LMFDB - Embedded newform 50.22.b.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,22,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$139.738672144$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.22.b.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1024.00i q^{2} -59316.0i q^{3} -1.04858e6 q^{4} +6.07396e7 q^{6} +1.42743e9i q^{7} -1.07374e9i q^{8} +6.94197e9 q^{9} +O(q^{10})$	\(q+1024.00i q^{2} -59316.0i q^{3} -1.04858e6 q^{4} +6.07396e7 q^{6} +1.42743e9i q^{7} -1.07374e9i q^{8} +6.94197e9 q^{9} -1.06768e11 q^{11} +6.21973e10i q^{12} +1.50151e11i q^{13} -1.46168e12 q^{14} +1.09951e12 q^{16} -1.12040e13i q^{17} +7.10857e12i q^{18} -1.10241e13 q^{19} +8.46692e13 q^{21} -1.09330e14i q^{22} -1.29503e14i q^{23} -6.36901e13 q^{24} -1.53754e14 q^{26} -1.03224e15i q^{27} -1.49676e15i q^{28} -2.38237e15 q^{29} -8.78553e14 q^{31} +1.12590e15i q^{32} +6.33304e15i q^{33} +1.14729e16 q^{34} -7.27918e15 q^{36} +3.11300e16i q^{37} -1.12886e16i q^{38} +8.90633e15 q^{39} -2.46129e16 q^{41} +8.67013e16i q^{42} +1.33386e17i q^{43} +1.11954e17 q^{44} +1.32611e17 q^{46} -1.92524e17i q^{47} -6.52186e16i q^{48} -1.47900e18 q^{49} -6.64575e17 q^{51} -1.57444e17i q^{52} +5.94166e17i q^{53} +1.05701e18 q^{54} +1.53269e18 q^{56} +6.53903e17i q^{57} -2.43955e18i q^{58} +2.95595e18 q^{59} +7.98415e18 q^{61} -8.99638e17i q^{62} +9.90914e18i q^{63} -1.15292e18 q^{64} -6.48504e18 q^{66} +4.83704e18i q^{67} +1.17482e19i q^{68} -7.68159e18 q^{69} +8.84902e18 q^{71} -7.45388e18i q^{72} -3.66844e19i q^{73} -3.18771e19 q^{74} +1.15596e19 q^{76} -1.52403e20i q^{77} +9.12008e18i q^{78} -3.38406e19 q^{79} +1.13873e19 q^{81} -2.52036e19i q^{82} -2.04215e20i q^{83} -8.87821e19 q^{84} -1.36587e20 q^{86} +1.41313e20i q^{87} +1.14641e20i q^{88} +4.10241e19 q^{89} -2.14329e20 q^{91} +1.35794e20i q^{92} +5.21122e19i q^{93} +1.97145e20 q^{94} +6.67839e19 q^{96} -7.27592e20i q^{97} -1.51449e21i q^{98} -7.41179e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2097152 q^{4} + 121479168 q^{6} + 13883930694 q^{9}+O(q^{10}) $ 2 * q - 2097152 * q^4 + 121479168 * q^6 + 13883930694 * q^9	$ 2 q - 2097152 q^{4} + 121479168 q^{6} + 13883930694 q^{9} - 213535789896 q^{11} - 2923368103936 q^{14} + 2199023255552 q^{16} - 22048111910920 q^{19} + 169338381301824 q^{21} - 127380140064768 q^{24} - 307508358090752 q^{26} - 47\!\cdots\!20 q^{29}+ \cdots - 14\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 2097152 * q^4 + 121479168 * q^6 + 13883930694 * q^9 - 213535789896 * q^11 - 2923368103936 * q^14 + 2199023255552 * q^16 - 22048111910920 * q^19 + 169338381301824 * q^21 - 127380140064768 * q^24 - 307508358090752 * q^26 - 4764741653216220 * q^29 - 1757105914755776 * q^31 + 22945752555024384 * q^34 - 14558356511391744 * q^36 + 17812661883311568 * q^39 - 49225851891437676 * q^41 + 223908504425988096 * q^44 + 265221828075307008 * q^46 - 2957997283555216434 * q^49 - 1329150643118971056 * q^51 + 2114019178724966400 * q^54 + 3065373632952795136 * q^56 + 5911908268967347560 * q^59 + 15968300180105692444 * q^61 - 2305843009213693952 * q^64 - 12970075047394443264 * q^66 - 15363181595815342272 * q^69 + 17698034677866016464 * q^71 - 63754251994234925056 * q^74 + 23119120995104849920 * q^76 - 67681219157273547040 * q^79 + 22774606400085855282 * q^81 - 177564162511941402624 * q^84 - 273174773684872159232 * q^86 + 82048113487384545420 * q^89 - 428657591693989848736 * q^91 + 394289187730270224384 * q^94 + 133567757748554170368 * q^96 - 1482358053802304733912 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1024.00i	0.707107i
$2$	1024.00i	0.707107i
$3$	− 59316.0i	− 0.579961i	−0.957033	−	0.289980i	$-0.906351\pi$
$3$	− 59316.0i	− 0.579961i	0.957033	−	0.289980i	$-0.0936488\pi$
$4$	−1.04858e6	−0.500000
$5$	0	0
$5$	0	0
$6$	6.07396e7	0.410094
$7$	1.42743e9i	1.90996i	0.296671	+	0.954980i	$0.404123\pi$
$7$	1.42743e9i	1.90996i	−0.296671	+	0.954980i	$0.595877\pi$
$8$	− 1.07374e9i	− 0.353553i
$9$	6.94197e9	0.663645
$10$	0	0
$11$	−1.06768e11	−1.24113	−0.620565	−	0.784155i	$-0.713097\pi$
$11$	−1.06768e11	−1.24113	−0.620565	+	0.784155i	$0.713097\pi$
$12$	6.21973e10i	0.289980i
$13$	1.50151e11i	0.302080i	0.988528	+	0.151040i	$0.0482622\pi$
$13$	1.50151e11i	0.302080i	−0.988528	+	0.151040i	$0.951738\pi$
$14$	−1.46168e12	−1.35055
$15$	0	0
$16$	1.09951e12	0.250000
$17$	− 1.12040e13i	− 1.34790i	−0.738776	−	0.673952i	$-0.764596\pi$
$17$	− 1.12040e13i	− 1.34790i	0.738776	−	0.673952i	$-0.235404\pi$
$18$	7.10857e12i	0.469268i
$19$	−1.10241e13	−0.412504	−0.206252	−	0.978499i	$-0.566127\pi$
$19$	−1.10241e13	−0.412504	−0.206252	+	0.978499i	$0.566127\pi$
$20$	0	0
$21$	8.46692e13	1.10770
$22$	− 1.09330e14i	− 0.877612i
$23$	− 1.29503e14i	− 0.651834i	−0.945398	−	0.325917i	$-0.894327\pi$
$23$	− 1.29503e14i	− 0.651834i	0.945398	−	0.325917i	$-0.105673\pi$
$24$	−6.36901e13	−0.205047
$25$	0	0
$26$	−1.53754e14	−0.213603
$27$	− 1.03224e15i	− 0.964849i
$28$	− 1.49676e15i	− 0.954980i
$29$	−2.38237e15	−1.05155	−0.525776	−	0.850623i	$-0.676225\pi$
$29$	−2.38237e15	−1.05155	−0.525776	+	0.850623i	$0.676225\pi$
$30$	0	0
$31$	−8.78553e14	−0.192517	−0.0962587	−	0.995356i	$-0.530688\pi$
$31$	−8.78553e14	−0.192517	−0.0962587	+	0.995356i	$0.530688\pi$
$32$	1.12590e15i	0.176777i
$33$	6.33304e15i	0.719807i
$34$	1.14729e16	0.953111
$35$	0	0
$36$	−7.27918e15	−0.331823
$37$	3.11300e16i	1.06429i	0.846652	+	0.532146i	$0.178614\pi$
$37$	3.11300e16i	1.06429i	−0.846652	+	0.532146i	$0.821386\pi$
$38$	− 1.12886e16i	− 0.291685i
$39$	8.90633e15	0.175194
$40$	0	0
$41$	−2.46129e16	−0.286373	−0.143187	−	0.989696i	$-0.545735\pi$
$41$	−2.46129e16	−0.286373	−0.143187	+	0.989696i	$0.545735\pi$
$42$	8.67013e16i	0.783263i
$43$	1.33386e17i	0.941222i	0.882341	+	0.470611i	$0.155966\pi$
$43$	1.33386e17i	0.941222i	−0.882341	+	0.470611i	$0.844034\pi$
$44$	1.11954e17	0.620565
$45$	0	0
$46$	1.32611e17	0.460916
$47$	− 1.92524e17i	− 0.533897i	−0.963711	−	0.266948i	$-0.913985\pi$
$47$	− 1.92524e17i	− 0.533897i	0.963711	−	0.266948i	$-0.0860153\pi$
$48$	− 6.52186e16i	− 0.144990i
$49$	−1.47900e18	−2.64794
$50$	0	0
$51$	−6.64575e17	−0.781731
$52$	− 1.57444e17i	− 0.151040i
$53$	5.94166e17i	0.466672i	0.972396	+	0.233336i	$0.0749641\pi$
$53$	5.94166e17i	0.466672i	−0.972396	+	0.233336i	$0.925036\pi$
$54$	1.05701e18	0.682251
$55$	0	0
$56$	1.53269e18	0.675273
$57$	6.53903e17i	0.239236i
$58$	− 2.43955e18i	− 0.743559i
$59$	2.95595e18	0.752925	0.376462	−	0.926432i	$-0.377140\pi$
$59$	2.95595e18	0.752925	0.376462	+	0.926432i	$0.377140\pi$
$60$	0	0
$61$	7.98415e18	1.43306	0.716532	−	0.697554i	$-0.245728\pi$
$61$	7.98415e18	1.43306	0.716532	+	0.697554i	$0.245728\pi$
$62$	− 8.99638e17i	− 0.136130i
$63$	9.90914e18i	1.26754i
$64$	−1.15292e18	−0.125000
$65$	0	0
$66$	−6.48504e18	−0.508981
$67$	4.83704e18i	0.324186i	0.986775	+	0.162093i	$0.0518245\pi$
$67$	4.83704e18i	0.324186i	−0.986775	+	0.162093i	$0.948176\pi$
$68$	1.17482e19i	0.673952i
$69$	−7.68159e18	−0.378038
$70$	0	0
$71$	8.84902e18	0.322613	0.161307	−	0.986904i	$-0.448429\pi$
$71$	8.84902e18	0.322613	0.161307	+	0.986904i	$0.448429\pi$
$72$	− 7.45388e18i	− 0.234634i
$73$	− 3.66844e19i	− 0.999060i	−0.866297	−	0.499530i	$-0.833506\pi$
$73$	− 3.66844e19i	− 0.999060i	0.866297	−	0.499530i	$-0.166494\pi$
$74$	−3.18771e19	−0.752569
$75$	0	0
$76$	1.15596e19	0.206252
$77$	− 1.52403e20i	− 2.37051i
$78$	9.12008e18i	0.123881i
$79$	−3.38406e19	−0.402118	−0.201059	−	0.979579i	$-0.564438\pi$
$79$	−3.38406e19	−0.402118	−0.201059	+	0.979579i	$0.564438\pi$
$80$	0	0
$81$	1.13873e19	0.104071
$82$	− 2.52036e19i	− 0.202497i
$83$	− 2.04215e20i	− 1.44466i	−0.691547	−	0.722332i	$-0.743070\pi$
$83$	− 2.04215e20i	− 1.44466i	0.691547	−	0.722332i	$-0.256930\pi$
$84$	−8.87821e19	−0.553851
$85$	0	0
$86$	−1.36587e20	−0.665544
$87$	1.41313e20i	0.609858i
$88$	1.14641e20i	0.438806i
$89$	4.10241e19	0.139458	0.0697290	−	0.997566i	$-0.477787\pi$
$89$	4.10241e19	0.139458	0.0697290	+	0.997566i	$0.477787\pi$
$90$	0	0
$91$	−2.14329e20	−0.576960
$92$	1.35794e20i	0.325917i
$93$	5.21122e19i	0.111653i
$94$	1.97145e20	0.377522
$95$	0	0
$96$	6.67839e19	0.102524
$97$	− 7.27592e20i	− 1.00181i	−0.865503	−	0.500905i	$-0.833001\pi$
$97$	− 7.27592e20i	− 1.00181i	0.865503	−	0.500905i	$-0.166999\pi$
$98$	− 1.51449e21i	− 1.87238i
$99$	−7.41179e20	−0.823671
$100$	0	0
$101$	5.93965e20	0.535040	0.267520	−	0.963552i	$-0.413796\pi$
$101$	5.93965e20	0.535040	0.267520	+	0.963552i	$0.413796\pi$
$102$	− 6.80525e20i	− 0.552767i
$103$	6.95712e20i	0.510080i	0.966930	+	0.255040i	$0.0820887\pi$
$103$	6.95712e20i	0.510080i	−0.966930	+	0.255040i	$0.917911\pi$
$104$	1.61223e20	0.106801
$105$	0	0
$106$	−6.08426e20	−0.329987
$107$	− 2.38158e21i	− 1.17041i	−0.810887	−	0.585203i	$-0.801015\pi$
$107$	− 2.38158e21i	− 1.17041i	0.810887	−	0.585203i	$-0.198985\pi$
$108$	1.08238e21i	0.482425i
$109$	−2.01913e21	−0.816933	−0.408466	−	0.912773i	$-0.633936\pi$
$109$	−2.01913e21	−0.816933	−0.408466	+	0.912773i	$0.633936\pi$
$110$	0	0
$111$	1.84651e21	0.617248
$112$	1.56947e21i	0.477490i
$113$	− 1.81974e21i	− 0.504296i	−0.967689	−	0.252148i	$-0.918863\pi$
$113$	− 1.81974e21i	− 0.504296i	0.967689	−	0.252148i	$-0.0811369\pi$
$114$	−6.69597e20	−0.169166
$115$	0	0
$116$	2.49810e21	0.525776
$117$	1.04234e21i	0.200474i
$118$	3.02690e21i	0.532398i
$119$	1.59929e22	2.57444
$120$	0	0
$121$	3.99913e21	0.540405
$122$	8.17577e21i	1.01333i
$123$	1.45994e21i	0.166085i
$124$	9.21230e20	0.0962587
$125$	0	0
$126$	−1.01470e22	−0.896283
$127$	2.20220e22i	1.79027i	0.445797	+	0.895134i	$0.352920\pi$
$127$	2.20220e22i	1.79027i	−0.445797	+	0.895134i	$0.647080\pi$
$128$	− 1.18059e21i	− 0.0883883i
$129$	7.91193e21	0.545872
$130$	0	0
$131$	1.44136e22	0.846101	0.423051	−	0.906106i	$-0.360959\pi$
$131$	1.44136e22	0.846101	0.423051	+	0.906106i	$0.360959\pi$
$132$	− 6.64068e21i	− 0.359904i
$133$	− 1.57360e22i	− 0.787867i
$134$	−4.95313e21	−0.229234
$135$	0	0
$136$	−1.20302e22	−0.476556
$137$	− 3.57623e22i	− 1.31177i	−0.754859	−	0.655887i	$-0.772295\pi$
$137$	− 3.57623e22i	− 1.31177i	0.754859	−	0.655887i	$-0.227705\pi$
$138$	− 7.86595e21i	− 0.267313i
$139$	2.10431e22	0.662909	0.331454	−	0.943471i	$-0.392461\pi$
$139$	2.10431e22	0.662909	0.331454	+	0.943471i	$0.392461\pi$
$140$	0	0
$141$	−1.14198e22	−0.309639
$142$	9.06139e21i	0.228122i
$143$	− 1.60313e22i	− 0.374921i
$144$	7.63277e21	0.165911
$145$	0	0
$146$	3.75648e22	0.706442
$147$	8.77283e22i	1.53570i
$148$	− 3.26422e22i	− 0.532146i
$149$	8.71910e22	1.32439	0.662195	−	0.749332i	$-0.269625\pi$
$149$	8.71910e22	1.32439	0.662195	+	0.749332i	$0.269625\pi$
$150$	0	0
$151$	−4.00667e22	−0.529086	−0.264543	−	0.964374i	$-0.585221\pi$
$151$	−4.00667e22	−0.529086	−0.264543	+	0.964374i	$0.585221\pi$
$152$	1.18370e22i	0.145842i
$153$	− 7.77776e22i	− 0.894530i
$154$	1.56061e23	1.67620
$155$	0	0
$156$	−9.33896e21	−0.0875972
$157$	− 4.60441e22i	− 0.403857i	−0.979400	−	0.201929i	$-0.935279\pi$
$157$	− 4.60441e22i	− 0.403857i	0.979400	−	0.201929i	$-0.0647209\pi$
$158$	− 3.46528e22i	− 0.284340i
$159$	3.52436e22	0.270651
$160$	0	0
$161$	1.84856e23	1.24498
$162$	1.16606e22i	0.0735890i
$163$	− 5.72127e22i	− 0.338472i	−0.985576	−	0.169236i	$-0.945870\pi$
$163$	− 5.72127e22i	− 0.338472i	0.985576	−	0.169236i	$-0.0541300\pi$
$164$	2.58085e22	0.143187
$165$	0	0
$166$	2.09116e23	1.02153
$167$	− 1.32913e23i	− 0.609600i	−0.952416	−	0.304800i	$-0.901410\pi$
$167$	− 1.32913e23i	− 0.609600i	0.952416	−	0.304800i	$-0.0985897\pi$
$168$	− 9.09129e22i	− 0.391632i
$169$	2.24519e23	0.908748
$170$	0	0
$171$	−7.65286e22	−0.273757
$172$	− 1.39865e23i	− 0.470611i
$173$	− 5.53136e23i	− 1.75125i	−0.482994	−	0.875624i	$-0.660451\pi$
$173$	− 5.53136e23i	− 1.75125i	0.482994	−	0.875624i	$-0.339549\pi$
$174$	−1.44704e23	−0.431235
$175$	0	0
$176$	−1.17393e23	−0.310283
$177$	− 1.75335e23i	− 0.436667i
$178$	4.20086e22i	0.0986117i
$179$	5.31479e22	0.117633	0.0588165	−	0.998269i	$-0.481267\pi$
$179$	5.31479e22	0.117633	0.0588165	+	0.998269i	$0.481267\pi$
$180$	0	0
$181$	7.59350e23	1.49560	0.747802	−	0.663921i	$-0.231109\pi$
$181$	7.59350e23	1.49560	0.747802	+	0.663921i	$0.231109\pi$
$182$	− 2.19473e23i	− 0.407973i
$183$	− 4.73588e23i	− 0.831121i
$184$	−1.39053e23	−0.230458
$185$	0	0
$186$	−5.33629e22	−0.0789503
$187$	1.19623e24i	1.67292i
$188$	2.01876e23i	0.266948i
$189$	1.47344e24	1.84282
$190$	0	0
$191$	−9.64674e23	−1.08026	−0.540132	−	0.841580i	$-0.681626\pi$
$191$	−9.64674e23	−1.08026	−0.540132	+	0.841580i	$0.681626\pi$
$192$	6.83867e22i	0.0724951i
$193$	3.41192e23i	0.342489i	0.985229	+	0.171245i	$0.0547788\pi$
$193$	3.41192e23i	0.342489i	−0.985229	+	0.171245i	$0.945221\pi$
$194$	7.45055e23	0.708386
$195$	0	0
$196$	1.55084e24	1.32397
$197$	− 5.00591e23i	− 0.405124i	−0.979269	−	0.202562i	$-0.935073\pi$
$197$	− 5.00591e23i	− 0.405124i	0.979269	−	0.202562i	$-0.0649268\pi$
$198$	− 7.58967e23i	− 0.582423i
$199$	5.09875e23	0.371113	0.185557	−	0.982634i	$-0.440591\pi$
$199$	5.09875e23	0.371113	0.185557	+	0.982634i	$0.440591\pi$
$200$	0	0
$201$	2.86914e23	0.188015
$202$	6.08220e23i	0.378330i
$203$	− 3.40066e24i	− 2.00842i
$204$	6.96858e23	0.390866
$205$	0	0
$206$	−7.12409e23	−0.360681
$207$	− 8.99004e23i	− 0.432587i
$208$	1.65092e23i	0.0755200i
$209$	1.17702e24	0.511972
$210$	0	0
$211$	7.29976e23	0.287305	0.143652	−	0.989628i	$-0.454115\pi$
$211$	7.29976e23	0.287305	0.143652	+	0.989628i	$0.454115\pi$
$212$	− 6.23029e23i	− 0.233336i
$213$	− 5.24888e23i	− 0.187103i
$214$	2.43874e24	0.827602
$215$	0	0
$216$	−1.10835e24	−0.341126
$217$	− 1.25407e24i	− 0.367701i
$218$	− 2.06759e24i	− 0.577659i
$219$	−2.17597e24	−0.579416
$220$	0	0
$221$	1.68228e24	0.407174
$222$	1.89082e24i	0.436460i
$223$	5.87017e24i	1.29256i	0.763101	+	0.646279i	$0.223676\pi$
$223$	5.87017e24i	1.29256i	−0.763101	+	0.646279i	$0.776324\pi$
$224$	−1.60714e24	−0.337636
$225$	0	0
$226$	1.86341e24	0.356591
$227$	6.13596e24i	1.12101i	0.828150	+	0.560507i	$0.189394\pi$
$227$	6.13596e24i	1.12101i	−0.828150	+	0.560507i	$0.810606\pi$
$228$	− 6.85667e23i	− 0.119618i
$229$	3.05217e24	0.508552	0.254276	−	0.967132i	$-0.418163\pi$
$229$	3.05217e24	0.508552	0.254276	+	0.967132i	$0.418163\pi$
$230$	0	0
$231$	−9.03995e24	−1.37480
$232$	2.55805e24i	0.371779i
$233$	7.45995e23i	0.103633i	0.998657	+	0.0518166i	$0.0165011\pi$
$233$	7.45995e23i	0.103633i	−0.998657	+	0.0518166i	$0.983499\pi$
$234$	−1.06736e24	−0.141756
$235$	0	0
$236$	−3.09954e24	−0.376462
$237$	2.00729e24i	0.233213i
$238$	1.63767e25i	1.82040i
$239$	1.02561e25	1.09095	0.545473	−	0.838128i	$-0.316350\pi$
$239$	1.02561e25	1.09095	0.545473	+	0.838128i	$0.316350\pi$
$240$	0	0
$241$	1.46660e25	1.42933	0.714663	−	0.699469i	$-0.246580\pi$
$241$	1.46660e25	1.42933	0.714663	+	0.699469i	$0.246580\pi$
$242$	4.09511e24i	0.382124i
$243$	− 1.14730e25i	− 1.02521i
$244$	−8.37199e24	−0.716532
$245$	0	0
$246$	−1.49498e24	−0.117440
$247$	− 1.65527e24i	− 0.124609i
$248$	9.43339e23i	0.0680652i
$249$	−1.21132e25	−0.837848
$250$	0	0
$251$	−1.52767e25	−0.971526	−0.485763	−	0.874090i	$-0.661458\pi$
$251$	−1.52767e25	−0.971526	−0.485763	+	0.874090i	$0.661458\pi$
$252$	− 1.03905e25i	− 0.633768i
$253$	1.38267e25i	0.809011i
$254$	−2.25505e25	−1.26591
$255$	0	0
$256$	1.20893e24	0.0625000
$257$	− 3.66073e25i	− 1.81665i	−0.418270	−	0.908323i	$-0.637364\pi$
$257$	− 3.66073e25i	− 1.81665i	0.418270	−	0.908323i	$-0.362636\pi$
$258$	8.10182e24i	0.385990i
$259$	−4.44358e25	−2.03276
$260$	0	0
$261$	−1.65383e25	−0.697857
$262$	1.47595e25i	0.598284i
$263$	1.74317e25i	0.678899i	0.940624	+	0.339449i	$0.110241\pi$
$263$	1.74317e25i	0.678899i	−0.940624	+	0.339449i	$0.889759\pi$
$264$	6.80005e24	0.254490
$265$	0	0
$266$	1.61137e25	0.557106
$267$	− 2.43338e24i	− 0.0808802i
$268$	− 5.07201e24i	− 0.162093i
$269$	−4.63224e25	−1.42361	−0.711807	−	0.702375i	$-0.752123\pi$
$269$	−4.63224e25	−1.42361	−0.711807	+	0.702375i	$0.752123\pi$
$270$	0	0
$271$	1.79840e25	0.511338	0.255669	−	0.966764i	$-0.417704\pi$
$271$	1.79840e25	0.511338	0.255669	+	0.966764i	$0.417704\pi$
$272$	− 1.23189e25i	− 0.336976i
$273$	1.27131e25i	0.334614i
$274$	3.66206e25	0.927564
$275$	0	0
$276$	8.05473e24	0.189019
$277$	− 1.07659e25i	− 0.243227i	−0.992578	−	0.121614i	$-0.961193\pi$
$277$	− 1.07659e25i	− 0.243227i	0.992578	−	0.121614i	$-0.0388069\pi$
$278$	2.15481e25i	0.468747i
$279$	−6.09888e24	−0.127763
$280$	0	0
$281$	−8.52851e25	−1.65751	−0.828756	−	0.559610i	$-0.810951\pi$
$281$	−8.52851e25	−1.65751	−0.828756	+	0.559610i	$0.810951\pi$
$282$	− 1.16938e25i	− 0.218948i
$283$	− 8.16776e23i	− 0.0147348i	−0.999973	−	0.00736742i	$-0.997655\pi$
$283$	− 8.16776e23i	− 0.0147348i	0.999973	−	0.00736742i	$-0.00234514\pi$
$284$	−9.27887e24	−0.161307
$285$	0	0
$286$	1.64160e25	0.265109
$287$	− 3.51331e25i	− 0.546962i
$288$	7.81596e24i	0.117317i
$289$	−5.64373e25	−0.816843
$290$	0	0
$291$	−4.31579e25	−0.581010
$292$	3.84664e25i	0.499530i
$293$	− 5.29341e25i	− 0.663171i	−0.943425	−	0.331586i	$-0.892416\pi$
$293$	− 5.29341e25i	− 0.663171i	0.943425	−	0.331586i	$-0.107584\pi$
$294$	−8.98338e25	−1.08591
$295$	0	0
$296$	3.34256e25	0.376284
$297$	1.10210e26i	1.19750i
$298$	8.92836e25i	0.936485i
$299$	1.94449e25	0.196906
$300$	0	0
$301$	−1.90399e26	−1.79769
$302$	− 4.10283e25i	− 0.374120i
$303$	− 3.52316e25i	− 0.310302i
$304$	−1.21211e25	−0.103126
$305$	0	0
$306$	7.96443e25	0.632528
$307$	− 1.79951e26i	− 1.38103i	−0.723319	−	0.690514i	$-0.757385\pi$
$307$	− 1.79951e26i	− 1.38103i	0.723319	−	0.690514i	$-0.242615\pi$
$308$	1.59806e26i	1.18525i
$309$	4.12669e25	0.295827
$310$	0	0
$311$	2.49771e26	1.67324	0.836620	−	0.547783i	$-0.184528\pi$
$311$	2.49771e26	1.67324	0.836620	+	0.547783i	$0.184528\pi$
$312$	− 9.56310e24i	− 0.0619406i
$313$	− 2.14796e26i	− 1.34527i	−0.739972	−	0.672637i	$-0.765161\pi$
$313$	− 2.14796e26i	− 1.34527i	0.739972	−	0.672637i	$-0.234839\pi$
$314$	4.71492e25	0.285570
$315$	0	0
$316$	3.54845e25	0.201059
$317$	3.06450e26i	1.67972i	0.542803	+	0.839860i	$0.317363\pi$
$317$	3.06450e26i	1.67972i	−0.542803	+	0.839860i	$0.682637\pi$
$318$	3.60894e25i	0.191379i
$319$	2.54361e26	1.30511
$320$	0	0
$321$	−1.41266e26	−0.678789
$322$	1.89292e26i	0.880331i
$323$	1.23513e26i	0.556016i
$324$	−1.19405e25	−0.0520353
$325$	0	0
$326$	5.85859e25	0.239336
$327$	1.19767e26i	0.473789i
$328$	2.64279e25i	0.101248i
$329$	2.74814e26	1.01972
$330$	0	0
$331$	−1.04905e26	−0.365261	−0.182631	−	0.983182i	$-0.558461\pi$
$331$	−1.04905e26	−0.365261	−0.182631	+	0.983182i	$0.558461\pi$
$332$	2.14134e26i	0.722332i
$333$	2.16103e26i	0.706313i
$334$	1.36103e26	0.431053
$335$	0	0
$336$	9.30948e25	0.276925
$337$	− 1.95001e26i	− 0.562242i	−0.959672	−	0.281121i	$-0.909294\pi$
$337$	− 1.95001e26i	− 0.562242i	0.959672	−	0.281121i	$-0.0907062\pi$
$338$	2.29908e26i	0.642582i
$339$	−1.07940e26	−0.292472
$340$	0	0
$341$	9.38012e25	0.238939
$342$	− 7.83653e25i	− 0.193575i
$343$	− 1.31388e27i	− 3.14751i
$344$	1.43222e26	0.332772
$345$	0	0
$346$	5.66411e26	1.23832
$347$	− 5.59947e26i	− 1.18765i	−0.804595	−	0.593824i	$-0.797618\pi$
$347$	− 5.59947e26i	− 1.18765i	0.804595	−	0.593824i	$-0.202382\pi$
$348$	− 1.48177e26i	− 0.304929i
$349$	2.09819e26	0.418966	0.209483	−	0.977812i	$-0.432822\pi$
$349$	2.09819e26	0.418966	0.209483	+	0.977812i	$0.432822\pi$
$350$	0	0
$351$	1.54991e26	0.291462
$352$	− 1.20210e26i	− 0.219403i
$353$	− 5.72422e26i	− 1.01410i	−0.861916	−	0.507051i	$-0.830736\pi$
$353$	− 5.72422e26i	− 1.01410i	0.861916	−	0.507051i	$-0.169264\pi$
$354$	1.79543e26	0.308770
$355$	0	0
$356$	−4.30168e25	−0.0697290
$357$	− 9.48632e26i	− 1.49307i
$358$	5.44234e25i	0.0831791i
$359$	4.84990e26	0.719848	0.359924	−	0.932982i	$-0.382803\pi$
$359$	4.84990e26	0.719848	0.359924	+	0.932982i	$0.382803\pi$
$360$	0	0
$361$	−5.92680e26	−0.829840
$362$	7.77574e26i	1.05755i
$363$	− 2.37213e26i	− 0.313414i
$364$	2.24740e26	0.288480
$365$	0	0
$366$	4.84954e26	0.587691
$367$	6.65755e26i	0.784008i	0.919963	+	0.392004i	$0.128218\pi$
$367$	6.65755e26i	0.784008i	−0.919963	+	0.392004i	$0.871782\pi$
$368$	− 1.42390e26i	− 0.162959i
$369$	−1.70862e26	−0.190050
$370$	0	0
$371$	−8.48128e26	−0.891324
$372$	− 5.46437e25i	− 0.0558263i
$373$	− 1.46537e27i	− 1.45547i	−0.685858	−	0.727735i	$-0.740573\pi$
$373$	− 1.46537e27i	− 1.45547i	0.685858	−	0.727735i	$-0.259427\pi$
$374$	−1.22493e27	−1.18294
$375$	0	0
$376$	−2.06721e26	−0.188761
$377$	− 3.57714e26i	− 0.317652i
$378$	1.50880e27i	1.30307i
$379$	1.80711e27	1.51800	0.759002	−	0.651088i	$-0.225687\pi$
$379$	1.80711e27	1.51800	0.759002	+	0.651088i	$0.225687\pi$
$380$	0	0
$381$	1.30626e27	1.03829
$382$	− 9.87826e26i	− 0.763862i
$383$	− 9.69700e26i	− 0.729542i	−0.931097	−	0.364771i	$-0.881147\pi$
$383$	− 9.69700e26i	− 0.729542i	0.931097	−	0.364771i	$-0.118853\pi$
$384$	−7.00280e25	−0.0512618
$385$	0	0
$386$	−3.49380e26	−0.242176
$387$	9.25962e26i	0.624637i
$388$	7.62936e26i	0.500905i
$389$	−3.19483e25	−0.0204163	−0.0102081	−	0.999948i	$-0.503249\pi$
$389$	−3.19483e25	−0.0204163	−0.0102081	+	0.999948i	$0.503249\pi$
$390$	0	0
$391$	−1.45095e27	−0.878609
$392$	1.58806e27i	0.936190i
$393$	− 8.54954e26i	− 0.490706i
$394$	5.12605e26	0.286466
$395$	0	0
$396$	7.77183e26	0.411835
$397$	− 5.23867e26i	− 0.270346i	−0.990822	−	0.135173i	$-0.956841\pi$
$397$	− 5.23867e26i	− 0.270346i	0.990822	−	0.135173i	$-0.0431591\pi$
$398$	5.22112e26i	0.262417i
$399$	−9.33398e26	−0.456932
$400$	0	0
$401$	1.65135e27	0.767049	0.383525	−	0.923531i	$-0.374710\pi$
$401$	1.65135e27	0.767049	0.383525	+	0.923531i	$0.374710\pi$
$402$	2.93800e26i	0.132947i
$403$	− 1.31915e26i	− 0.0581557i
$404$	−6.22817e26	−0.267520
$405$	0	0
$406$	3.48227e27	1.42017
$407$	− 3.32369e27i	− 1.32093i
$408$	7.13582e26i	0.276384i
$409$	−1.41506e27	−0.534172	−0.267086	−	0.963673i	$-0.586061\pi$
$409$	−1.41506e27	−0.534172	−0.267086	+	0.963673i	$0.586061\pi$
$410$	0	0
$411$	−2.12127e27	−0.760778
$412$	− 7.29507e26i	− 0.255040i
$413$	4.21941e27i	1.43806i
$414$	9.20580e26	0.305885
$415$	0	0
$416$	−1.69055e26	−0.0534007
$417$	− 1.24819e27i	− 0.384461i
$418$	1.20526e27i	0.362019i
$419$	−1.80515e27	−0.528769	−0.264385	−	0.964417i	$-0.585169\pi$
$419$	−1.80515e27	−0.528769	−0.264385	+	0.964417i	$0.585169\pi$
$420$	0	0
$421$	−1.98386e27	−0.552775	−0.276388	−	0.961046i	$-0.589137\pi$
$421$	−1.98386e27	−0.552775	−0.276388	+	0.961046i	$0.589137\pi$
$422$	7.47496e26i	0.203155i
$423$	− 1.33650e27i	− 0.354318i
$424$	6.37981e26	0.164993
$425$	0	0
$426$	5.37486e26	0.132302
$427$	1.13968e28i	2.73709i
$428$	2.49727e27i	0.585203i
$429$	−9.50910e26	−0.217439
$430$	0	0
$431$	−3.46591e27	−0.754756	−0.377378	−	0.926059i	$-0.623174\pi$
$431$	−3.46591e27	−0.754756	−0.377378	+	0.926059i	$0.623174\pi$
$432$	− 1.13496e27i	− 0.241212i
$433$	5.88060e27i	1.21983i	0.792467	+	0.609915i	$0.208796\pi$
$433$	5.88060e27i	1.21983i	−0.792467	+	0.609915i	$0.791204\pi$
$434$	1.28417e27	0.260004
$435$	0	0
$436$	2.11721e27	0.408466
$437$	1.42765e27i	0.268884i
$438$	− 2.22820e27i	− 0.409709i
$439$	6.95231e26	0.124811	0.0624053	−	0.998051i	$-0.480123\pi$
$439$	6.95231e26	0.124811	0.0624053	+	0.998051i	$0.480123\pi$
$440$	0	0
$441$	−1.02672e28	−1.75730
$442$	1.72266e27i	0.287916i
$443$	4.77606e26i	0.0779526i	0.999240	+	0.0389763i	$0.0124097\pi$
$443$	4.77606e26i	0.0779526i	−0.999240	+	0.0389763i	$0.987590\pi$
$444$	−1.93620e27	−0.308624
$445$	0	0
$446$	−6.01106e27	−0.913976
$447$	− 5.17182e27i	− 0.768094i
$448$	− 1.64571e27i	− 0.238745i
$449$	−6.02792e27	−0.854241	−0.427121	−	0.904195i	$-0.640472\pi$
$449$	−6.02792e27	−0.854241	−0.427121	+	0.904195i	$0.640472\pi$
$450$	0	0
$451$	2.62787e27	0.355427
$452$	1.90813e27i	0.252148i
$453$	2.37660e27i	0.306849i
$454$	−6.28322e27	−0.792676
$455$	0	0
$456$	7.02123e26	0.0845828
$457$	− 3.92994e27i	− 0.462664i	−0.972875	−	0.231332i	$-0.925692\pi$
$457$	− 3.92994e27i	− 0.462664i	0.972875	−	0.231332i	$-0.0743083\pi$
$458$	3.12542e27i	0.359601i
$459$	−1.15652e28	−1.30052
$460$	0	0
$461$	1.19082e28	1.27934	0.639672	−	0.768648i	$-0.279070\pi$
$461$	1.19082e28	1.27934	0.639672	+	0.768648i	$0.279070\pi$
$462$	− 9.25691e27i	− 0.972132i
$463$	6.15811e27i	0.632189i	0.948728	+	0.316095i	$0.102372\pi$
$463$	6.15811e27i	0.632189i	−0.948728	+	0.316095i	$0.897628\pi$
$464$	−2.61944e27	−0.262888
$465$	0	0
$466$	−7.63899e26	−0.0732797
$467$	− 1.30147e28i	− 1.22069i	−0.792135	−	0.610346i	$-0.791030\pi$
$467$	− 1.30147e28i	− 1.22069i	0.792135	−	0.610346i	$-0.208970\pi$
$468$	− 1.09297e27i	− 0.100237i
$469$	−6.90452e27	−0.619182
$470$	0	0
$471$	−2.73115e27	−0.234221
$472$	− 3.17393e27i	− 0.266199i
$473$	− 1.42414e28i	− 1.16818i
$474$	−2.05546e27	−0.164906
$475$	0	0
$476$	−1.67697e28	−1.28722
$477$	4.12468e27i	0.309705i
$478$	1.05022e28i	0.771416i
$479$	1.70133e28	1.22255	0.611273	−	0.791420i	$-0.290658\pi$
$479$	1.70133e28	1.22255	0.611273	+	0.791420i	$0.290658\pi$
$480$	0	0
$481$	−4.67419e27	−0.321501
$482$	1.50179e28i	1.01069i
$483$	− 1.09649e28i	− 0.722038i
$484$	−4.19340e27	−0.270203
$485$	0	0
$486$	1.17484e28	0.724930
$487$	− 2.45443e27i	− 0.148216i	−0.997250	−	0.0741082i	$-0.976389\pi$
$487$	− 2.45443e27i	− 0.148216i	0.997250	−	0.0741082i	$-0.0236110\pi$
$488$	− 8.57292e27i	− 0.506664i
$489$	−3.39363e27	−0.196301
$490$	0	0
$491$	3.07994e28	1.70682	0.853408	−	0.521243i	$-0.174532\pi$
$491$	3.07994e28	1.70682	0.853408	+	0.521243i	$0.174532\pi$
$492$	− 1.53086e27i	− 0.0830427i
$493$	2.66920e28i	1.41739i
$494$	1.69499e27	0.0881121
$495$	0	0
$496$	−9.65979e26	−0.0481294
$497$	1.26313e28i	0.616178i
$498$	− 1.24039e28i	− 0.592448i
$499$	2.07463e28	0.970252	0.485126	−	0.874444i	$-0.338774\pi$
$499$	2.07463e28	0.970252	0.485126	+	0.874444i	$0.338774\pi$
$500$	0	0
$501$	−7.88388e27	−0.353544
$502$	− 1.56433e28i	− 0.686973i
$503$	3.54838e28i	1.52604i	0.646373	+	0.763022i	$0.276285\pi$
$503$	3.54838e28i	1.52604i	−0.646373	+	0.763022i	$0.723715\pi$
$504$	1.06399e28	0.448142
$505$	0	0
$506$	−1.41586e28	−0.572057
$507$	− 1.33176e28i	− 0.527038i
$508$	− 2.30918e28i	− 0.895134i
$509$	−2.04071e28	−0.774900	−0.387450	−	0.921891i	$-0.626644\pi$
$509$	−2.04071e28	−0.774900	−0.387450	+	0.921891i	$0.626644\pi$
$510$	0	0
$511$	5.23643e28	1.90816
$512$	1.23794e27i	0.0441942i
$513$	1.13794e28i	0.398005i
$514$	3.74859e28	1.28456
$515$	0	0
$516$	−8.29626e27	−0.272936
$517$	2.05554e28i	0.662636i
$518$	− 4.55022e28i	− 1.43738i
$519$	−3.28098e28	−1.01566
$520$	0	0
$521$	−2.64349e28	−0.785927	−0.392963	−	0.919554i	$-0.628550\pi$
$521$	−2.64349e28	−0.785927	−0.392963	+	0.919554i	$0.628550\pi$
$522$	− 1.69353e28i	− 0.493459i
$523$	− 3.70305e28i	− 1.05753i	−0.848769	−	0.528763i	$-0.822656\pi$
$523$	− 3.70305e28i	− 1.05753i	0.848769	−	0.528763i	$-0.177344\pi$
$524$	−1.51137e28	−0.423051
$525$	0	0
$526$	−1.78501e28	−0.480054
$527$	9.84329e27i	0.259495i
$528$	6.96326e27i	0.179952i
$529$	2.27006e28	0.575112
$530$	0	0
$531$	2.05201e28	0.499675
$532$	1.65004e28i	0.393933i
$533$	− 3.69564e27i	− 0.0865077i
$534$	2.49178e27	0.0571909
$535$	0	0
$536$	5.19373e27	0.114617
$537$	− 3.15252e27i	− 0.0682225i
$538$	− 4.74341e28i	− 1.00665i
$539$	1.57910e29	3.28645
$540$	0	0
$541$	−9.59401e27	−0.192056	−0.0960282	−	0.995379i	$-0.530614\pi$
$541$	−9.59401e27	−0.192056	−0.0960282	+	0.995379i	$0.530614\pi$
$542$	1.84156e28i	0.361570i
$543$	− 4.50416e28i	− 0.867392i
$544$	1.26146e28	0.238278
$545$	0	0
$546$	−1.30182e28	−0.236608
$547$	7.60716e28i	1.35630i	0.734924	+	0.678150i	$0.237218\pi$
$547$	7.60716e28i	1.35630i	−0.734924	+	0.678150i	$0.762782\pi$
$548$	3.74995e28i	0.655887i
$549$	5.54257e28	0.951046
$550$	0	0
$551$	2.62634e28	0.433769
$552$	8.24805e27i	0.133657i
$553$	− 4.83050e28i	− 0.768029i
$554$	1.10243e28	0.171988
$555$	0	0
$556$	−2.20653e28	−0.331454
$557$	4.97908e28i	0.733956i	0.930230	+	0.366978i	$0.119608\pi$
$557$	4.97908e28i	0.733956i	−0.930230	+	0.366978i	$0.880392\pi$
$558$	− 6.24526e27i	− 0.0903423i
$559$	−2.00280e28	−0.284324
$560$	0	0
$561$	7.09553e28	0.970230
$562$	− 8.73319e28i	− 1.17204i
$563$	8.49629e28i	1.11916i	0.828777	+	0.559579i	$0.189037\pi$
$563$	8.49629e28i	1.11916i	−0.828777	+	0.559579i	$0.810963\pi$
$564$	1.19745e28	0.154820
$565$	0	0
$566$	8.36379e26	0.0104191
$567$	1.62545e28i	0.198771i
$568$	− 9.50156e27i	− 0.114061i
$569$	−5.57042e28	−0.656461	−0.328230	−	0.944598i	$-0.606452\pi$
$569$	−5.57042e28	−0.656461	−0.328230	+	0.944598i	$0.606452\pi$
$570$	0	0
$571$	−1.58127e29	−1.79608	−0.898041	−	0.439911i	$-0.855010\pi$
$571$	−1.58127e29	−1.79608	−0.898041	+	0.439911i	$0.855010\pi$
$572$	1.68100e28i	0.187460i
$573$	5.72206e28i	0.626511i
$574$	3.59763e28	0.386760
$575$	0	0
$576$	−8.00354e27	−0.0829557
$577$	− 1.14412e29i	− 1.16446i	−0.813025	−	0.582229i	$-0.802181\pi$
$577$	− 1.14412e29i	− 1.16446i	0.813025	−	0.582229i	$-0.197819\pi$
$578$	− 5.77917e28i	− 0.577595i
$579$	2.02381e28	0.198630
$580$	0	0
$581$	2.91501e29	2.75925
$582$	− 4.41937e28i	− 0.410836i
$583$	− 6.34379e28i	− 0.579200i
$584$	−3.93896e28	−0.353221
$585$	0	0
$586$	5.42045e28	0.468933
$587$	3.03657e28i	0.258038i	0.991642	+	0.129019i	$0.0411828\pi$
$587$	3.03657e28i	0.258038i	−0.991642	+	0.129019i	$0.958817\pi$
$588$	− 9.19898e28i	− 0.767852i
$589$	9.68522e27	0.0794143
$590$	0	0
$591$	−2.96931e28	−0.234956
$592$	3.42278e28i	0.266073i
$593$	1.80310e29i	1.37704i	0.725218	+	0.688519i	$0.241739\pi$
$593$	1.80310e29i	1.37704i	−0.725218	+	0.688519i	$0.758261\pi$
$594$	−1.12855e29	−0.846763
$595$	0	0
$596$	−9.14264e28	−0.662195
$597$	− 3.02437e28i	− 0.215231i
$598$	1.99116e28i	0.139234i
$599$	−2.43184e29	−1.67091	−0.835455	−	0.549558i	$-0.814796\pi$
$599$	−2.43184e29	−1.67091	−0.835455	+	0.549558i	$0.814796\pi$
$600$	0	0
$601$	−1.53373e29	−1.01758	−0.508789	−	0.860891i	$-0.669907\pi$
$601$	−1.53373e29	−1.01758	−0.508789	+	0.860891i	$0.669907\pi$
$602$	− 1.94968e29i	− 1.27116i
$603$	3.35786e28i	0.215145i
$604$	4.20130e28	0.264543
$605$	0	0
$606$	3.60772e28	0.219417
$607$	− 2.90773e28i	− 0.173809i	−0.996217	−	0.0869047i	$-0.972302\pi$
$607$	− 2.90773e28i	− 0.173809i	0.996217	−	0.0869047i	$-0.0276976\pi$
$608$	− 1.24120e28i	− 0.0729212i
$609$	−2.01713e29	−1.16480
$610$	0	0
$611$	2.89076e28	0.161280
$612$	8.15558e28i	0.447265i
$613$	1.21635e29i	0.655726i	0.944725	+	0.327863i	$0.106329\pi$
$613$	1.21635e29i	0.655726i	−0.944725	+	0.327863i	$0.893671\pi$
$614$	1.84270e29	0.976534
$615$	0	0
$616$	−1.63642e29	−0.838102
$617$	8.98199e28i	0.452250i	0.974098	+	0.226125i	$0.0726057\pi$
$617$	8.98199e28i	0.452250i	−0.974098	+	0.226125i	$0.927394\pi$
$618$	4.22573e28i	0.209181i
$619$	−3.27118e29	−1.59203	−0.796017	−	0.605275i	$-0.793063\pi$
$619$	−3.27118e29	−1.59203	−0.796017	+	0.605275i	$0.793063\pi$
$620$	0	0
$621$	−1.33677e29	−0.628922
$622$	2.55766e29i	1.18316i
$623$	5.85588e28i	0.266359i
$624$	9.79261e27	0.0437986
$625$	0	0
$626$	2.19951e29	0.951253
$627$	− 6.98158e28i	− 0.296924i
$628$	4.82807e28i	0.201929i
$629$	3.48780e29	1.43456
$630$	0	0
$631$	9.03181e28	0.359308	0.179654	−	0.983730i	$-0.442502\pi$
$631$	9.03181e28	0.359308	0.179654	+	0.983730i	$0.442502\pi$
$632$	3.63361e28i	0.142170i
$633$	− 4.32993e28i	− 0.166626i
$634$	−3.13804e29	−1.18774
$635$	0	0
$636$	−3.69556e28	−0.135326
$637$	− 2.22072e29i	− 0.799891i
$638$	2.60465e29i	0.922854i
$639$	6.14296e28	0.214101
$640$	0	0
$641$	−3.16031e29	−1.06591	−0.532955	−	0.846144i	$-0.678918\pi$
$641$	−3.16031e29	−1.06591	−0.532955	+	0.846144i	$0.678918\pi$
$642$	− 1.44656e29i	− 0.479977i
$643$	1.84895e29i	0.603546i	0.953380	+	0.301773i	$0.0975785\pi$
$643$	1.84895e29i	0.603546i	−0.953380	+	0.301773i	$0.902422\pi$
$644$	−1.93835e29	−0.622488
$645$	0	0
$646$	−1.26478e29	−0.393163
$647$	− 1.55883e29i	− 0.476765i	−0.971171	−	0.238383i	$-0.923383\pi$
$647$	− 1.55883e29i	− 0.476765i	0.971171	−	0.238383i	$-0.0766172\pi$
$648$	− 1.22270e28i	− 0.0367945i
$649$	−3.15601e29	−0.934478
$650$	0	0
$651$	−7.43864e28	−0.213252
$652$	5.99919e28i	0.169236i
$653$	− 5.45219e29i	− 1.51350i	−0.653704	−	0.756751i	$-0.726786\pi$
$653$	− 5.45219e29i	− 1.51350i	0.653704	−	0.756751i	$-0.273214\pi$
$654$	−1.22641e29	−0.335019
$655$	0	0
$656$	−2.70622e28	−0.0715934
$657$	− 2.54662e29i	− 0.663022i
$658$	2.81409e29i	0.721052i
$659$	−3.88443e29	−0.979558	−0.489779	−	0.871847i	$-0.662923\pi$
$659$	−3.88443e29	−0.979558	−0.489779	+	0.871847i	$0.662923\pi$
$660$	0	0
$661$	5.22430e29	1.27618	0.638091	−	0.769961i	$-0.279724\pi$
$661$	5.22430e29	1.27618	0.638091	+	0.769961i	$0.279724\pi$
$662$	− 1.07423e29i	− 0.258279i
$663$	− 9.97864e28i	− 0.236145i
$664$	−2.19274e29	−0.510766
$665$	0	0
$666$	−2.21290e29	−0.499439
$667$	3.08524e29i	0.685437i
$668$	1.39370e29i	0.304800i
$669$	3.48195e29	0.749633
$670$	0	0
$671$	−8.52451e29	−1.77862
$672$	9.53290e28i	0.195816i
$673$	3.52401e29i	0.712655i	0.934361	+	0.356327i	$0.115971\pi$
$673$	3.52401e29i	0.712655i	−0.934361	+	0.356327i	$0.884029\pi$
$674$	1.99681e29	0.397565
$675$	0	0
$676$	−2.35426e29	−0.454374
$677$	4.45535e29i	0.846644i	0.905979	+	0.423322i	$0.139136\pi$
$677$	4.45535e29i	0.846644i	−0.905979	+	0.423322i	$0.860864\pi$
$678$	− 1.10530e29i	− 0.206809i
$679$	1.03858e30	1.91341
$680$	0	0
$681$	3.63961e29	0.650144
$682$	9.60525e28i	0.168956i
$683$	6.32620e29i	1.09579i	0.836548	+	0.547893i	$0.184570\pi$
$683$	6.32620e29i	1.09579i	−0.836548	+	0.547893i	$0.815430\pi$
$684$	8.02461e28	0.136878
$685$	0	0
$686$	1.34541e30	2.22562
$687$	− 1.81042e29i	− 0.294940i
$688$	1.46660e29i	0.235305i
$689$	−8.92144e28	−0.140972
$690$	0	0
$691$	3.28853e29	0.504061	0.252030	−	0.967719i	$-0.418902\pi$
$691$	3.28853e29	0.504061	0.252030	+	0.967719i	$0.418902\pi$
$692$	5.80005e29i	0.875624i
$693$	− 1.05798e30i	− 1.57318i
$694$	5.73386e29	0.839794
$695$	0	0
$696$	1.51733e29	0.215618
$697$	2.75763e29i	0.386004i
$698$	2.14855e29i	0.296253i
$699$	4.42494e28	0.0601032
$700$	0	0
$701$	−1.17358e30	−1.54694	−0.773471	−	0.633832i	$-0.781481\pi$
$701$	−1.17358e30	−1.54694	−0.773471	+	0.633832i	$0.781481\pi$
$702$	1.58711e29i	0.206094i
$703$	− 3.43179e29i	− 0.439025i
$704$	1.23095e29	0.155141
$705$	0	0
$706$	5.86160e29	0.717078
$707$	8.47841e29i	1.02190i
$708$	1.83852e29i	0.218333i
$709$	−4.17850e28	−0.0488917	−0.0244458	−	0.999701i	$-0.507782\pi$
$709$	−4.17850e28	−0.0488917	−0.0244458	+	0.999701i	$0.507782\pi$
$710$	0	0
$711$	−2.34920e29	−0.266864
$712$	− 4.40492e28i	− 0.0493059i
$713$	1.13775e29i	0.125489i
$714$	9.71399e29	1.05576
$715$	0	0
$716$	−5.57296e28	−0.0588165
$717$	− 6.08350e29i	− 0.632706i
$718$	4.96629e29i	0.509009i
$719$	−1.11149e30	−1.12267	−0.561336	−	0.827588i	$-0.689713\pi$
$719$	−1.11149e30	−1.12267	−0.561336	+	0.827588i	$0.689713\pi$
$720$	0	0
$721$	−9.93077e29	−0.974233
$722$	− 6.06904e29i	− 0.586786i
$723$	− 8.69926e29i	− 0.828954i
$724$	−7.96236e29	−0.747802
$725$	0	0
$726$	2.42906e29	0.221617
$727$	− 1.37984e30i	− 1.24084i	−0.784269	−	0.620421i	$-0.786962\pi$
$727$	− 1.37984e30i	− 1.24084i	0.784269	−	0.620421i	$-0.213038\pi$
$728$	2.30134e29i	0.203986i
$729$	−5.61417e29	−0.490509
$730$	0	0
$731$	1.49446e30	1.26868
$732$	4.96593e29i	0.415560i
$733$	− 2.24957e30i	− 1.85570i	−0.372956	−	0.927849i	$-0.621656\pi$
$733$	− 2.24957e30i	− 1.85570i	0.372956	−	0.927849i	$-0.378344\pi$
$734$	−6.81733e29	−0.554378
$735$	0	0
$736$	1.45807e29	0.115229
$737$	− 5.16441e29i	− 0.402357i
$738$	− 1.74963e29i	− 0.134386i
$739$	1.72254e30	1.30438	0.652188	−	0.758057i	$-0.273851\pi$
$739$	1.72254e30	1.30438	0.652188	+	0.758057i	$0.273851\pi$
$740$	0	0
$741$	−9.81839e28	−0.0722685
$742$	− 8.68483e29i	− 0.630261i
$743$	− 1.06638e30i	− 0.763006i	−0.924368	−	0.381503i	$-0.875407\pi$
$743$	− 1.06638e30i	− 0.763006i	0.924368	−	0.381503i	$-0.124593\pi$
$744$	5.59551e28	0.0394752
$745$	0	0
$746$	1.50053e30	1.02917
$747$	− 1.41765e30i	− 0.958744i
$748$	− 1.25433e30i	− 0.836462i
$749$	3.39954e30	2.23543
$750$	0	0
$751$	4.90593e29	0.313691	0.156846	−	0.987623i	$-0.449868\pi$
$751$	4.90593e29	0.313691	0.156846	+	0.987623i	$0.449868\pi$
$752$	− 2.11682e29i	− 0.133474i
$753$	9.06151e29i	0.563447i
$754$	3.66299e29	0.224614
$755$	0	0
$756$	−1.54501e30	−0.921411
$757$	1.80527e30i	1.06178i	0.847440	+	0.530891i	$0.178143\pi$
$757$	1.80527e30i	1.06178i	−0.847440	+	0.530891i	$0.821857\pi$
$758$	1.85048e30i	1.07339i
$759$	8.20147e29	0.469195
$760$	0	0
$761$	1.03009e30	0.573240	0.286620	−	0.958044i	$-0.407468\pi$
$761$	1.03009e30	0.573240	0.286620	+	0.958044i	$0.407468\pi$
$762$	1.33761e30i	0.734179i
$763$	− 2.88216e30i	− 1.56031i
$764$	1.01153e30	0.540132
$765$	0	0
$766$	9.92973e29	0.515864
$767$	4.43838e29i	0.227443i
$768$	− 7.17086e28i	− 0.0362476i
$769$	−7.98485e29	−0.398144	−0.199072	−	0.979985i	$-0.563793\pi$
$769$	−7.98485e29	−0.398144	−0.199072	+	0.979985i	$0.563793\pi$
$770$	0	0
$771$	−2.17140e30	−1.05358
$772$	− 3.57765e29i	− 0.171245i
$773$	− 2.56868e30i	− 1.21290i	−0.795122	−	0.606450i	$-0.792593\pi$
$773$	− 2.56868e30i	− 1.21290i	0.795122	−	0.606450i	$-0.207407\pi$
$774$	−9.48185e29	−0.441685
$775$	0	0
$776$	−7.81246e29	−0.354193
$777$	2.63575e30i	1.17892i
$778$	− 3.27150e28i	− 0.0144365i
$779$	2.71334e29	0.118130
$780$	0	0
$781$	−9.44791e29	−0.400405
$782$	− 1.48577e30i	− 0.621270i
$783$	2.45917e30i	1.01459i
$784$	−1.62618e30	−0.661986
$785$	0	0
$786$	8.75473e29	0.346981
$787$	− 3.43359e30i	− 1.34281i	−0.741092	−	0.671403i	$-0.765692\pi$
$787$	− 3.43359e30i	− 1.34281i	0.741092	−	0.671403i	$-0.234308\pi$
$788$	5.24908e29i	0.202562i
$789$	1.03398e30	0.393735
$790$	0	0
$791$	2.59754e30	0.963184
$792$	7.95835e29i	0.291212i
$793$	1.19882e30i	0.432900i
$794$	5.36440e29	0.191164
$795$	0	0
$796$	−5.34642e29	−0.185557
$797$	− 3.29683e30i	− 1.12923i	−0.825353	−	0.564617i	$-0.809024\pi$
$797$	− 3.29683e30i	− 1.12923i	0.825353	−	0.564617i	$-0.190976\pi$
$798$	− 9.55799e29i	− 0.323100i
$799$	−2.15704e30	−0.719641
$800$	0	0
$801$	2.84788e29	0.0925507
$802$	1.69098e30i	0.542386i
$803$	3.91672e30i	1.23996i
$804$	−3.00851e29	−0.0940076
$805$	0	0
$806$	1.35081e29	0.0411223
$807$	2.74766e30i	0.825640i
$808$	− 6.37765e29i	− 0.189165i
$809$	−5.34854e30	−1.56594	−0.782971	−	0.622059i	$-0.786297\pi$
$809$	−5.34854e30	−1.56594	−0.782971	+	0.622059i	$0.786297\pi$
$810$	0	0
$811$	−5.96622e30	−1.70208	−0.851041	−	0.525099i	$-0.824028\pi$
$811$	−5.96622e30	−1.70208	−0.851041	+	0.525099i	$0.824028\pi$
$812$	3.56585e30i	1.00421i
$813$	− 1.06674e30i	− 0.296556i
$814$	3.40345e30	0.934036
$815$	0	0
$816$	−7.30708e29	−0.195433
$817$	− 1.47046e30i	− 0.388258i
$818$	− 1.44902e30i	− 0.377716i
$819$	−1.48786e30	−0.382897
$820$	0	0
$821$	6.73645e30	1.68977	0.844886	−	0.534947i	$-0.179668\pi$
$821$	6.73645e30	1.68977	0.844886	+	0.534947i	$0.179668\pi$
$822$	− 2.17219e30i	− 0.537951i
$823$	2.93477e29i	0.0717588i	0.999356	+	0.0358794i	$0.0114232\pi$
$823$	2.93477e29i	0.0717588i	−0.999356	+	0.0358794i	$0.988577\pi$
$824$	7.47015e29	0.180341
$825$	0	0
$826$	−4.32067e30	−1.01686
$827$	6.88636e30i	1.60023i	0.599847	+	0.800114i	$0.295228\pi$
$827$	6.88636e30i	1.60023i	−0.599847	+	0.800114i	$0.704772\pi$
$828$	9.42674e29i	0.216293i
$829$	4.58006e30	1.03764	0.518822	−	0.854882i	$-0.326371\pi$
$829$	4.58006e30	1.03764	0.518822	+	0.854882i	$0.326371\pi$
$830$	0	0
$831$	−6.38590e29	−0.141062
$832$	− 1.73112e29i	− 0.0377600i
$833$	1.65707e31i	3.56917i
$834$	1.27815e30	0.271855
$835$	0	0
$836$	−1.23419e30	−0.255986
$837$	9.06874e29i	0.185750i
$838$	− 1.84847e30i	− 0.373896i
$839$	−6.83025e30	−1.36438	−0.682191	−	0.731174i	$-0.738973\pi$
$839$	−6.83025e30	−1.36438	−0.682191	+	0.731174i	$0.738973\pi$
$840$	0	0
$841$	5.42848e29	0.105760
$842$	− 2.03147e30i	− 0.390871i
$843$	5.05877e30i	0.961292i
$844$	−7.65436e29	−0.143652
$845$	0	0
$846$	1.36857e30	0.250541
$847$	5.70847e30i	1.03215i
$848$	6.53293e29i	0.116668i
$849$	−4.84479e28	−0.00854563
$850$	0	0
$851$	4.03142e30	0.693742
$852$	5.50385e29i	0.0935516i
$853$	− 6.29163e30i	− 1.05633i	−0.849143	−	0.528164i	$-0.822881\pi$
$853$	− 6.29163e30i	− 1.05633i	0.849143	−	0.528164i	$-0.177119\pi$
$854$	−1.16703e31	−1.93542
$855$	0	0
$856$	−2.55721e30	−0.413801
$857$	− 7.23134e30i	− 1.15590i	−0.816072	−	0.577950i	$-0.803853\pi$
$857$	− 7.23134e30i	− 1.15590i	0.816072	−	0.577950i	$-0.196147\pi$
$858$	− 9.73732e29i	− 0.153753i
$859$	3.32473e30	0.518594	0.259297	−	0.965798i	$-0.416509\pi$
$859$	3.32473e30	0.518594	0.259297	+	0.965798i	$0.416509\pi$
$860$	0	0
$861$	−2.08396e30	−0.317216
$862$	− 3.54910e30i	− 0.533693i
$863$	3.34330e30i	0.496664i	0.968675	+	0.248332i	$0.0798823\pi$
$863$	3.34330e30i	0.496664i	−0.968675	+	0.248332i	$0.920118\pi$
$864$	1.16219e30	0.170563
$865$	0	0
$866$	−6.02174e30	−0.862550
$867$	3.34763e30i	0.473737i
$868$	1.31499e30i	0.183850i
$869$	3.61309e30	0.499081
$870$	0	0
$871$	−7.26285e29	−0.0979301
$872$	2.16803e30i	0.288829i
$873$	− 5.05092e30i	− 0.664846i
$874$	−1.46191e30	−0.190130
$875$	0	0
$876$	2.28167e30	0.289708
$877$	− 1.00355e31i	− 1.25905i	−0.776982	−	0.629523i	$-0.783251\pi$
$877$	− 1.00355e31i	− 1.25905i	0.776982	−	0.629523i	$-0.216749\pi$
$878$	7.11916e29i	0.0882544i
$879$	−3.13984e30	−0.384613
$880$	0	0
$881$	−2.14507e29	−0.0256563	−0.0128281	−	0.999918i	$-0.504083\pi$
$881$	−2.14507e29	−0.0256563	−0.0128281	+	0.999918i	$0.504083\pi$
$882$	− 1.05136e31i	− 1.24260i
$883$	− 8.37555e30i	− 0.978196i	−0.872229	−	0.489098i	$-0.837326\pi$
$883$	− 8.37555e30i	− 0.978196i	0.872229	−	0.489098i	$-0.162674\pi$
$884$	−1.76400e30	−0.203587
$885$	0	0
$886$	−4.89068e29	−0.0551208
$887$	− 6.39937e30i	− 0.712754i	−0.934342	−	0.356377i	$-0.884012\pi$
$887$	− 6.39937e30i	− 0.712754i	0.934342	−	0.356377i	$-0.115988\pi$
$888$	− 1.98267e30i	− 0.218230i
$889$	−3.14348e31	−3.41934
$890$	0	0
$891$	−1.21580e30	−0.129165
$892$	− 6.15532e30i	− 0.646279i
$893$	2.12240e30i	0.220235i
$894$	5.29595e30	0.543125
$895$	0	0
$896$	1.68521e30	0.168818
$897$	− 1.15340e30i	− 0.114198i
$898$	− 6.17259e30i	− 0.604040i
$899$	2.09304e30	0.202442
$900$	0	0
$901$	6.65703e30	0.629028
$902$	2.69094e30i	0.251325i
$903$	1.12937e31i	1.04259i
$904$	−1.95393e30	−0.178295
$905$	0	0
$906$	−2.43364e30	−0.216975
$907$	3.33701e30i	0.294091i	0.989130	+	0.147045i	$0.0469763\pi$
$907$	3.33701e30i	0.294091i	−0.989130	+	0.147045i	$0.953024\pi$
$908$	− 6.43402e30i	− 0.560507i
$909$	4.12328e30	0.355077
$910$	0	0
$911$	−5.75477e30	−0.484267	−0.242134	−	0.970243i	$-0.577847\pi$
$911$	−5.75477e30	−0.484267	−0.242134	+	0.970243i	$0.577847\pi$
$912$	7.18974e29i	0.0598091i
$913$	2.18036e31i	1.79302i
$914$	4.02426e30	0.327153
$915$	0	0
$916$	−3.20043e30	−0.254276
$917$	2.05743e31i	1.61602i
$918$	− 1.18427e31i	− 0.919609i
$919$	2.25413e31	1.73048	0.865239	−	0.501359i	$-0.167166\pi$
$919$	2.25413e31	1.73048	0.865239	+	0.501359i	$0.167166\pi$
$920$	0	0
$921$	−1.06740e31	−0.800942
$922$	1.21940e31i	0.904633i
$923$	1.32868e30i	0.0974550i
$924$	9.47908e30	0.687401
$925$	0	0
$926$	−6.30591e30	−0.447025
$927$	4.82961e30i	0.338513i
$928$	− 2.68231e30i	− 0.185890i
$929$	−2.59042e30	−0.177503	−0.0887513	−	0.996054i	$-0.528288\pi$
$929$	−2.59042e30	−0.177503	−0.0887513	+	0.996054i	$0.528288\pi$
$930$	0	0
$931$	1.63046e31	1.09229
$932$	− 7.82232e29i	− 0.0518166i
$933$	− 1.48154e31i	− 0.970414i
$934$	1.33270e31	0.863160
$935$	0	0
$936$	1.11920e30	0.0708782
$937$	5.29691e30i	0.331709i	0.986150	+	0.165854i	$0.0530381\pi$
$937$	5.29691e30i	0.331709i	−0.986150	+	0.165854i	$0.946962\pi$
$938$	− 7.07023e30i	− 0.437828i
$939$	−1.27408e31	−0.780207
$940$	0	0
$941$	1.38757e31	0.830930	0.415465	−	0.909609i	$-0.363619\pi$
$941$	1.38757e31	0.830930	0.415465	+	0.909609i	$0.363619\pi$
$942$	− 2.79670e30i	− 0.165619i
$943$	3.18744e30i	0.186668i
$944$	3.25011e30	0.188231
$945$	0	0
$946$	1.45831e31	0.826027
$947$	− 8.16878e30i	− 0.457596i	−0.973474	−	0.228798i	$-0.926520\pi$
$947$	− 8.16878e30i	− 0.457596i	0.973474	−	0.228798i	$-0.0734796\pi$
$948$	− 2.10480e30i	− 0.116606i
$949$	5.50819e30	0.301796
$950$	0	0
$951$	1.81774e31	0.974172
$952$	− 1.71722e31i	− 0.910202i
$953$	− 2.02516e31i	− 1.06166i	−0.847479	−	0.530828i	$-0.821881\pi$
$953$	− 2.02516e31i	− 1.06166i	0.847479	−	0.530828i	$-0.178119\pi$
$954$	−4.22367e30	−0.218994
$955$	0	0
$956$	−1.07543e31	−0.545473
$957$	− 1.50877e31i	− 0.756914i
$958$	1.74216e31i	0.864471i
$959$	5.10480e31	2.50544
$960$	0	0
$961$	−2.00537e31	−0.962937
$962$	− 4.78637e30i	− 0.227336i
$963$	− 1.65329e31i	− 0.776734i
$964$	−1.53784e31	−0.714663
$965$	0	0
$966$	1.12281e31	0.510558
$967$	1.34251e31i	0.603864i	0.953329	+	0.301932i	$0.0976316\pi$
$967$	1.34251e31i	0.603864i	−0.953329	+	0.301932i	$0.902368\pi$
$968$	− 4.29404e30i	− 0.191062i
$969$	7.32632e30	0.322468
$970$	0	0
$971$	4.11059e31	1.77053	0.885263	−	0.465090i	$-0.153978\pi$
$971$	4.11059e31	1.77053	0.885263	+	0.465090i	$0.153978\pi$
$972$	1.20303e31i	0.512603i
$973$	3.00374e31i	1.26613i
$974$	2.51333e30	0.104805
$975$	0	0
$976$	8.77867e30	0.358266
$977$	3.60772e30i	0.145660i	0.997344	+	0.0728299i	$0.0232030\pi$
$977$	3.60772e30i	0.145660i	−0.997344	+	0.0728299i	$0.976797\pi$
$978$	− 3.47508e30i	− 0.138805i
$979$	−4.38005e30	−0.173086
$980$	0	0
$981$	−1.40167e31	−0.542154
$982$	3.15386e31i	1.20690i
$983$	− 3.62646e31i	− 1.37300i	−0.727130	−	0.686500i	$-0.759146\pi$
$983$	− 3.62646e31i	− 1.37300i	0.727130	−	0.686500i	$-0.240854\pi$
$984$	1.56760e30	0.0587201
$985$	0	0
$986$	−2.73326e31	−1.00225
$987$	− 1.63009e31i	− 0.591399i
$988$	1.73567e30i	0.0623046i
$989$	1.72739e31	0.613520
$990$	0	0
$991$	−2.38846e31	−0.830508	−0.415254	−	0.909706i	$-0.636307\pi$
$991$	−2.38846e31	−0.830508	−0.415254	+	0.909706i	$0.636307\pi$
$992$	− 9.89163e29i	− 0.0340326i
$993$	6.22256e30i	0.211837i
$994$	−1.29345e31	−0.435704
$995$	0	0
$996$	1.27016e31	0.418924
$997$	5.34032e31i	1.74288i	0.490499	+	0.871442i	$0.336814\pi$
$997$	5.34032e31i	1.74288i	−0.490499	+	0.871442i	$0.663186\pi$
$998$	2.12442e31i	0.686072i
$999$	3.21335e31	1.02688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.22.b.c.49.2		2
5.2	odd	4		50.22.a.a.1.1		1
5.3	odd	4		2.22.a.b.1.1	✓	1
5.4	even	2	inner	50.22.b.c.49.1		2
15.8	even	4		18.22.a.b.1.1		1
20.3	even	4		16.22.a.b.1.1		1
40.3	even	4		64.22.a.e.1.1		1
40.13	odd	4		64.22.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.22.a.b.1.1	✓	1	5.3	odd	4
16.22.a.b.1.1		1	20.3	even	4
18.22.a.b.1.1		1	15.8	even	4
50.22.a.a.1.1		1	5.2	odd	4
50.22.b.c.49.1		2	5.4	even	2	inner
50.22.b.c.49.2		2	1.1	even	1	trivial
64.22.a.c.1.1		1	40.13	odd	4
64.22.a.e.1.1		1	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1024.00i q^{2} -59316.0i q^{3} -1.04858e6 q^{4} +6.07396e7 q^{6} +1.42743e9i q^{7} -1.07374e9i q^{8} +6.94197e9 q^{9} +O(q^{10})\)	\(q+1024.00i q^{2} -59316.0i q^{3} -1.04858e6 q^{4} +6.07396e7 q^{6} +1.42743e9i q^{7} -1.07374e9i q^{8} +6.94197e9 q^{9} -1.06768e11 q^{11} +6.21973e10i q^{12} +1.50151e11i q^{13} -1.46168e12 q^{14} +1.09951e12 q^{16} -1.12040e13i q^{17} +7.10857e12i q^{18} -1.10241e13 q^{19} +8.46692e13 q^{21} -1.09330e14i q^{22} -1.29503e14i q^{23} -6.36901e13 q^{24} -1.53754e14 q^{26} -1.03224e15i q^{27} -1.49676e15i q^{28} -2.38237e15 q^{29} -8.78553e14 q^{31} +1.12590e15i q^{32} +6.33304e15i q^{33} +1.14729e16 q^{34} -7.27918e15 q^{36} +3.11300e16i q^{37} -1.12886e16i q^{38} +8.90633e15 q^{39} -2.46129e16 q^{41} +8.67013e16i q^{42} +1.33386e17i q^{43} +1.11954e17 q^{44} +1.32611e17 q^{46} -1.92524e17i q^{47} -6.52186e16i q^{48} -1.47900e18 q^{49} -6.64575e17 q^{51} -1.57444e17i q^{52} +5.94166e17i q^{53} +1.05701e18 q^{54} +1.53269e18 q^{56} +6.53903e17i q^{57} -2.43955e18i q^{58} +2.95595e18 q^{59} +7.98415e18 q^{61} -8.99638e17i q^{62} +9.90914e18i q^{63} -1.15292e18 q^{64} -6.48504e18 q^{66} +4.83704e18i q^{67} +1.17482e19i q^{68} -7.68159e18 q^{69} +8.84902e18 q^{71} -7.45388e18i q^{72} -3.66844e19i q^{73} -3.18771e19 q^{74} +1.15596e19 q^{76} -1.52403e20i q^{77} +9.12008e18i q^{78} -3.38406e19 q^{79} +1.13873e19 q^{81} -2.52036e19i q^{82} -2.04215e20i q^{83} -8.87821e19 q^{84} -1.36587e20 q^{86} +1.41313e20i q^{87} +1.14641e20i q^{88} +4.10241e19 q^{89} -2.14329e20 q^{91} +1.35794e20i q^{92} +5.21122e19i q^{93} +1.97145e20 q^{94} +6.67839e19 q^{96} -7.27592e20i q^{97} -1.51449e21i q^{98} -7.41179e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2097152 q^{4} + 121479168 q^{6} + 13883930694 q^{9}+O(q^{10}) \) 2 * q - 2097152 * q^4 + 121479168 * q^6 + 13883930694 * q^9	\( 2 q - 2097152 q^{4} + 121479168 q^{6} + 13883930694 q^{9} - 213535789896 q^{11} - 2923368103936 q^{14} + 2199023255552 q^{16} - 22048111910920 q^{19} + 169338381301824 q^{21} - 127380140064768 q^{24} - 307508358090752 q^{26} - 47\!\cdots\!20 q^{29}+ \cdots - 14\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 2097152 * q^4 + 121479168 * q^6 + 13883930694 * q^9 - 213535789896 * q^11 - 2923368103936 * q^14 + 2199023255552 * q^16 - 22048111910920 * q^19 + 169338381301824 * q^21 - 127380140064768 * q^24 - 307508358090752 * q^26 - 4764741653216220 * q^29 - 1757105914755776 * q^31 + 22945752555024384 * q^34 - 14558356511391744 * q^36 + 17812661883311568 * q^39 - 49225851891437676 * q^41 + 223908504425988096 * q^44 + 265221828075307008 * q^46 - 2957997283555216434 * q^49 - 1329150643118971056 * q^51 + 2114019178724966400 * q^54 + 3065373632952795136 * q^56 + 5911908268967347560 * q^59 + 15968300180105692444 * q^61 - 2305843009213693952 * q^64 - 12970075047394443264 * q^66 - 15363181595815342272 * q^69 + 17698034677866016464 * q^71 - 63754251994234925056 * q^74 + 23119120995104849920 * q^76 - 67681219157273547040 * q^79 + 22774606400085855282 * q^81 - 177564162511941402624 * q^84 - 273174773684872159232 * q^86 + 82048113487384545420 * q^89 - 428657591693989848736 * q^91 + 394289187730270224384 * q^94 + 133567757748554170368 * q^96 - 1482358053802304733912 * q^99

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