886e16i	0.250132i
$473$	5.38821e17i	2.21231i
$474$	1.04104e17	0.421607
$475$	0	0
$476$	−1.11710e17	−0.440198
$477$	− 1.15912e16i	− 0.0450565i
$478$	− 1.40340e17i	− 0.538144i
$479$	−5.71489e16	−0.216186	−0.108093	−	0.994141i	$-0.534474\pi$
$479$	−5.71489e16	−0.216186	−0.108093	+	0.994141i	$0.534474\pi$
$480$	0	0
$481$	−4.81307e17	−1.77206
$482$	5.71561e16i	0.207614i
$483$	− 4.53724e16i	− 0.162605i
$484$	−3.76889e16	−0.133266
$485$	0	0
$486$	−1.31770e16	−0.0453609
$487$	− 1.70959e17i	− 0.580703i	−0.956920	−	0.290352i	$-0.906228\pi$
$487$	− 1.70959e17i	− 0.580703i	0.956920	−	0.290352i	$-0.0937723\pi$
$488$	− 2.56894e15i	− 0.00861044i
$489$	1.54778e17	0.511920
$490$	0	0
$491$	7.30125e15	0.0235162	0.0117581	−	0.999931i	$-0.496257\pi$
$491$	7.30125e15	0.0235162	0.0117581	+	0.999931i	$0.496257\pi$
$492$	1.18318e17i	0.376079i
$493$	− 4.33694e17i	− 1.36044i
$494$	2.92246e17	0.904739
$495$	0	0
$496$	4.63665e16	0.139821
$497$	− 6.51570e16i	− 0.193930i
$498$	9.72464e16i	0.285682i
$499$	−3.45599e17	−1.00212	−0.501059	−	0.865413i	$-0.667056\pi$
$499$	−3.45599e17	−1.00212	−0.501059	+	0.865413i	$0.667056\pi$
$500$	0	0
$501$	2.32631e17	0.657237
$502$	− 4.69164e17i	− 1.30843i
$503$	8.21237e16i	0.226087i	0.993590	+	0.113044i	$0.0360600\pi$
$503$	8.21237e16i	0.226087i	−0.993590	+	0.113044i	$0.963940\pi$
$504$	−2.45661e16	−0.0667633
$505$	0	0
$506$	−1.49370e17	−0.395626
$507$	− 2.00123e17i	− 0.523293i
$508$	− 1.82859e17i	− 0.472064i
$509$	−6.11607e17	−1.55886	−0.779430	−	0.626489i	$-0.784491\pi$
$509$	−6.11607e17	−1.55886	−0.779430	+	0.626489i	$0.784491\pi$
$510$	0	0
$511$	−1.22215e17	−0.303660
$512$	1.80144e16i	0.0441942i
$513$	7.36234e16i	0.178342i
$514$	−4.84521e17	−1.15892
$515$	0	0
$516$	2.43316e17	0.567477
$517$	− 2.25722e17i	− 0.519858i
$518$	− 2.26052e17i	− 0.514119i
$519$	−3.13110e16	−0.0703250
$520$	0	0
$521$	2.42378e17	0.530944	0.265472	−	0.964119i	$-0.414472\pi$
$521$	2.42378e17	0.530944	0.265472	+	0.964119i	$0.414472\pi$
$522$	− 9.53732e16i	− 0.206333i
$523$	6.89943e17i	1.47419i	0.675791	+	0.737093i	$0.263802\pi$
$523$	6.89943e17i	1.47419i	−0.675791	+	0.737093i	$0.736198\pi$
$524$	7.66387e16	0.161732
$525$	0	0
$526$	2.66979e17	0.549629
$527$	− 4.27442e17i	− 0.869177i
$528$	8.08738e16i	0.162438i
$529$	3.79457e17	0.752837
$530$	0	0
$531$	1.21817e17	0.235826
$532$	1.37257e17i	0.262488i
$533$	− 9.52137e17i	− 1.79876i
$534$	1.03668e17	0.193475
$535$	0	0
$536$	2.06843e17	0.376764
$537$	− 2.09297e17i	− 0.376644i
$538$	7.58561e16i	0.134867i
$539$	4.35062e17	0.764230
$540$	0	0
$541$	−3.61547e17	−0.619986	−0.309993	−	0.950739i	$-0.600327\pi$
$541$	−3.61547e17	−0.619986	−0.309993	+	0.950739i	$0.600327\pi$
$542$	− 4.72646e17i	− 0.800830i
$543$	− 3.20232e17i	− 0.536126i
$544$	1.66070e17	0.274726
$545$	0	0
$546$	1.97690e17	0.319324
$547$	7.88310e17i	1.25829i	0.777290	+	0.629143i	$0.216594\pi$
$547$	7.88310e17i	1.25829i	−0.777290	+	0.629143i	$0.783406\pi$
$548$	− 5.59425e16i	− 0.0882405i
$549$	−5.20798e15	−0.00811800
$550$	0	0
$551$	−5.32874e17	−0.811221
$552$	6.74513e16i	0.101481i
$553$	− 3.93460e17i	− 0.585043i
$554$	5.70059e17	0.837735
$555$	0	0
$556$	−3.87548e17	−0.556339
$557$	− 1.25406e18i	− 1.77934i	−0.456601	−	0.889672i	$-0.650933\pi$
$557$	− 1.25406e18i	− 1.77934i	0.456601	−	0.889672i	$-0.349067\pi$
$558$	− 9.39983e16i	− 0.131825i
$559$	−1.95803e18	−2.71420
$560$	0	0
$561$	7.45556e17	1.00977
$562$	4.65988e17i	0.623863i
$563$	− 9.12869e17i	− 1.20810i	−0.796945	−	0.604052i	$-0.793552\pi$
$563$	− 9.12869e17i	− 1.20810i	0.796945	−	0.604052i	$-0.206448\pi$
$564$	−1.01930e17	−0.133348
$565$	0	0
$566$	1.44076e17	0.184198
$567$	4.98025e16i	0.0629450i
$568$	9.68634e16i	0.121031i
$569$	−2.67735e17	−0.330731	−0.165366	−	0.986232i	$-0.552880\pi$
$569$	−2.67735e17	−0.330731	−0.165366	+	0.986232i	$0.552880\pi$
$570$	0	0
$571$	7.01225e17	0.846687	0.423343	−	0.905969i	$-0.360856\pi$
$571$	7.01225e17	0.846687	0.423343	+	0.905969i	$0.360856\pi$
$572$	− 6.50812e17i	− 0.776929i
$573$	4.66004e17i	0.550028i
$574$	4.47183e17	0.521865
$575$	0	0
$576$	3.65203e16	0.0416667
$577$	− 5.15072e17i	− 0.581066i	−0.956865	−	0.290533i	$-0.906167\pi$
$577$	− 5.15072e17i	− 0.581066i	0.956865	−	0.290533i	$-0.0938325\pi$
$578$	− 8.97069e17i	− 1.00068i
$579$	1.97321e16	0.0217652
$580$	0	0
$581$	3.67542e17	0.396426
$582$	− 4.79082e17i	− 0.510987i
$583$	1.44222e17i	0.152120i
$584$	1.81686e17	0.189513
$585$	0	0
$586$	−9.46634e17	−0.965712
$587$	− 1.23894e18i	− 1.24998i	−0.780635	−	0.624988i	$-0.785104\pi$
$587$	− 1.23894e18i	− 1.24998i	0.780635	−	0.624988i	$-0.214896\pi$
$588$	− 1.96462e17i	− 0.196031i
$589$	−5.25192e17	−0.518285
$590$	0	0
$591$	9.83223e17	0.949147
$592$	3.36052e17i	0.320860i
$593$	1.33259e18i	1.25846i	0.777219	+	0.629230i	$0.216630\pi$
$593$	1.33259e18i	1.25846i	−0.777219	+	0.629230i	$0.783370\pi$
$594$	1.63954e17	0.153148
$595$	0	0
$596$	4.99784e17	0.456753
$597$	− 4.21533e17i	− 0.381064i
$598$	− 5.42798e17i	− 0.485378i
$599$	−7.57281e17	−0.669858	−0.334929	−	0.942243i	$-0.608712\pi$
$599$	−7.57281e17	−0.669858	−0.334929	+	0.942243i	$0.608712\pi$
$600$	0	0
$601$	−3.36665e17	−0.291416	−0.145708	−	0.989328i	$-0.546546\pi$
$601$	−3.36665e17	−0.291416	−0.145708	+	0.989328i	$0.546546\pi$
$602$	− 9.19613e17i	− 0.787459i
$603$	− 4.19330e17i	− 0.355216i
$604$	−6.78704e17	−0.568775
$605$	0	0
$606$	1.28040e17	0.105020
$607$	3.04072e17i	0.246746i	0.992360	+	0.123373i	$0.0393711\pi$
$607$	3.04072e17i	0.246746i	−0.992360	+	0.123373i	$0.960629\pi$
$608$	− 2.04048e17i	− 0.163817i
$609$	−3.60462e17	−0.286317
$610$	0	0
$611$	8.20254e17	0.637794
$612$	− 3.36672e17i	− 0.259014i
$613$	1.31576e18i	1.00157i	0.865571	+	0.500786i	$0.166956\pi$
$613$	1.31576e18i	1.00157i	−0.865571	+	0.500786i	$0.833044\pi$
$614$	−1.58854e18	−1.19647
$615$	0	0
$616$	3.05662e17	0.225407
$617$	3.45123e15i	0.00251837i	0.999999	+	0.00125919i	$0.000400812\pi$
$617$	3.45123e15i	0.00251837i	−0.999999	+	0.00125919i	$0.999599\pi$
$618$	− 1.24931e17i	− 0.0902084i
$619$	−2.18078e17	−0.155820	−0.0779100	−	0.996960i	$-0.524825\pi$
$619$	−2.18078e17	−0.155820	−0.0779100	+	0.996960i	$0.524825\pi$
$620$	0	0
$621$	1.36743e17	0.0956775
$622$	− 2.12608e17i	− 0.147211i
$623$	− 3.91812e17i	− 0.268476i
$624$	−2.93889e17	−0.199289
$625$	0	0
$626$	6.08733e17	0.404291
$627$	− 9.16054e17i	− 0.602119i
$628$	5.66914e17i	0.368791i
$629$	3.09798e18	1.99457
$630$	0	0
$631$	−1.17875e18	−0.743417	−0.371708	−	0.928350i	$-0.621228\pi$
$631$	−1.17875e18	−0.743417	−0.371708	+	0.928350i	$0.621228\pi$
$632$	5.84925e17i	0.365123i
$633$	9.04875e17i	0.559068i
$634$	9.67365e17	0.591575
$635$	0	0
$636$	6.51268e16	0.0390201
$637$	1.58098e18i	0.937604i
$638$	1.18667e18i	0.696622i
$639$	1.96370e17	0.114109
$640$	0	0
$641$	6.21780e16	0.0354046	0.0177023	−	0.999843i	$-0.494365\pi$
$641$	6.21780e16	0.0354046	0.0177023	+	0.999843i	$0.494365\pi$
$642$	8.74324e17i	0.492827i
$643$	− 8.88490e17i	− 0.495771i	−0.968789	−	0.247886i	$-0.920264\pi$
$643$	− 8.88490e17i	− 0.495771i	0.968789	−	0.247886i	$-0.0797357\pi$
$644$	2.54932e17	0.140820
$645$	0	0
$646$	−1.88107e18	−1.01834
$647$	− 4.06655e17i	− 0.217945i	−0.994045	−	0.108973i	$-0.965244\pi$
$647$	− 4.06655e17i	− 0.217945i	0.994045	−	0.108973i	$-0.0347561\pi$
$648$	− 7.40372e16i	− 0.0392837i
$649$	−1.51570e18	−0.796199
$650$	0	0
$651$	−3.55266e17	−0.182927
$652$	8.69645e17i	0.443336i
$653$	9.49096e17i	0.479043i	0.970891	+	0.239521i	$0.0769906\pi$
$653$	9.49096e17i	0.479043i	−0.970891	+	0.239521i	$0.923009\pi$
$654$	6.39167e17	0.319418
$655$	0	0
$656$	−6.64790e17	−0.325694
$657$	− 3.68330e17i	− 0.178674i
$658$	3.85242e17i	0.185040i
$659$	6.18766e17	0.294287	0.147143	−	0.989115i	$-0.452992\pi$
$659$	6.18766e17	0.294287	0.147143	+	0.989115i	$0.452992\pi$
$660$	0	0
$661$	−2.04001e18	−0.951312	−0.475656	−	0.879632i	$-0.657789\pi$
$661$	−2.04001e18	−0.951312	−0.475656	+	0.879632i	$0.657789\pi$
$662$	2.35353e17i	0.108678i
$663$	2.70929e18i	1.23885i
$664$	−5.46394e17	−0.247408
$665$	0	0
$666$	6.81274e17	0.302510
$667$	9.89724e17i	0.435207i
$668$	1.30707e18i	0.569184i
$669$	2.39119e18	1.03120
$670$	0	0
$671$	6.48000e16	0.0274081
$672$	− 1.38028e17i	− 0.0578187i
$673$	− 5.44223e17i	− 0.225777i	−0.993608	−	0.112888i	$-0.963990\pi$
$673$	− 5.44223e17i	− 0.225777i	0.993608	−	0.112888i	$-0.0360102\pi$
$674$	−1.82924e18	−0.751590
$675$	0	0
$676$	1.12442e18	0.453185
$677$	3.81683e18i	1.52362i	0.647801	+	0.761810i	$0.275689\pi$
$677$	3.81683e18i	1.52362i	−0.647801	+	0.761810i	$0.724311\pi$
$678$	3.71475e17i	0.146871i
$679$	−1.81069e18	−0.709070
$680$	0	0
$681$	2.06898e18	0.794877
$682$	1.16957e18i	0.445068i
$683$	− 4.08234e18i	− 1.53877i	−0.638782	−	0.769387i	$-0.720562\pi$
$683$	− 4.08234e18i	− 1.53877i	0.638782	−	0.769387i	$-0.279438\pi$
$684$	−4.13665e17	−0.154448
$685$	0	0
$686$	−1.83597e18	−0.672602
$687$	− 1.83309e18i	− 0.665221i
$688$	1.36711e18i	0.491450i
$689$	−5.24092e17	−0.186630
$690$	0	0
$691$	−4.38187e18	−1.53127	−0.765635	−	0.643275i	$-0.777575\pi$
$691$	−4.38187e18	−1.53127	−0.765635	+	0.643275i	$0.777575\pi$
$692$	− 1.75926e17i	− 0.0609032i
$693$	− 6.19664e17i	− 0.212515i
$694$	−1.24731e18	−0.423777
$695$	0	0
$696$	5.35869e17	0.178689
$697$	6.12853e18i	2.02462i
$698$	− 3.74225e18i	− 1.22482i
$699$	1.00043e18	0.324402
$700$	0	0
$701$	−3.88454e18	−1.23644	−0.618220	−	0.786005i	$-0.712146\pi$
$701$	−3.88454e18	−1.23644	−0.618220	+	0.786005i	$0.712146\pi$
$702$	5.95796e17i	0.187891i
$703$	− 3.80645e18i	− 1.18935i
$704$	−4.54402e17	−0.140675
$705$	0	0
$706$	−3.15653e18	−0.959355
$707$	− 4.83925e17i	− 0.145731i
$708$	6.84446e17i	0.204232i
$709$	6.58185e18	1.94602	0.973011	−	0.230758i	$-0.0741207\pi$
$709$	6.58185e18	1.94602	0.973011	+	0.230758i	$0.0741207\pi$
$710$	0	0
$711$	1.18581e18	0.344241
$712$	5.82474e17i	0.167555i
$713$	9.75456e17i	0.278052i
$714$	−1.27245e18	−0.359420
$715$	0	0
$716$	1.17597e18	0.326183
$717$	− 1.59855e18i	− 0.439393i
$718$	− 1.81683e18i	− 0.494886i
$719$	1.83431e18	0.495147	0.247573	−	0.968869i	$-0.420367\pi$
$719$	1.83431e18	0.495147	0.247573	+	0.968869i	$0.420367\pi$
$720$	0	0
$721$	−4.72178e17	−0.125177
$722$	− 3.80143e17i	− 0.0998746i
$723$	6.51044e17i	0.169516i
$724$	1.79928e18	0.464298
$725$	0	0
$726$	−4.29300e17	−0.108811
$727$	5.49594e18i	1.38060i	0.723522	+	0.690301i	$0.242522\pi$
$727$	5.49594e18i	1.38060i	−0.723522	+	0.690301i	$0.757478\pi$
$728$	1.11075e18i	0.276543i
$729$	−1.50095e17	−0.0370370
$730$	0	0
$731$	1.26031e19	3.05501
$732$	− 2.92619e16i	− 0.00703040i
$733$	− 1.68080e18i	− 0.400259i	−0.979769	−	0.200130i	$-0.935864\pi$
$733$	− 1.68080e18i	− 0.400259i	0.979769	−	0.200130i	$-0.0641363\pi$
$734$	1.95634e18	0.461763
$735$	0	0
$736$	−3.78986e17	−0.0878854
$737$	5.21748e18i	1.19928i
$738$	1.34772e18i	0.307067i
$739$	7.12858e18	1.60996	0.804979	−	0.593304i	$-0.202177\pi$
$739$	7.12858e18	1.60996	0.804979	+	0.593304i	$0.202177\pi$
$740$	0	0
$741$	3.32886e18	0.738716
$742$	− 2.46146e17i	− 0.0541462i
$743$	4.83565e18i	1.05445i	0.849725	+	0.527227i	$0.176768\pi$
$743$	4.83565e18i	1.05445i	−0.849725	+	0.527227i	$0.823232\pi$
$744$	5.28144e17	0.114164
$745$	0	0
$746$	2.99189e18	0.635540
$747$	1.10770e18i	0.233258i
$748$	4.18902e18i	0.874485i
$749$	3.30450e18	0.683871
$750$	0	0
$751$	−6.52041e18	−1.32622	−0.663110	−	0.748522i	$-0.730764\pi$
$751$	−6.52041e18	−1.32622	−0.663110	+	0.748522i	$0.730764\pi$
$752$	− 5.72707e17i	− 0.115483i
$753$	− 5.34407e18i	− 1.06833i
$754$	−4.31228e18	−0.854659
$755$	0	0
$756$	−2.79823e17	−0.0545120
$757$	5.37572e18i	1.03828i	0.854690	+	0.519138i	$0.173747\pi$
$757$	5.37572e18i	1.03828i	−0.854690	+	0.519138i	$0.826253\pi$
$758$	5.07866e18i	0.972521i
$759$	−1.70142e18	−0.323027
$760$	0	0
$761$	−6.77293e17	−0.126408	−0.0632042	−	0.998001i	$-0.520132\pi$
$761$	−6.77293e17	−0.126408	−0.0632042	+	0.998001i	$0.520132\pi$
$762$	− 2.08287e18i	− 0.385439i
$763$	− 2.41573e18i	− 0.443239i
$764$	−2.61832e18	−0.476338
$765$	0	0
$766$	−7.20942e18	−1.28948
$767$	− 5.50791e18i	− 0.976826i
$768$	2.05195e17i	0.0360844i
$769$	1.97210e18	0.343881	0.171941	−	0.985107i	$-0.444996\pi$
$769$	1.97210e18	0.343881	0.171941	+	0.985107i	$0.444996\pi$
$770$	0	0
$771$	−5.51900e18	−0.946252
$772$	1.10868e17i	0.0188492i
$773$	3.13942e17i	0.0529277i	0.999650	+	0.0264639i	$0.00842469\pi$
$773$	3.13942e17i	0.0529277i	−0.999650	+	0.0264639i	$0.991575\pi$
$774$	2.77153e18	0.463343
$775$	0	0
$776$	2.69179e18	0.442528
$777$	− 2.57487e18i	− 0.419777i
$778$	5.03453e18i	0.813938i
$779$	7.53005e18	1.20727
$780$	0	0
$781$	−2.44332e18	−0.385255
$782$	3.49378e18i	0.546325i
$783$	− 1.08636e18i	− 0.168470i
$784$	1.10385e18	0.169768
$785$	0	0
$786$	8.72963e17	0.132053
$787$	6.80238e18i	1.02053i	0.860018	+	0.510264i	$0.170452\pi$
$787$	6.80238e18i	1.02053i	−0.860018	+	0.510264i	$0.829548\pi$
$788$	5.52439e18i	0.821985i
$789$	3.04105e18	0.448770
$790$	0	0
$791$	1.40399e18	0.203805
$792$	9.21203e17i	0.132630i
$793$	2.35478e17i	0.0336259i
$794$	−2.77045e18	−0.392389
$795$	0	0
$796$	2.36845e18	0.330011
$797$	− 7.76728e18i	− 1.07347i	−0.843751	−	0.536735i	$-0.819657\pi$
$797$	− 7.76728e18i	− 1.07347i	0.843751	−	0.536735i	$-0.180343\pi$
$798$	1.56344e18i	0.214320i
$799$	−5.27965e18	−0.717879
$800$	0	0
$801$	1.18084e18	0.157972
$802$	6.50029e18i	0.862580i
$803$	4.58292e18i	0.603242i
$804$	2.35607e18	0.307626
$805$	0	0
$806$	−4.25011e18	−0.546037
$807$	8.64049e17i	0.110119i
$808$	7.19410e17i	0.0909500i
$809$	6.55504e18	0.822072	0.411036	−	0.911619i	$-0.365167\pi$
$809$	6.55504e18	0.822072	0.411036	+	0.911619i	$0.365167\pi$
$810$	0	0
$811$	8.02074e18	0.989871	0.494936	−	0.868930i	$-0.335192\pi$
$811$	8.02074e18	0.989871	0.494936	+	0.868930i	$0.335192\pi$
$812$	− 2.02531e18i	− 0.247958i
$813$	− 5.38373e18i	− 0.653875i
$814$	−8.47670e18	−1.02134
$815$	0	0
$816$	1.89164e18	0.224313
$817$	− 1.54852e19i	− 1.82169i
$818$	6.17332e18i	0.720481i
$819$	2.25181e18	0.260727
$820$	0	0
$821$	1.05423e19	1.20145	0.600723	−	0.799457i	$-0.294880\pi$
$821$	1.05423e19	1.20145	0.600723	+	0.799457i	$0.294880\pi$
$822$	− 6.37220e17i	− 0.0720481i
$823$	− 6.50382e18i	− 0.729574i	−0.931091	−	0.364787i	$-0.881142\pi$
$823$	− 6.50382e18i	− 0.729574i	0.931091	−	0.364787i	$-0.118858\pi$
$824$	7.01947e17	0.0781227
$825$	0	0
$826$	2.58686e18	0.283402
$827$	1.47825e19i	1.60680i	0.595442	+	0.803398i	$0.296977\pi$
$827$	1.47825e19i	1.60680i	−0.595442	+	0.803398i	$0.703023\pi$
$828$	7.68312e17i	0.0828592i
$829$	−4.72547e18	−0.505639	−0.252820	−	0.967513i	$-0.581358\pi$
$829$	−4.72547e18	−0.505639	−0.252820	+	0.967513i	$0.581358\pi$
$830$	0	0
$831$	6.49333e18	0.684008
$832$	− 1.65126e18i	− 0.172589i
$833$	− 1.01761e19i	− 1.05533i
$834$	−4.41441e18	−0.454249
$835$	0	0
$836$	5.14699e18	0.521450
$837$	− 1.07070e18i	− 0.107635i
$838$	− 1.87510e18i	− 0.187042i
$839$	1.19196e19	1.17980	0.589899	−	0.807477i	$-0.299168\pi$
$839$	1.19196e19	1.17980	0.589899	+	0.807477i	$0.299168\pi$
$840$	0	0
$841$	−2.39773e18	−0.233682
$842$	− 1.16194e19i	− 1.12371i
$843$	5.30790e18i	0.509382i
$844$	−5.08418e18	−0.484167
$845$	0	0
$846$	−1.16104e18	−0.108878
$847$	1.62254e18i	0.150991i
$848$	3.65925e17i	0.0337924i
$849$	1.64111e18	0.150397
$850$	0	0
$851$	−7.06984e18	−0.638068
$852$	1.10334e18i	0.0988212i
$853$	1.10343e19i	0.980786i	0.871501	+	0.490393i	$0.163147\pi$
$853$	1.10343e19i	0.980786i	−0.871501	+	0.490393i	$0.836853\pi$
$854$	−1.10595e17	−0.00975572
$855$	0	0
$856$	−4.91252e18	−0.426801
$857$	1.61936e18i	0.139627i	0.997560	+	0.0698134i	$0.0222404\pi$
$857$	1.61936e18i	0.139627i	−0.997560	+	0.0698134i	$0.977760\pi$
$858$	− 7.41316e18i	− 0.634360i
$859$	−1.01776e19	−0.864354	−0.432177	−	0.901789i	$-0.642254\pi$
$859$	−1.01776e19	−0.864354	−0.432177	+	0.901789i	$0.642254\pi$
$860$	0	0
$861$	5.09369e18	0.426101
$862$	− 3.27039e18i	− 0.271520i
$863$	1.21087e19i	0.997765i	0.866670	+	0.498882i	$0.166256\pi$
$863$	1.21087e19i	0.997765i	−0.866670	+	0.498882i	$0.833744\pi$
$864$	4.15990e17	0.0340207
$865$	0	0
$866$	−1.30840e19	−1.05408
$867$	− 1.02182e19i	− 0.817051i
$868$	− 1.99612e18i	− 0.158419i
$869$	−1.47544e19	−1.16223
$870$	0	0
$871$	−1.89599e19	−1.47136
$872$	3.59126e18i	0.276624i
$873$	− 5.45704e18i	− 0.417219i
$874$	4.29275e18	0.325771
$875$	0	0
$876$	2.06952e18	0.154736
$877$	− 1.48201e18i	− 0.109990i	−0.998487	−	0.0549952i	$-0.982486\pi$
$877$	− 1.48201e18i	− 0.109990i	0.998487	−	0.0549952i	$-0.0175144\pi$
$878$	− 1.54490e19i	− 1.13812i
$879$	−1.07828e19	−0.788501
$880$	0	0
$881$	2.07849e19	1.49763	0.748814	−	0.662780i	$-0.230624\pi$
$881$	2.07849e19	1.49763	0.748814	+	0.662780i	$0.230624\pi$
$882$	− 2.23782e18i	− 0.160059i
$883$	− 6.95449e18i	− 0.493765i	−0.969045	−	0.246883i	$-0.920594\pi$
$883$	− 6.95449e18i	− 0.493765i	0.969045	−	0.246883i	$-0.0794062\pi$
$884$	−1.52226e19	−1.07287
$885$	0	0
$886$	1.08505e19	0.753583
$887$	− 1.85085e19i	− 1.27605i	−0.770015	−	0.638026i	$-0.779751\pi$
$887$	− 1.85085e19i	− 1.27605i	0.770015	−	0.638026i	$-0.220249\pi$
$888$	3.82784e18i	0.261981i
$889$	−7.87221e18	−0.534854
$890$	0	0
$891$	1.86754e18	0.125045
$892$	1.34353e19i	0.893049i
$893$	6.48703e18i	0.428067i
$894$	5.69285e18	0.372937
$895$	0	0
$896$	7.75534e17	0.0500724
$897$	− 6.18281e18i	− 0.396310i
$898$	− 9.39106e18i	− 0.597611i
$899$	7.74954e18	0.489596
$900$	0	0
$901$	3.37337e18	0.210065
$902$	− 1.67689e19i	− 1.03672i
$903$	− 1.04750e19i	− 0.642957i
$904$	−2.08719e18	−0.127194
$905$	0	0
$906$	−7.73087e18	−0.464403
$907$	− 1.68306e19i	− 1.00381i	−0.864922	−	0.501906i	$-0.832632\pi$
$907$	− 1.68306e19i	− 1.00381i	0.864922	−	0.501906i	$-0.167368\pi$
$908$	1.16249e19i	0.688384i
$909$	1.45845e18	0.0857485
$910$	0	0
$911$	2.31651e17	0.0134266	0.00671328	−	0.999977i	$-0.497863\pi$
$911$	2.31651e17	0.0134266	0.00671328	+	0.999977i	$0.497863\pi$
$912$	− 2.32424e18i	− 0.133756i
$913$	− 1.37825e19i	− 0.787529i
$914$	−2.26042e19	−1.28244
$915$	0	0
$916$	1.02995e19	0.576099
$917$	− 3.29936e18i	− 0.183243i
$918$	− 3.83491e18i	− 0.211484i
$919$	1.51806e19	0.831261	0.415631	−	0.909533i	$-0.363561\pi$
$919$	1.51806e19	0.831261	0.415631	+	0.909533i	$0.363561\pi$
$920$	0	0
$921$	−1.80944e19	−0.976916
$922$	5.20341e17i	0.0278957i
$923$	− 8.87882e18i	− 0.472655i
$924$	3.48168e18	0.184044
$925$	0	0
$926$	−2.64008e18	−0.137609
$927$	− 1.42305e18i	− 0.0736548i
$928$	3.01086e18i	0.154750i
$929$	−8.58574e17	−0.0438203	−0.0219102	−	0.999760i	$-0.506975\pi$
$929$	−8.58574e17	−0.0438203	−0.0219102	+	0.999760i	$0.506975\pi$
$930$	0	0
$931$	−1.25033e19	−0.629290
$932$	5.62106e18i	0.280941i
$933$	− 2.42173e18i	− 0.120198i
$934$	1.13047e19	0.557194
$935$	0	0
$936$	−3.34757e18	−0.162719
$937$	− 7.24328e18i	− 0.349645i	−0.984600	−	0.174823i	$-0.944065\pi$
$937$	− 7.24328e18i	− 0.349645i	0.984600	−	0.174823i	$-0.0559352\pi$
$938$	− 8.90474e18i	− 0.426877i
$939$	6.93385e18	0.330102
$940$	0	0
$941$	1.32405e19	0.621685	0.310842	−	0.950461i	$-0.399389\pi$
$941$	1.32405e19	0.621685	0.310842	+	0.950461i	$0.399389\pi$
$942$	6.45751e18i	0.301116i
$943$	− 1.39858e19i	− 0.647681i
$944$	−3.84567e18	−0.176870
$945$	0	0
$946$	−3.44845e19	−1.56434
$947$	3.98644e19i	1.79601i	0.439981	+	0.898007i	$0.354985\pi$
$947$	3.98644e19i	1.79601i	−0.439981	+	0.898007i	$0.645015\pi$
$948$	6.66266e18i	0.298121i
$949$	−1.66539e19	−0.740094
$950$	0	0
$951$	1.10189e19	0.483019
$952$	− 7.14946e18i	− 0.311267i
$953$	− 1.00415e19i	− 0.434206i	−0.976149	−	0.217103i	$-0.930339\pi$
$953$	− 1.00415e19i	− 0.434206i	0.976149	−	0.217103i	$-0.0696607\pi$
$954$	7.41835e17	0.0318598
$955$	0	0
$956$	8.98173e18	0.380525
$957$	1.35170e19i	0.568790i
$958$	− 3.65753e18i	− 0.152867i
$959$	−2.40837e18	−0.0999774
$960$	0	0
$961$	−1.67797e19	−0.687199
$962$	− 3.08036e19i	− 1.25304i
$963$	9.95910e18i	0.402392i
$964$	−3.65799e18	−0.146805
$965$	0	0
$966$	2.90383e18	0.114979
$967$	− 6.52823e18i	− 0.256758i	−0.991725	−	0.128379i	$-0.959023\pi$
$967$	− 6.52823e18i	− 0.256758i	0.991725	−	0.128379i	$-0.0409773\pi$
$968$	− 2.41209e18i	− 0.0942331i
$969$	−2.14266e19	−0.831474
$970$	0	0
$971$	−3.40758e19	−1.30473	−0.652365	−	0.757905i	$-0.726223\pi$
$971$	−3.40758e19	−1.30473	−0.652365	+	0.757905i	$0.726223\pi$
$972$	− 8.43330e17i	− 0.0320750i
$973$	1.66842e19i	0.630337i
$974$	1.09414e19	0.410619
$975$	0	0
$976$	1.64412e17	0.00608850
$977$	1.53719e18i	0.0565473i	0.999600	+	0.0282737i	$0.00900099\pi$
$977$	1.53719e18i	0.0565473i	−0.999600	+	0.0282737i	$0.990999\pi$
$978$	9.90580e18i	0.361982i
$979$	−1.46925e19	−0.533346
$980$	0	0
$981$	7.28051e18	0.260803
$982$	4.67280e17i	0.0166285i
$983$	1.30768e19i	0.462279i	0.972921	+	0.231140i	$0.0742454\pi$
$983$	1.30768e19i	0.462279i	−0.972921	+	0.231140i	$0.925755\pi$
$984$	−7.57237e18	−0.265928
$985$	0	0
$986$	2.77564e19	0.961975
$987$	4.38815e18i	0.151084i
$988$	1.87037e19i	0.639747i
$989$	−2.87612e19	−0.977307
$990$	0	0
$991$	4.81640e19	1.61526	0.807632	−	0.589687i	$-0.200749\pi$
$991$	4.81640e19	1.61526	0.807632	+	0.589687i	$0.200749\pi$
$992$	2.96746e18i	0.0988687i
$993$	2.68082e18i	0.0887355i
$994$	4.17005e18	0.137129
$995$	0	0
$996$	−6.22377e18	−0.202008
$997$	− 3.51994e19i	− 1.13506i	−0.823354	−	0.567528i	$-0.807900\pi$
$997$	− 3.51994e19i	− 1.13506i	0.823354	−	0.567528i	$-0.192100\pi$
$998$	− 2.21183e19i	− 0.708604i
$999$	7.76013e18	0.246998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.14.c.d.49.2		2
5.2	odd	4		150.14.a.b.1.1		1
5.3	odd	4		6.14.a.a.1.1	✓	1
5.4	even	2	inner	150.14.c.d.49.1		2
15.8	even	4		18.14.a.a.1.1		1
20.3	even	4		48.14.a.e.1.1		1
40.3	even	4		192.14.a.a.1.1		1
40.13	odd	4		192.14.a.f.1.1		1
60.23	odd	4		144.14.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.14.a.a.1.1	✓	1	5.3	odd	4
18.14.a.a.1.1		1	15.8	even	4
48.14.a.e.1.1		1	20.3	even	4
144.14.a.b.1.1		1	60.23	odd	4
150.14.a.b.1.1		1	5.2	odd	4
150.14.c.d.49.1		2	5.4	even	2	inner
150.14.c.d.49.2		2	1.1	even	1	trivial
192.14.a.a.1.1		1	40.3	even	4
192.14.a.f.1.1		1	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+64.0000i q^{2} +729.000i q^{3} -4096.00 q^{4} -46656.0 q^{6} +176336. i q^{7} -262144. i q^{8} -531441. q^{9} +6.61242e6 q^{11} -2.98598e6i q^{12} +2.40290e7i q^{13} -1.12855e7 q^{14} +1.67772e7 q^{16} -1.54665e8i q^{17} -3.40122e7i q^{18} -1.90035e8 q^{19} -1.28549e8 q^{21} +4.23195e8i q^{22} +3.52958e8i q^{23} +1.91103e8 q^{24} -1.53785e9 q^{26} -3.87420e8i q^{27} -7.22272e8i q^{28} +2.80409e9 q^{29} +2.76366e9 q^{31} +1.07374e9i q^{32} +4.82045e9i q^{33} +9.89856e9 q^{34} +2.17678e9 q^{36} +2.00303e10i q^{37} -1.21622e10i q^{38} -1.75171e10 q^{39} -3.96245e10 q^{41} -8.22713e9i q^{42} +8.14862e10i q^{43} -2.70845e10 q^{44} -2.25893e10 q^{46} -3.41360e10i q^{47} +1.22306e10i q^{48} +6.57946e10 q^{49} +1.12751e11 q^{51} -9.84227e10i q^{52} +2.18108e10i q^{53} +2.47949e10 q^{54} +4.62254e10 q^{56} -1.38535e11i q^{57} +1.79462e11i q^{58} -2.29220e11 q^{59} +9.79974e9 q^{61} +1.76874e11i q^{62} -9.37122e10i q^{63} -6.87195e10 q^{64} -3.08509e11 q^{66} +7.89043e11i q^{67} +6.33508e11i q^{68} -2.57306e11 q^{69} -3.69505e11 q^{71} +1.39314e11i q^{72} +6.93078e11i q^{73} -1.28194e12 q^{74} +7.78383e11 q^{76} +1.16601e12i q^{77} -1.12110e12i q^{78} -2.23131e12 q^{79} +2.82430e11 q^{81} -2.53597e12i q^{82} -2.08433e12i q^{83} +5.26536e11 q^{84} -5.21512e12 q^{86} +2.04418e12i q^{87} -1.73341e12i q^{88} -2.22196e12 q^{89} -4.23717e12 q^{91} -1.44572e12i q^{92} +2.01471e12i q^{93} +2.18471e12 q^{94} -7.82758e11 q^{96} +1.02684e13i q^{97} +4.21086e12i q^{98} -3.51411e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{4} - 93312 q^{6} - 1062882 q^{9} + 13224840 q^{11} - 22571008 q^{14} + 33554432 q^{16} - 380069752 q^{19} - 257097888 q^{21} + 382205952 q^{24} - 3075709184 q^{26} + 5608172532 q^{29} + 5527322416 q^{31}+ \cdots - 7028222194440 q^{99}+O(q^{100}) \) 2 * q - 8192 * q^4 - 93312 * q^6 - 1062882 * q^9 + 13224840 * q^11 - 22571008 * q^14 + 33554432 * q^16 - 380069752 * q^19 - 257097888 * q^21 + 382205952 * q^24 - 3075709184 * q^26 + 5608172532 * q^29 + 5527322416 * q^31 + 19797126912 * q^34 + 4353564672 * q^36 - 35034249924 * q^39 - 79249094412 * q^41 - 54168944640 * q^44 - 45178598400 * q^46 + 131589251022 * q^49 + 225501648732 * q^51 + 49589822592 * q^54 + 92450848768 * q^56 - 458439322440 * q^59 + 19599473500 * q^61 - 137438953472 * q^64 - 617018135040 * q^66 - 514612472400 * q^69 - 739009410480 * q^71 - 2563872975616 * q^74 + 1556765704192 * q^76 - 4462619990416 * q^79 + 564859072962 * q^81 + 1053072949248 * q^84 - 10430230380032 * q^86 - 4443922193076 * q^89 - 8474347729216 * q^91 + 4369410232320 * q^94 - 1565515579392 * q^96 - 7028222194440 * q^99

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