LMFDB - Embedded newform 75.10.b.f.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(49,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{241})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 121x^{2} + 3600 $ x^4 + 121*x^2 + 3600
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$7.26209i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.10.b.f.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-38.7863i q^{2} -81.0000i q^{3} -992.374 q^{4} -3141.69 q^{6} -12272.1i q^{7} +18631.9i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-38.7863i q^{2} -81.0000i q^{3} -992.374 q^{4} -3141.69 q^{6} -12272.1i q^{7} +18631.9i q^{8} -6561.00 q^{9} -65897.9 q^{11} +80382.3i q^{12} -112300. i q^{13} -475990. q^{14} +214567. q^{16} -96634.7i q^{17} +254477. i q^{18} +181332. q^{19} -994042. q^{21} +2.55593e6i q^{22} +244145. i q^{23} +1.50919e6 q^{24} -4.35569e6 q^{26} +531441. i q^{27} +1.21785e7i q^{28} +5.26461e6 q^{29} +1.83457e6 q^{31} +1.21730e6i q^{32} +5.33773e6i q^{33} -3.74810e6 q^{34} +6.51097e6 q^{36} -6.36194e6i q^{37} -7.03318e6i q^{38} -9.09628e6 q^{39} +1.57111e6 q^{41} +3.85552e7i q^{42} -1.99504e7i q^{43} +6.53953e7 q^{44} +9.46946e6 q^{46} -3.00961e7i q^{47} -1.73799e7i q^{48} -1.10251e8 q^{49} -7.82741e6 q^{51} +1.11443e8i q^{52} -2.57306e6i q^{53} +2.06126e7 q^{54} +2.28653e8 q^{56} -1.46879e7i q^{57} -2.04195e8i q^{58} +1.19004e8 q^{59} +1.92875e8 q^{61} -7.11559e7i q^{62} +8.05174e7i q^{63} +1.57073e8 q^{64} +2.07030e8 q^{66} +1.20193e8i q^{67} +9.58978e7i q^{68} +1.97757e7 q^{69} -699549. q^{71} -1.22244e8i q^{72} -8.91287e7i q^{73} -2.46756e8 q^{74} -1.79949e8 q^{76} +8.08707e8i q^{77} +3.52811e8i q^{78} -4.31205e8 q^{79} +4.30467e7 q^{81} -6.09375e7i q^{82} -1.69761e7i q^{83} +9.86461e8 q^{84} -7.73800e8 q^{86} -4.26433e8i q^{87} -1.22780e9i q^{88} +3.09863e6 q^{89} -1.37816e9 q^{91} -2.42283e8i q^{92} -1.48600e8i q^{93} -1.16732e9 q^{94} +9.86009e7 q^{96} -5.72609e8i q^{97} +4.27624e9i q^{98} +4.32356e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1082 q^{4} - 5022 q^{6} - 26244 q^{9}+O(q^{10}) $ 4 * q - 1082 * q^4 - 5022 * q^6 - 26244 * q^9	$ 4 q - 1082 q^{4} - 5022 q^{6} - 26244 q^{9} - 43024 q^{11} - 923328 q^{14} + 774530 q^{16} + 191792 q^{19} - 2286144 q^{21} + 4233546 q^{24} - 10838332 q^{26} + 5356424 q^{29} + 21564864 q^{31} - 11445244 q^{34} + 7099002 q^{36} + 3934008 q^{39} + 52120744 q^{41} + 170859944 q^{44} + 34190784 q^{46} - 146565860 q^{49} + 25426872 q^{51} + 32949342 q^{54} + 484908480 q^{56} + 70989328 q^{59} + 682994680 q^{61} + 410240942 q^{64} + 470048184 q^{66} - 119112768 q^{69} + 420572128 q^{71} - 250480468 q^{74} - 437024728 q^{76} + 49510080 q^{79} + 172186884 q^{81} + 1838386368 q^{84} - 1746292744 q^{86} + 855278232 q^{89} - 2253718656 q^{91} - 3295087792 q^{94} + 1037208726 q^{96} + 282280464 q^{99}+O(q^{100}) $ 4 * q - 1082 * q^4 - 5022 * q^6 - 26244 * q^9 - 43024 * q^11 - 923328 * q^14 + 774530 * q^16 + 191792 * q^19 - 2286144 * q^21 + 4233546 * q^24 - 10838332 * q^26 + 5356424 * q^29 + 21564864 * q^31 - 11445244 * q^34 + 7099002 * q^36 + 3934008 * q^39 + 52120744 * q^41 + 170859944 * q^44 + 34190784 * q^46 - 146565860 * q^49 + 25426872 * q^51 + 32949342 * q^54 + 484908480 * q^56 + 70989328 * q^59 + 682994680 * q^61 + 410240942 * q^64 + 470048184 * q^66 - 119112768 * q^69 + 420572128 * q^71 - 250480468 * q^74 - 437024728 * q^76 + 49510080 * q^79 + 172186884 * q^81 + 1838386368 * q^84 - 1746292744 * q^86 + 855278232 * q^89 - 2253718656 * q^91 - 3295087792 * q^94 + 1037208726 * q^96 + 282280464 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	− 38.7863i	− 1.71413i	−0.515211	−	0.857063i	$-0.672286\pi$
$2$	− 38.7863i	− 1.71413i	0.515211	−	0.857063i	$-0.327714\pi$
$3$	− 81.0000i	− 0.577350i
$3$	− 81.0000i	− 0.577350i
$4$	−992.374	−1.93823
$5$	0	0
$5$	0	0
$6$	−3141.69	−0.989652
$7$	− 12272.1i	− 1.93187i	−0.258780	−	0.965936i	$-0.583320\pi$
$7$	− 12272.1i	− 1.93187i	0.258780	−	0.965936i	$-0.416680\pi$
$8$	18631.9i	1.60825i
$9$	−6561.00	−0.333333
$10$	0	0
$11$	−65897.9	−1.35708	−0.678538	−	0.734565i	$-0.737386\pi$
$11$	−65897.9	−1.35708	−0.678538	+	0.734565i	$0.737386\pi$
$12$	80382.3i	1.11904i
$13$	− 112300.i	− 1.09052i	−0.838267	−	0.545260i	$-0.816431\pi$
$13$	− 112300.i	− 1.09052i	0.838267	−	0.545260i	$-0.183569\pi$
$14$	−475990.	−3.31147
$15$	0	0
$16$	214567.	0.818508
$17$	− 96634.7i	− 0.280616i	−0.990108	−	0.140308i	$-0.955191\pi$
$17$	− 96634.7i	− 0.280616i	0.990108	−	0.140308i	$-0.0448093\pi$
$18$	254477.i	0.571376i
$19$	181332.	0.319214	0.159607	−	0.987181i	$-0.448977\pi$
$19$	181332.	0.319214	0.159607	+	0.987181i	$0.448977\pi$
$20$	0	0
$21$	−994042.	−1.11537
$22$	2.55593e6i	2.32620i
$23$	244145.i	0.181916i	0.995855	+	0.0909582i	$0.0289930\pi$
$23$	244145.i	0.181916i	−0.995855	+	0.0909582i	$0.971007\pi$
$24$	1.50919e6	0.928521
$25$	0	0
$26$	−4.35569e6	−1.86929
$27$	531441.i	0.192450i
$28$	1.21785e7i	3.74442i
$29$	5.26461e6	1.38221	0.691107	−	0.722752i	$-0.257123\pi$
$29$	5.26461e6	1.38221	0.691107	+	0.722752i	$0.257123\pi$
$30$	0	0
$31$	1.83457e6	0.356784	0.178392	−	0.983959i	$-0.442910\pi$
$31$	1.83457e6	0.356784	0.178392	+	0.983959i	$0.442910\pi$
$32$	1.21730e6i	0.205221i
$33$	5.33773e6i	0.783508i
$34$	−3.74810e6	−0.481012
$35$	0	0
$36$	6.51097e6	0.646077
$37$	− 6.36194e6i	− 0.558061i	−0.960282	−	0.279030i	$-0.909987\pi$
$37$	− 6.36194e6i	− 0.558061i	0.960282	−	0.279030i	$-0.0900130\pi$
$38$	− 7.03318e6i	− 0.547174i
$39$	−9.09628e6	−0.629612
$40$	0	0
$41$	1.57111e6	0.0868319	0.0434159	−	0.999057i	$-0.486176\pi$
$41$	1.57111e6	0.0868319	0.0434159	+	0.999057i	$0.486176\pi$
$42$	3.85552e7i	1.91188i
$43$	− 1.99504e7i	− 0.889903i	−0.895555	−	0.444952i	$-0.853221\pi$
$43$	− 1.99504e7i	− 0.889903i	0.895555	−	0.444952i	$-0.146779\pi$
$44$	6.53953e7	2.63033
$45$	0	0
$46$	9.46946e6	0.311828
$47$	− 3.00961e7i	− 0.899643i	−0.893119	−	0.449821i	$-0.851488\pi$
$47$	− 3.00961e7i	− 0.899643i	0.893119	−	0.449821i	$-0.148512\pi$
$48$	− 1.73799e7i	− 0.472566i
$49$	−1.10251e8	−2.73213
$50$	0	0
$51$	−7.82741e6	−0.162014
$52$	1.11443e8i	2.11368i
$53$	− 2.57306e6i	− 0.0447929i	−0.999749	−	0.0223964i	$-0.992870\pi$
$53$	− 2.57306e6i	− 0.0447929i	0.999749	−	0.0223964i	$-0.00712960\pi$
$54$	2.06126e7	0.329884
$55$	0	0
$56$	2.28653e8	3.10693
$57$	− 1.46879e7i	− 0.184299i
$58$	− 2.04195e8i	− 2.36929i
$59$	1.19004e8	1.27858	0.639290	−	0.768965i	$-0.279228\pi$
$59$	1.19004e8	1.27858	0.639290	+	0.768965i	$0.279228\pi$
$60$	0	0
$61$	1.92875e8	1.78358	0.891790	−	0.452449i	$-0.149450\pi$
$61$	1.92875e8	1.78358	0.891790	+	0.452449i	$0.149450\pi$
$62$	− 7.11559e7i	− 0.611573i
$63$	8.05174e7i	0.643958i
$64$	1.57073e8	1.17028
$65$	0	0
$66$	2.07030e8	1.34303
$67$	1.20193e8i	0.728691i	0.931264	+	0.364345i	$0.118707\pi$
$67$	1.20193e8i	0.728691i	−0.931264	+	0.364345i	$0.881293\pi$
$68$	9.58978e7i	0.543899i
$69$	1.97757e7	0.105030
$70$	0	0
$71$	−699549.	−0.00326705	−0.00163352	−	0.999999i	$-0.500520\pi$
$71$	−699549.	−0.00326705	−0.00163352	+	0.999999i	$0.500520\pi$
$72$	− 1.22244e8i	− 0.536082i
$73$	− 8.91287e7i	− 0.367337i	−0.982988	−	0.183669i	$-0.941203\pi$
$73$	− 8.91287e7i	− 0.367337i	0.982988	−	0.183669i	$-0.0587973\pi$
$74$	−2.46756e8	−0.956587
$75$	0	0
$76$	−1.79949e8	−0.618711
$77$	8.08707e8i	2.62170i
$78$	3.52811e8i	1.07924i
$79$	−4.31205e8	−1.24555	−0.622776	−	0.782400i	$-0.713995\pi$
$79$	−4.31205e8	−1.24555	−0.622776	+	0.782400i	$0.713995\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	− 6.09375e7i	− 0.148841i
$83$	− 1.69761e7i	− 0.0392633i	−0.999807	−	0.0196316i	$-0.993751\pi$
$83$	− 1.69761e7i	− 0.0392633i	0.999807	−	0.0196316i	$-0.00624935\pi$
$84$	9.86461e8	2.16184
$85$	0	0
$86$	−7.73800e8	−1.52541
$87$	− 4.26433e8i	− 0.798022i
$88$	− 1.22780e9i	− 2.18251i
$89$	3.09863e6	0.00523498	0.00261749	−	0.999997i	$-0.499167\pi$
$89$	3.09863e6	0.00523498	0.00261749	+	0.999997i	$0.499167\pi$
$90$	0	0
$91$	−1.37816e9	−2.10675
$92$	− 2.42283e8i	− 0.352596i
$93$	− 1.48600e8i	− 0.205989i
$94$	−1.16732e9	−1.54210
$95$	0	0
$96$	9.86009e7	0.118484
$97$	− 5.72609e8i	− 0.656727i	−0.944551	−	0.328364i	$-0.893503\pi$
$97$	− 5.72609e8i	− 0.656727i	0.944551	−	0.328364i	$-0.106497\pi$
$98$	4.27624e9i	4.68322i
$99$	4.32356e8	0.452359
$100$	0	0
$101$	1.78445e9	1.70631	0.853156	−	0.521655i	$-0.174685\pi$
$101$	1.78445e9	1.70631	0.853156	+	0.521655i	$0.174685\pi$
$102$	3.03596e8i	0.277712i
$103$	1.16632e9i	1.02106i	0.859861	+	0.510528i	$0.170550\pi$
$103$	1.16632e9i	1.02106i	−0.859861	+	0.510528i	$0.829450\pi$
$104$	2.09236e9	1.75383
$105$	0	0
$106$	−9.97995e7	−0.0767807
$107$	1.72229e9i	1.27022i	0.772422	+	0.635109i	$0.219045\pi$
$107$	1.72229e9i	1.27022i	−0.772422	+	0.635109i	$0.780955\pi$
$108$	− 5.27388e8i	− 0.373013i
$109$	−2.08468e9	−1.41456	−0.707279	−	0.706934i	$-0.750078\pi$
$109$	−2.08468e9	−1.41456	−0.707279	+	0.706934i	$0.750078\pi$
$110$	0	0
$111$	−5.15317e8	−0.322197
$112$	− 2.63319e9i	− 1.58125i
$113$	− 1.81995e9i	− 1.05004i	−0.851090	−	0.525020i	$-0.824058\pi$
$113$	− 1.81995e9i	− 1.05004i	0.851090	−	0.525020i	$-0.175942\pi$
$114$	−5.69688e8	−0.315911
$115$	0	0
$116$	−5.22446e9	−2.67905
$117$	7.36799e8i	0.363507i
$118$	− 4.61573e9i	− 2.19165i
$119$	−1.18591e9	−0.542115
$120$	0	0
$121$	1.98458e9	0.841656
$122$	− 7.48092e9i	− 3.05728i
$123$	− 1.27260e8i	− 0.0501324i
$124$	−1.82058e9	−0.691530
$125$	0	0
$126$	3.12297e9	1.10382
$127$	3.74913e9i	1.27883i	0.768860	+	0.639417i	$0.220824\pi$
$127$	3.74913e9i	1.27883i	−0.768860	+	0.639417i	$0.779176\pi$
$128$	− 5.46900e9i	− 1.80079i
$129$	−1.61598e9	−0.513786
$130$	0	0
$131$	−1.96598e9	−0.583256	−0.291628	−	0.956532i	$-0.594197\pi$
$131$	−1.96598e9	−0.583256	−0.291628	+	0.956532i	$0.594197\pi$
$132$	− 5.29702e9i	− 1.51862i
$133$	− 2.22532e9i	− 0.616682i
$134$	4.66184e9	1.24907
$135$	0	0
$136$	1.80049e9	0.451300
$137$	3.63223e8i	0.0880909i	0.999030	+	0.0440455i	$0.0140246\pi$
$137$	3.63223e8i	0.0880909i	−0.999030	+	0.0440455i	$0.985975\pi$
$138$	− 7.67026e8i	− 0.180034i
$139$	−4.55580e9	−1.03514	−0.517569	−	0.855642i	$-0.673163\pi$
$139$	−4.55580e9	−1.03514	−0.517569	+	0.855642i	$0.673163\pi$
$140$	0	0
$141$	−2.43779e9	−0.519409
$142$	2.71329e7i	0.00560014i
$143$	7.40032e9i	1.47992i
$144$	−1.40777e9	−0.272836
$145$	0	0
$146$	−3.45697e9	−0.629662
$147$	8.93036e9i	1.57740i
$148$	6.31342e9i	1.08165i
$149$	−8.79830e9	−1.46238	−0.731191	−	0.682173i	$-0.761035\pi$
$149$	−8.79830e9	−1.46238	−0.731191	+	0.682173i	$0.761035\pi$
$150$	0	0
$151$	−2.70702e8	−0.0423736	−0.0211868	−	0.999776i	$-0.506744\pi$
$151$	−2.70702e8	−0.0423736	−0.0211868	+	0.999776i	$0.506744\pi$
$152$	3.37856e9i	0.513376i
$153$	6.34020e8i	0.0935388i
$154$	3.13667e10	4.49392
$155$	0	0
$156$	9.02692e9	1.22033
$157$	− 9.73240e9i	− 1.27841i	−0.769035	−	0.639207i	$-0.779263\pi$
$157$	− 9.73240e9i	− 1.27841i	0.769035	−	0.639207i	$-0.220737\pi$
$158$	1.67248e10i	2.13504i
$159$	−2.08418e8	−0.0258612
$160$	0	0
$161$	2.99617e9	0.351439
$162$	− 1.66962e9i	− 0.190459i
$163$	7.76823e9i	0.861941i	0.902366	+	0.430971i	$0.141829\pi$
$163$	7.76823e9i	0.861941i	−0.902366	+	0.430971i	$0.858171\pi$
$164$	−1.55913e9	−0.168300
$165$	0	0
$166$	−6.58440e8	−0.0673023
$167$	8.41748e9i	0.837448i	0.908114	+	0.418724i	$0.137522\pi$
$167$	8.41748e9i	0.837448i	−0.908114	+	0.418724i	$0.862478\pi$
$168$	− 1.85209e10i	− 1.79379i
$169$	−2.00674e9	−0.189235
$170$	0	0
$171$	−1.18972e9	−0.106405
$172$	1.97982e10i	1.72484i
$173$	3.59838e8i	0.0305422i	0.999883	+	0.0152711i	$0.00486112\pi$
$173$	3.59838e8i	0.0305422i	−0.999883	+	0.0152711i	$0.995139\pi$
$174$	−1.65398e10	−1.36791
$175$	0	0
$176$	−1.41395e10	−1.11078
$177$	− 9.63934e9i	− 0.738189i
$178$	− 1.20184e8i	− 0.00897342i
$179$	8.65338e9	0.630009	0.315005	−	0.949090i	$-0.397994\pi$
$179$	8.65338e9	0.630009	0.315005	+	0.949090i	$0.397994\pi$
$180$	0	0
$181$	6.09713e9	0.422252	0.211126	−	0.977459i	$-0.432287\pi$
$181$	6.09713e9	0.422252	0.211126	+	0.977459i	$0.432287\pi$
$182$	5.34535e10i	3.61123i
$183$	− 1.56229e10i	− 1.02975i
$184$	−4.54888e9	−0.292566
$185$	0	0
$186$	−5.76363e9	−0.353092
$187$	6.36802e9i	0.380818i
$188$	2.98666e10i	1.74371i
$189$	6.52191e9	0.371789
$190$	0	0
$191$	−2.96238e10	−1.61061	−0.805306	−	0.592859i	$-0.797999\pi$
$191$	−2.96238e10	−1.61061	−0.805306	+	0.592859i	$0.797999\pi$
$192$	− 1.27229e10i	− 0.675662i
$193$	− 4.63438e8i	− 0.0240427i	−0.999928	−	0.0120214i	$-0.996173\pi$
$193$	− 4.63438e8i	− 0.0240427i	0.999928	−	0.0120214i	$-0.00382661\pi$
$194$	−2.22094e10	−1.12571
$195$	0	0
$196$	1.09411e11	5.29550
$197$	− 1.23414e10i	− 0.583803i	−0.956448	−	0.291902i	$-0.905712\pi$
$197$	− 1.23414e10i	− 0.583803i	0.956448	−	0.291902i	$-0.0942880\pi$
$198$	− 1.67695e10i	− 0.775400i
$199$	1.00354e10	0.453624	0.226812	−	0.973939i	$-0.427170\pi$
$199$	1.00354e10	0.453624	0.226812	+	0.973939i	$0.427170\pi$
$200$	0	0
$201$	9.73565e9	0.420710
$202$	− 6.92122e10i	− 2.92484i
$203$	− 6.46080e10i	− 2.67026i
$204$	7.76772e9	0.314020
$205$	0	0
$206$	4.52371e10	1.75022
$207$	− 1.60183e9i	− 0.0606388i
$208$	− 2.40958e10i	− 0.892599i
$209$	−1.19494e10	−0.433198
$210$	0	0
$211$	−3.56268e10	−1.23739	−0.618693	−	0.785633i	$-0.712338\pi$
$211$	−3.56268e10	−1.23739	−0.618693	+	0.785633i	$0.712338\pi$
$212$	2.55344e9i	0.0868189i
$213$	5.66635e7i	0.00188623i
$214$	6.68011e10	2.17732
$215$	0	0
$216$	−9.90176e9	−0.309507
$217$	− 2.25140e10i	− 0.689262i
$218$	8.08571e10i	2.42473i
$219$	−7.21943e9	−0.212082
$220$	0	0
$221$	−1.08521e10	−0.306018
$222$	1.99872e10i	0.552286i
$223$	− 3.41646e10i	− 0.925133i	−0.886585	−	0.462566i	$-0.846929\pi$
$223$	− 3.41646e10i	− 0.925133i	0.886585	−	0.462566i	$-0.153071\pi$
$224$	1.49388e10	0.396460
$225$	0	0
$226$	−7.05889e10	−1.79990
$227$	− 3.64936e10i	− 0.912221i	−0.889923	−	0.456110i	$-0.849242\pi$
$227$	− 3.64936e10i	− 0.912221i	0.889923	−	0.456110i	$-0.150758\pi$
$228$	1.45759e10i	0.357213i
$229$	−3.87446e10	−0.931005	−0.465502	−	0.885047i	$-0.654126\pi$
$229$	−3.87446e10	−0.931005	−0.465502	+	0.885047i	$0.654126\pi$
$230$	0	0
$231$	6.55052e10	1.51364
$232$	9.80898e10i	2.22294i
$233$	− 2.68717e10i	− 0.597302i	−0.954362	−	0.298651i	$-0.903463\pi$
$233$	− 2.68717e10i	− 0.597302i	0.954362	−	0.298651i	$-0.0965367\pi$
$234$	2.85777e10	0.623097
$235$	0	0
$236$	−1.18097e11	−2.47818
$237$	3.49276e10i	0.719120i
$238$	4.59971e10i	0.929254i
$239$	−1.34711e10	−0.267063	−0.133531	−	0.991045i	$-0.542632\pi$
$239$	−1.34711e10	−0.267063	−0.133531	+	0.991045i	$0.542632\pi$
$240$	0	0
$241$	−1.85860e10	−0.354902	−0.177451	−	0.984130i	$-0.556785\pi$
$241$	−1.85860e10	−0.354902	−0.177451	+	0.984130i	$0.556785\pi$
$242$	− 7.69745e10i	− 1.44271i
$243$	− 3.48678e9i	− 0.0641500i
$244$	−1.91405e11	−3.45699
$245$	0	0
$246$	−4.93593e9	−0.0859333
$247$	− 2.03635e10i	− 0.348110i
$248$	3.41815e10i	0.573797i
$249$	−1.37506e9	−0.0226687
$250$	0	0
$251$	4.30327e10	0.684332	0.342166	−	0.939640i	$-0.388839\pi$
$251$	4.30327e10	0.684332	0.342166	+	0.939640i	$0.388839\pi$
$252$	− 7.99034e10i	− 1.24814i
$253$	− 1.60886e10i	− 0.246875i
$254$	1.45415e11	2.19208
$255$	0	0
$256$	−1.31701e11	−1.91650
$257$	6.26858e8i	0.00896335i	0.999990	+	0.00448168i	$0.00142657\pi$
$257$	6.26858e8i	0.00896335i	−0.999990	+	0.00448168i	$0.998573\pi$
$258$	6.26778e10i	0.880694i
$259$	−7.80745e10	−1.07810
$260$	0	0
$261$	−3.45411e10	−0.460738
$262$	7.62532e10i	0.999774i
$263$	6.21446e10i	0.800944i	0.916309	+	0.400472i	$0.131154\pi$
$263$	6.21446e10i	0.800944i	−0.916309	+	0.400472i	$0.868846\pi$
$264$	−9.94521e10	−1.26007
$265$	0	0
$266$	−8.63120e10	−1.05707
$267$	− 2.50989e8i	− 0.00302242i
$268$	− 1.19277e11i	− 1.41237i
$269$	5.44876e10	0.634472	0.317236	−	0.948347i	$-0.397245\pi$
$269$	5.44876e10	0.634472	0.317236	+	0.948347i	$0.397245\pi$
$270$	0	0
$271$	−9.74930e10	−1.09802	−0.549012	−	0.835815i	$-0.684996\pi$
$271$	−9.74930e10	−1.09802	−0.549012	+	0.835815i	$0.684996\pi$
$272$	− 2.07346e10i	− 0.229687i
$273$	1.11631e11i	1.21633i
$274$	1.40881e10	0.150999
$275$	0	0
$276$	−1.96249e10	−0.203571
$277$	− 1.43195e11i	− 1.46140i	−0.682697	−	0.730702i	$-0.739193\pi$
$277$	− 1.43195e11i	− 1.46140i	0.682697	−	0.730702i	$-0.260807\pi$
$278$	1.76702e11i	1.77436i
$279$	−1.20366e10	−0.118928
$280$	0	0
$281$	6.51280e10	0.623146	0.311573	−	0.950222i	$-0.399144\pi$
$281$	6.51280e10	0.623146	0.311573	+	0.950222i	$0.399144\pi$
$282$	9.45526e10i	0.890333i
$283$	− 1.65431e11i	− 1.53312i	−0.642171	−	0.766561i	$-0.721966\pi$
$283$	− 1.65431e11i	− 1.53312i	0.642171	−	0.766561i	$-0.278034\pi$
$284$	6.94214e8	0.00633229
$285$	0	0
$286$	2.87031e11	2.53677
$287$	− 1.92808e10i	− 0.167748i
$288$	− 7.98667e9i	− 0.0684069i
$289$	1.09250e11	0.921254
$290$	0	0
$291$	−4.63813e10	−0.379162
$292$	8.84490e10i	0.711984i
$293$	5.64261e10i	0.447277i	0.974672	+	0.223638i	$0.0717934\pi$
$293$	5.64261e10i	0.447277i	−0.974672	+	0.223638i	$0.928207\pi$
$294$	3.46375e11	2.70386
$295$	0	0
$296$	1.18535e11	0.897499
$297$	− 3.50208e10i	− 0.261169i
$298$	3.41253e11i	2.50671i
$299$	2.74174e10	0.198384
$300$	0	0
$301$	−2.44833e11	−1.71918
$302$	1.04995e10i	0.0726338i
$303$	− 1.44541e11i	− 0.985140i
$304$	3.89078e10	0.261279
$305$	0	0
$306$	2.45913e10	0.160337
$307$	− 1.79360e10i	− 0.115240i	−0.998339	−	0.0576200i	$-0.981649\pi$
$307$	− 1.79360e10i	− 0.115240i	0.998339	−	0.0576200i	$-0.0183512\pi$
$308$	− 8.02540e11i	− 5.08146i
$309$	9.44717e10	0.589507
$310$	0	0
$311$	3.19953e11	1.93938	0.969692	−	0.244330i	$-0.0785680\pi$
$311$	3.19953e11	1.93938	0.969692	+	0.244330i	$0.0785680\pi$
$312$	− 1.69481e11i	− 1.01257i
$313$	− 3.16987e11i	− 1.86677i	−0.358872	−	0.933387i	$-0.616838\pi$
$313$	− 3.16987e11i	− 1.86677i	0.358872	−	0.933387i	$-0.383162\pi$
$314$	−3.77483e11	−2.19136
$315$	0	0
$316$	4.27917e11	2.41417
$317$	3.08157e11i	1.71398i	0.515334	+	0.856990i	$0.327668\pi$
$317$	3.08157e11i	1.71398i	−0.515334	+	0.856990i	$0.672332\pi$
$318$	8.08376e9i	0.0443293i
$319$	−3.46927e11	−1.87577
$320$	0	0
$321$	1.39505e11	0.733361
$322$	− 1.16210e11i	− 0.602412i
$323$	− 1.75229e10i	− 0.0895768i
$324$	−4.27185e10	−0.215359
$325$	0	0
$326$	3.01301e11	1.47748
$327$	1.68859e11i	0.816696i
$328$	2.92728e10i	0.139647i
$329$	−3.69343e11	−1.73800
$330$	0	0
$331$	−1.79184e11	−0.820490	−0.410245	−	0.911975i	$-0.634557\pi$
$331$	−1.79184e11	−0.820490	−0.410245	+	0.911975i	$0.634557\pi$
$332$	1.68466e10i	0.0761013i
$333$	4.17407e10i	0.186020i
$334$	3.26482e11	1.43549
$335$	0	0
$336$	−2.13288e11	−0.912937
$337$	9.73351e10i	0.411088i	0.978648	+	0.205544i	$0.0658964\pi$
$337$	9.73351e10i	0.411088i	−0.978648	+	0.205544i	$0.934104\pi$
$338$	7.78340e10i	0.324373i
$339$	−1.47416e11	−0.606241
$340$	0	0
$341$	−1.20894e11	−0.484183
$342$	4.61447e10i	0.182391i
$343$	8.57794e11i	3.34626i
$344$	3.71713e11	1.43118
$345$	0	0
$346$	1.39568e10	0.0523531
$347$	3.47750e11i	1.28761i	0.765189	+	0.643806i	$0.222646\pi$
$347$	3.47750e11i	1.28761i	−0.765189	+	0.643806i	$0.777354\pi$
$348$	4.23182e11i	1.54675i
$349$	1.10131e11	0.397372	0.198686	−	0.980063i	$-0.436333\pi$
$349$	1.10131e11	0.397372	0.198686	+	0.980063i	$0.436333\pi$
$350$	0	0
$351$	5.96807e10	0.209871
$352$	− 8.02172e10i	− 0.278500i
$353$	− 3.40052e11i	− 1.16563i	−0.812606	−	0.582814i	$-0.801952\pi$
$353$	− 3.40052e11i	− 1.16563i	0.812606	−	0.582814i	$-0.198048\pi$
$354$	−3.73874e11	−1.26535
$355$	0	0
$356$	−3.07500e9	−0.0101466
$357$	9.60589e10i	0.312990i
$358$	− 3.35632e11i	− 1.07992i
$359$	2.75063e11	0.873993	0.436996	−	0.899463i	$-0.356042\pi$
$359$	2.75063e11	0.873993	0.436996	+	0.899463i	$0.356042\pi$
$360$	0	0
$361$	−2.89807e11	−0.898102
$362$	− 2.36485e11i	− 0.723793i
$363$	− 1.60751e11i	− 0.485930i
$364$	1.36765e12	4.08336
$365$	0	0
$366$	−6.05954e11	−1.76512
$367$	2.12218e11i	0.610639i	0.952250	+	0.305320i	$0.0987633\pi$
$367$	2.12218e11i	0.610639i	−0.952250	+	0.305320i	$0.901237\pi$
$368$	5.23854e10i	0.148900i
$369$	−1.03081e10	−0.0289440
$370$	0	0
$371$	−3.15769e10	−0.0865341
$372$	1.47467e11i	0.399255i
$373$	6.08324e11i	1.62721i	0.581415	+	0.813607i	$0.302499\pi$
$373$	6.08324e11i	1.62721i	−0.581415	+	0.813607i	$0.697501\pi$
$374$	2.46992e11	0.652770
$375$	0	0
$376$	5.60748e11	1.44685
$377$	− 5.91215e11i	− 1.50733i
$378$	− 2.52960e11i	− 0.637294i
$379$	−4.64136e11	−1.15550	−0.577749	−	0.816214i	$-0.696069\pi$
$379$	−4.64136e11	−1.15550	−0.577749	+	0.816214i	$0.696069\pi$
$380$	0	0
$381$	3.03680e11	0.738335
$382$	1.14900e12i	2.76079i
$383$	5.22749e11i	1.24136i	0.784063	+	0.620681i	$0.213144\pi$
$383$	5.22749e11i	1.24136i	−0.784063	+	0.620681i	$0.786856\pi$
$384$	−4.42989e11	−1.03969
$385$	0	0
$386$	−1.79750e10	−0.0412123
$387$	1.30894e11i	0.296634i
$388$	5.68242e11i	1.27289i
$389$	1.18899e11	0.263271	0.131636	−	0.991298i	$-0.457977\pi$
$389$	1.18899e11	0.263271	0.131636	+	0.991298i	$0.457977\pi$
$390$	0	0
$391$	2.35928e10	0.0510487
$392$	− 2.05419e12i	− 4.39394i
$393$	1.59245e11i	0.336743i
$394$	−4.78677e11	−1.00071
$395$	0	0
$396$	−4.29059e11	−0.876776
$397$	2.76954e11i	0.559564i	0.960064	+	0.279782i	$0.0902622\pi$
$397$	2.76954e11i	0.559564i	−0.960064	+	0.279782i	$0.909738\pi$
$398$	− 3.89236e11i	− 0.777569i
$399$	−1.80251e11	−0.356041
$400$	0	0
$401$	−1.53482e11	−0.296421	−0.148210	−	0.988956i	$-0.547351\pi$
$401$	−1.53482e11	−0.296421	−0.148210	+	0.988956i	$0.547351\pi$
$402$	− 3.77609e11i	− 0.721150i
$403$	− 2.06021e11i	− 0.389080i
$404$	−1.77084e12	−3.30723
$405$	0	0
$406$	−2.50590e12	−4.57717
$407$	4.19238e11i	0.757331i
$408$	− 1.45840e11i	− 0.260558i
$409$	1.52364e11	0.269232	0.134616	−	0.990898i	$-0.457020\pi$
$409$	1.52364e11	0.269232	0.134616	+	0.990898i	$0.457020\pi$
$410$	0	0
$411$	2.94211e10	0.0508593
$412$	− 1.15742e12i	− 1.97904i
$413$	− 1.46043e12i	− 2.47006i
$414$	−6.21291e10	−0.103943
$415$	0	0
$416$	1.36702e11	0.223797
$417$	3.69020e11i	0.597637i
$418$	4.63472e11i	0.742557i
$419$	9.09824e11	1.44210	0.721049	−	0.692885i	$-0.243660\pi$
$419$	9.09824e11	1.44210	0.721049	+	0.692885i	$0.243660\pi$
$420$	0	0
$421$	9.88529e11	1.53363	0.766814	−	0.641869i	$-0.221841\pi$
$421$	9.88529e11	1.53363	0.766814	+	0.641869i	$0.221841\pi$
$422$	1.38183e12i	2.12104i
$423$	1.97461e11i	0.299881i
$424$	4.79411e10	0.0720380
$425$	0	0
$426$	2.19776e9	0.00323324
$427$	− 2.36699e12i	− 3.44565i
$428$	− 1.70915e12i	− 2.46198i
$429$	5.99426e11	0.854432
$430$	0	0
$431$	2.03278e11	0.283755	0.141878	−	0.989884i	$-0.454686\pi$
$431$	2.03278e11	0.283755	0.141878	+	0.989884i	$0.454686\pi$
$432$	1.14030e11i	0.157522i
$433$	− 2.10847e11i	− 0.288251i	−0.989559	−	0.144126i	$-0.953963\pi$
$433$	− 2.10847e11i	− 0.288251i	0.989559	−	0.144126i	$-0.0460369\pi$
$434$	−8.73234e11	−1.18148
$435$	0	0
$436$	2.06879e12	2.74174
$437$	4.42712e10i	0.0580704i
$438$	2.80015e11i	0.363536i
$439$	−2.11413e11	−0.271670	−0.135835	−	0.990732i	$-0.543372\pi$
$439$	−2.11413e11	−0.271670	−0.135835	+	0.990732i	$0.543372\pi$
$440$	0	0
$441$	7.23359e11	0.910711
$442$	4.20911e11i	0.524553i
$443$	1.45517e12i	1.79514i	0.440874	+	0.897569i	$0.354669\pi$
$443$	1.45517e12i	1.79514i	−0.440874	+	0.897569i	$0.645331\pi$
$444$	5.11387e11	0.624491
$445$	0	0
$446$	−1.32512e12	−1.58579
$447$	7.12663e11i	0.844306i
$448$	− 1.92761e12i	− 2.26084i
$449$	2.19470e11	0.254840	0.127420	−	0.991849i	$-0.459330\pi$
$449$	2.19470e11	0.254840	0.127420	+	0.991849i	$0.459330\pi$
$450$	0	0
$451$	−1.03533e11	−0.117837
$452$	1.80607e12i	2.03522i
$453$	2.19269e10i	0.0244644i
$454$	−1.41545e12	−1.56366
$455$	0	0
$456$	2.73663e11	0.296397
$457$	− 7.40816e11i	− 0.794488i	−0.917713	−	0.397244i	$-0.869967\pi$
$457$	− 7.40816e11i	− 0.794488i	0.917713	−	0.397244i	$-0.130033\pi$
$458$	1.50276e12i	1.59586i
$459$	5.13556e10	0.0540046
$460$	0	0
$461$	2.80170e11	0.288913	0.144457	−	0.989511i	$-0.453857\pi$
$461$	2.80170e11	0.288913	0.144457	+	0.989511i	$0.453857\pi$
$462$	− 2.54070e12i	− 2.59457i
$463$	− 5.07092e10i	− 0.0512828i	−0.999671	−	0.0256414i	$-0.991837\pi$
$463$	− 5.07092e10i	− 0.0512828i	0.999671	−	0.0256414i	$-0.00816281\pi$
$464$	1.12961e12	1.13135
$465$	0	0
$466$	−1.04225e12	−1.02385
$467$	− 1.77228e12i	− 1.72427i	−0.506678	−	0.862135i	$-0.669127\pi$
$467$	− 1.77228e12i	− 1.72427i	0.506678	−	0.862135i	$-0.330873\pi$
$468$	− 7.31180e11i	− 0.704560i
$469$	1.47503e12	1.40774
$470$	0	0
$471$	−7.88324e11	−0.738092
$472$	2.21728e12i	2.05627i
$473$	1.31469e12i	1.20767i
$474$	1.35471e12	1.23266
$475$	0	0
$476$	1.17687e12	1.05074
$477$	1.68819e10i	0.0149310i
$478$	5.22495e11i	0.457779i
$479$	7.79555e11	0.676608	0.338304	−	0.941037i	$-0.390147\pi$
$479$	7.79555e11	0.676608	0.338304	+	0.941037i	$0.390147\pi$
$480$	0	0
$481$	−7.14444e11	−0.608577
$482$	7.20880e11i	0.608347i
$483$	− 2.42690e11i	− 0.202904i
$484$	−1.96945e12	−1.63132
$485$	0	0
$486$	−1.35239e11	−0.109961
$487$	1.33958e12i	1.07916i	0.841933	+	0.539582i	$0.181418\pi$
$487$	1.33958e12i	1.07916i	−0.841933	+	0.539582i	$0.818582\pi$
$488$	3.59364e12i	2.86844i
$489$	6.29226e11	0.497642
$490$	0	0
$491$	−9.76349e11	−0.758121	−0.379061	−	0.925372i	$-0.623753\pi$
$491$	−9.76349e11	−0.758121	−0.379061	+	0.925372i	$0.623753\pi$
$492$	1.26289e11i	0.0971682i
$493$	− 5.08744e11i	− 0.387872i
$494$	−7.89825e11	−0.596705
$495$	0	0
$496$	3.93637e11	0.292031
$497$	8.58495e9i	0.00631152i
$498$	5.33336e10i	0.0388570i
$499$	−1.32057e12	−0.953472	−0.476736	−	0.879046i	$-0.658180\pi$
$499$	−1.32057e12	−0.953472	−0.476736	+	0.879046i	$0.658180\pi$
$500$	0	0
$501$	6.81815e11	0.483501
$502$	− 1.66908e12i	− 1.17303i
$503$	− 1.16421e12i	− 0.810917i	−0.914113	−	0.405459i	$-0.867112\pi$
$503$	− 1.16421e12i	− 0.810917i	0.914113	−	0.405459i	$-0.132888\pi$
$504$	−1.50019e12	−1.03564
$505$	0	0
$506$	−6.24017e11	−0.423174
$507$	1.62546e11i	0.109255i
$508$	− 3.72054e12i	− 2.47868i
$509$	−8.32285e11	−0.549594	−0.274797	−	0.961502i	$-0.588611\pi$
$509$	−8.32285e11	−0.549594	−0.274797	+	0.961502i	$0.588611\pi$
$510$	0	0
$511$	−1.09380e12	−0.709649
$512$	2.30806e12i	1.48434i
$513$	9.63671e10i	0.0614329i
$514$	2.43135e10	0.0153643
$515$	0	0
$516$	1.60366e12	0.995835
$517$	1.98327e12i	1.22088i
$518$	3.02822e12i	1.84800i
$519$	2.91469e10	0.0176335
$520$	0	0
$521$	2.43459e12	1.44763	0.723813	−	0.689997i	$-0.242388\pi$
$521$	2.43459e12	1.44763	0.723813	+	0.689997i	$0.242388\pi$
$522$	1.33972e12i	0.789763i
$523$	− 1.07631e12i	− 0.629043i	−0.949250	−	0.314522i	$-0.898156\pi$
$523$	− 1.07631e12i	− 0.629043i	0.949250	−	0.314522i	$-0.101844\pi$
$524$	1.95099e12	1.13048
$525$	0	0
$526$	2.41036e12	1.37292
$527$	− 1.77283e11i	− 0.100119i
$528$	1.14530e12i	0.641308i
$529$	1.74155e12	0.966906
$530$	0	0
$531$	−7.80787e11	−0.426194
$532$	2.20835e12i	1.19527i
$533$	− 1.76435e11i	− 0.0946919i
$534$	−9.73494e9	−0.00518081
$535$	0	0
$536$	−2.23943e12	−1.17191
$537$	− 7.00923e11i	− 0.363736i
$538$	− 2.11337e12i	− 1.08757i
$539$	7.26533e12	3.70771
$540$	0	0
$541$	−3.12532e12	−1.56858	−0.784291	−	0.620393i	$-0.786973\pi$
$541$	−3.12532e12	−1.56858	−0.784291	+	0.620393i	$0.786973\pi$
$542$	3.78139e12i	1.88215i
$543$	− 4.93867e11i	− 0.243787i
$544$	1.17633e11	0.0575883
$545$	0	0
$546$	4.32974e12	2.08495
$547$	− 1.59061e12i	− 0.759663i	−0.925056	−	0.379832i	$-0.875982\pi$
$547$	− 1.59061e12i	− 0.759663i	0.925056	−	0.379832i	$-0.124018\pi$
$548$	− 3.60453e11i	− 0.170741i
$549$	−1.26546e12	−0.594527
$550$	0	0
$551$	9.54641e11	0.441223
$552$	3.68460e11i	0.168913i
$553$	5.29180e12i	2.40625i
$554$	−5.55402e12	−2.50503
$555$	0	0
$556$	4.52106e12	2.00633
$557$	− 3.76617e12i	− 1.65787i	−0.559343	−	0.828937i	$-0.688946\pi$
$557$	− 3.76617e12i	− 1.65787i	0.559343	−	0.828937i	$-0.311054\pi$
$558$	4.66854e11i	0.203858i
$559$	−2.24042e12	−0.970458
$560$	0	0
$561$	5.15810e11	0.219865
$562$	− 2.52607e12i	− 1.06815i
$563$	− 2.32486e12i	− 0.975234i	−0.873058	−	0.487617i	$-0.837866\pi$
$563$	− 2.32486e12i	− 0.975234i	0.873058	−	0.487617i	$-0.162134\pi$
$564$	2.41919e12	1.00673
$565$	0	0
$566$	−6.41643e12	−2.62797
$567$	− 5.28275e11i	− 0.214653i
$568$	− 1.30339e10i	− 0.00525422i
$569$	−3.30244e11	−0.132078	−0.0660388	−	0.997817i	$-0.521036\pi$
$569$	−3.30244e11	−0.132078	−0.0660388	+	0.997817i	$0.521036\pi$
$570$	0	0
$571$	3.83190e12	1.50852	0.754261	−	0.656575i	$-0.227995\pi$
$571$	3.83190e12	1.50852	0.754261	+	0.656575i	$0.227995\pi$
$572$	− 7.34388e12i	− 2.86843i
$573$	2.39953e12i	0.929887i
$574$	−7.47832e11	−0.287542
$575$	0	0
$576$	−1.03055e12	−0.390094
$577$	1.66616e12i	0.625786i	0.949788	+	0.312893i	$0.101298\pi$
$577$	1.66616e12i	0.625786i	−0.949788	+	0.312893i	$0.898702\pi$
$578$	− 4.23738e12i	− 1.57915i
$579$	−3.75384e10	−0.0138811
$580$	0	0
$581$	−2.08333e11	−0.0758517
$582$	1.79896e12i	0.649931i
$583$	1.69559e11i	0.0607874i
$584$	1.66064e12	0.590769
$585$	0	0
$586$	2.18856e12	0.766689
$587$	− 2.00482e12i	− 0.696953i	−0.937318	−	0.348476i	$-0.886699\pi$
$587$	− 2.00482e12i	− 0.696953i	0.937318	−	0.348476i	$-0.113301\pi$
$588$	− 8.86226e12i	− 3.05736i
$589$	3.32665e11	0.113891
$590$	0	0
$591$	−9.99654e11	−0.337059
$592$	− 1.36506e12i	− 0.456777i
$593$	1.46848e12i	0.487666i	0.969817	+	0.243833i	$0.0784048\pi$
$593$	1.46848e12i	0.487666i	−0.969817	+	0.243833i	$0.921595\pi$
$594$	−1.35833e12	−0.447678
$595$	0	0
$596$	8.73121e12	2.83443
$597$	− 8.12868e11i	− 0.261900i
$598$	− 1.06342e12i	− 0.340055i
$599$	−5.67302e12	−1.80050	−0.900251	−	0.435370i	$-0.856617\pi$
$599$	−5.67302e12	−1.80050	−0.900251	+	0.435370i	$0.856617\pi$
$600$	0	0
$601$	2.23747e12	0.699555	0.349778	−	0.936833i	$-0.386257\pi$
$601$	2.23747e12	0.699555	0.349778	+	0.936833i	$0.386257\pi$
$602$	9.49617e12i	2.94689i
$603$	− 7.88587e11i	− 0.242897i
$604$	2.68638e11	0.0821299
$605$	0	0
$606$	−5.60619e12	−1.68865
$607$	− 7.87986e11i	− 0.235597i	−0.993038	−	0.117798i	$-0.962416\pi$
$607$	− 7.87986e11i	− 0.235597i	0.993038	−	0.117798i	$-0.0375837\pi$
$608$	2.20734e11i	0.0655094i
$609$	−5.23324e12	−1.54168
$610$	0	0
$611$	−3.37979e12	−0.981079
$612$	− 6.29185e11i	− 0.181300i
$613$	− 4.35930e12i	− 1.24694i	−0.781848	−	0.623468i	$-0.785723\pi$
$613$	− 4.35930e12i	− 1.24694i	0.781848	−	0.623468i	$-0.214277\pi$
$614$	−6.95671e11	−0.197536
$615$	0	0
$616$	−1.50678e13	−4.21634
$617$	2.04791e12i	0.568889i	0.958693	+	0.284444i	$0.0918091\pi$
$617$	2.04791e12i	0.568889i	−0.958693	+	0.284444i	$0.908191\pi$
$618$	− 3.66421e12i	− 1.01049i
$619$	6.31079e12	1.72773	0.863865	−	0.503723i	$-0.168037\pi$
$619$	6.31079e12	1.72773	0.863865	+	0.503723i	$0.168037\pi$
$620$	0	0
$621$	−1.29748e11	−0.0350098
$622$	− 1.24098e13i	− 3.32435i
$623$	− 3.80268e10i	− 0.0101133i
$624$	−1.95176e12	−0.515342
$625$	0	0
$626$	−1.22947e13	−3.19989
$627$	9.67899e11i	0.250107i
$628$	9.65818e12i	2.47786i
$629$	−6.14784e11	−0.156601
$630$	0	0
$631$	4.94106e12	1.24076	0.620380	−	0.784301i	$-0.286978\pi$
$631$	4.94106e12	1.24076	0.620380	+	0.784301i	$0.286978\pi$
$632$	− 8.03418e12i	− 2.00316i
$633$	2.88577e12i	0.714405i
$634$	1.19523e13	2.93798
$635$	0	0
$636$	2.06829e11	0.0501249
$637$	1.23812e13i	2.97945i
$638$	1.34560e13i	3.21531i
$639$	4.58974e9	0.00108902
$640$	0	0
$641$	−6.55819e11	−0.153434	−0.0767172	−	0.997053i	$-0.524444\pi$
$641$	−6.55819e11	−0.153434	−0.0767172	+	0.997053i	$0.524444\pi$
$642$	− 5.41089e12i	− 1.25707i
$643$	5.76324e11i	0.132959i	0.997788	+	0.0664794i	$0.0211767\pi$
$643$	5.76324e11i	0.132959i	−0.997788	+	0.0664794i	$0.978823\pi$
$644$	−2.97332e12	−0.681171
$645$	0	0
$646$	−6.79649e11	−0.153546
$647$	3.52372e12i	0.790556i	0.918562	+	0.395278i	$0.129352\pi$
$647$	3.52372e12i	0.790556i	−0.918562	+	0.395278i	$0.870648\pi$
$648$	8.02043e11i	0.178694i
$649$	−7.84212e12	−1.73513
$650$	0	0
$651$	−1.82364e12	−0.397945
$652$	− 7.70899e12i	− 1.67064i
$653$	− 4.37841e11i	− 0.0942338i	−0.998889	−	0.0471169i	$-0.984997\pi$
$653$	− 4.37841e11i	− 0.0942338i	0.998889	−	0.0471169i	$-0.0150033\pi$
$654$	6.54942e12	1.39992
$655$	0	0
$656$	3.37108e11	0.0710725
$657$	5.84774e11i	0.122446i
$658$	1.43254e13i	2.97914i
$659$	−1.98477e12	−0.409945	−0.204972	−	0.978768i	$-0.565710\pi$
$659$	−1.98477e12	−0.409945	−0.204972	+	0.978768i	$0.565710\pi$
$660$	0	0
$661$	2.80945e12	0.572420	0.286210	−	0.958167i	$-0.407604\pi$
$661$	2.80945e12	0.572420	0.286210	+	0.958167i	$0.407604\pi$
$662$	6.94988e12i	1.40642i
$663$	8.79016e11i	0.176679i
$664$	3.16297e11	0.0631450
$665$	0	0
$666$	1.61896e12	0.318862
$667$	1.28533e12i	0.251447i
$668$	− 8.35328e12i	− 1.62317i
$669$	−2.76733e12	−0.534126
$670$	0	0
$671$	−1.27101e13	−2.42045
$672$	− 1.21004e12i	− 0.228896i
$673$	− 2.08224e12i	− 0.391258i	−0.980678	−	0.195629i	$-0.937325\pi$
$673$	− 2.08224e12i	− 0.391258i	0.980678	−	0.195629i	$-0.0626749\pi$
$674$	3.77526e12	0.704657
$675$	0	0
$676$	1.99144e12	0.366781
$677$	6.44805e12i	1.17972i	0.807505	+	0.589861i	$0.200817\pi$
$677$	6.44805e12i	1.17972i	−0.807505	+	0.589861i	$0.799183\pi$
$678$	5.71770e12i	1.03917i
$679$	−7.02712e12	−1.26871
$680$	0	0
$681$	−2.95598e12	−0.526671
$682$	4.68902e12i	0.829952i
$683$	− 4.02024e12i	− 0.706902i	−0.935453	−	0.353451i	$-0.885008\pi$
$683$	− 4.02024e12i	− 0.706902i	0.935453	−	0.353451i	$-0.114992\pi$
$684$	1.18064e12	0.206237
$685$	0	0
$686$	3.32706e13	5.73591
$687$	3.13832e12i	0.537516i
$688$	− 4.28069e12i	− 0.728392i
$689$	−2.88954e11	−0.0488476
$690$	0	0
$691$	−8.43146e12	−1.40686	−0.703431	−	0.710763i	$-0.748350\pi$
$691$	−8.43146e12	−1.40686	−0.703431	+	0.710763i	$0.748350\pi$
$692$	− 3.57094e11i	− 0.0591978i
$693$	− 5.30592e12i	− 0.873900i
$694$	1.34879e13	2.20713
$695$	0	0
$696$	7.94527e12	1.28342
$697$	− 1.51824e11i	− 0.0243664i
$698$	− 4.27159e12i	− 0.681145i
$699$	−2.17661e12	−0.344853
$700$	0	0
$701$	6.55956e12	1.02599	0.512995	−	0.858391i	$-0.328536\pi$
$701$	6.55956e12	1.02599	0.512995	+	0.858391i	$0.328536\pi$
$702$	− 2.31479e12i	− 0.359745i
$703$	− 1.15362e12i	− 0.178141i
$704$	−1.03507e13	−1.58816
$705$	0	0
$706$	−1.31894e13	−1.99803
$707$	− 2.18990e13i	− 3.29638i
$708$	9.56583e12i	1.43078i
$709$	5.30959e12	0.789138	0.394569	−	0.918866i	$-0.370894\pi$
$709$	5.30959e12	0.789138	0.394569	+	0.918866i	$0.370894\pi$
$710$	0	0
$711$	2.82914e12	0.415184
$712$	5.77335e10i	0.00841914i
$713$	4.47899e11i	0.0649049i
$714$	3.72577e12	0.536505
$715$	0	0
$716$	−8.58739e12	−1.22110
$717$	1.09116e12i	0.154189i
$718$	− 1.06687e13i	− 1.49813i
$719$	−1.02053e13	−1.42411	−0.712056	−	0.702123i	$-0.752236\pi$
$719$	−1.02053e13	−1.42411	−0.712056	+	0.702123i	$0.752236\pi$
$720$	0	0
$721$	1.43132e13	1.97255
$722$	1.12405e13i	1.53946i
$723$	1.50546e12i	0.204903i
$724$	−6.05063e12	−0.818422
$725$	0	0
$726$	−6.23493e12	−0.832946
$727$	7.45813e12i	0.990206i	0.868834	+	0.495103i	$0.164870\pi$
$727$	7.45813e12i	0.990206i	−0.868834	+	0.495103i	$0.835130\pi$
$728$	− 2.56777e13i	− 3.38817i
$729$	−2.82430e11	−0.0370370
$730$	0	0
$731$	−1.92790e12	−0.249721
$732$	1.55038e13i	1.99589i
$733$	− 1.06610e13i	− 1.36405i	−0.731329	−	0.682024i	$-0.761100\pi$
$733$	− 1.06610e13i	− 1.36405i	0.731329	−	0.682024i	$-0.238900\pi$
$734$	8.23114e12	1.04671
$735$	0	0
$736$	−2.97196e11	−0.0373330
$737$	− 7.92047e12i	− 0.988889i
$738$	3.99811e11i	0.0496136i
$739$	−2.33179e12	−0.287601	−0.143800	−	0.989607i	$-0.545932\pi$
$739$	−2.33179e12	−0.287601	−0.143800	+	0.989607i	$0.545932\pi$
$740$	0	0
$741$	−1.64944e12	−0.200981
$742$	1.22475e12i	0.148330i
$743$	− 7.80869e12i	− 0.940001i	−0.882666	−	0.470001i	$-0.844254\pi$
$743$	− 7.80869e12i	− 0.940001i	0.882666	−	0.470001i	$-0.155746\pi$
$744$	2.76870e12	0.331282
$745$	0	0
$746$	2.35946e13	2.78925
$747$	1.11380e11i	0.0130878i
$748$	− 6.31946e12i	− 0.738113i
$749$	2.11361e13	2.45390
$750$	0	0
$751$	4.20664e12	0.482565	0.241283	−	0.970455i	$-0.422432\pi$
$751$	4.20664e12	0.482565	0.241283	+	0.970455i	$0.422432\pi$
$752$	− 6.45763e12i	− 0.736364i
$753$	− 3.48565e12i	− 0.395099i
$754$	−2.29310e13	−2.58376
$755$	0	0
$756$	−6.47217e12	−0.720613
$757$	1.54834e13i	1.71370i	0.515570	+	0.856848i	$0.327580\pi$
$757$	1.54834e13i	1.71370i	−0.515570	+	0.856848i	$0.672420\pi$
$758$	1.80021e13i	1.98067i
$759$	−1.30318e12	−0.142533
$760$	0	0
$761$	9.77615e12	1.05666	0.528332	−	0.849038i	$-0.322818\pi$
$761$	9.77615e12	1.05666	0.528332	+	0.849038i	$0.322818\pi$
$762$	− 1.17786e13i	− 1.26560i
$763$	2.55835e13i	2.73275i
$764$	2.93979e13	3.12174
$765$	0	0
$766$	2.02755e13	2.12785
$767$	− 1.33641e13i	− 1.39432i
$768$	1.06678e13i	1.10649i
$769$	−3.35411e12	−0.345867	−0.172933	−	0.984934i	$-0.555325\pi$
$769$	−3.35411e12	−0.345867	−0.172933	+	0.984934i	$0.555325\pi$
$770$	0	0
$771$	5.07755e10	0.00517499
$772$	4.59904e11i	0.0466003i
$773$	− 6.04474e12i	− 0.608933i	−0.952523	−	0.304467i	$-0.901522\pi$
$773$	− 6.04474e12i	− 0.608933i	0.952523	−	0.304467i	$-0.0984782\pi$
$774$	5.07690e12	0.508469
$775$	0	0
$776$	1.06688e13	1.05618
$777$	6.32403e12i	0.622443i
$778$	− 4.61163e12i	− 0.451280i
$779$	2.84892e11	0.0277180
$780$	0	0
$781$	4.60988e10	0.00443364
$782$	− 9.15078e11i	− 0.0875040i
$783$	2.79783e12i	0.266007i
$784$	−2.36563e13	−2.23627
$785$	0	0
$786$	6.17651e12	0.577220
$787$	− 4.16503e12i	− 0.387019i	−0.981098	−	0.193509i	$-0.938013\pi$
$787$	− 4.16503e12i	− 0.387019i	0.981098	−	0.193509i	$-0.0619870\pi$
$788$	1.22473e13i	1.13155i
$789$	5.03371e12	0.462425
$790$	0	0
$791$	−2.23346e13	−2.02854
$792$	8.05562e12i	0.727504i
$793$	− 2.16599e13i	− 1.94503i
$794$	1.07420e13	0.959164
$795$	0	0
$796$	−9.95887e12	−0.879228
$797$	− 2.14334e13i	− 1.88160i	−0.338957	−	0.940802i	$-0.610074\pi$
$797$	− 2.14334e13i	− 1.88160i	0.338957	−	0.940802i	$-0.389926\pi$
$798$	6.99128e12i	0.610300i
$799$	−2.90833e12	−0.252454
$800$	0	0
$801$	−2.03301e10	−0.00174499
$802$	5.95301e12i	0.508103i
$803$	5.87339e12i	0.498504i
$804$	−9.66140e12	−0.815432
$805$	0	0
$806$	−7.99080e12	−0.666933
$807$	− 4.41350e12i	− 0.366313i
$808$	3.32478e13i	2.74417i
$809$	1.82139e11	0.0149498	0.00747490	−	0.999972i	$-0.497621\pi$
$809$	1.82139e11	0.0149498	0.00747490	+	0.999972i	$0.497621\pi$
$810$	0	0
$811$	−1.32191e13	−1.07302	−0.536511	−	0.843894i	$-0.680258\pi$
$811$	−1.32191e13	−1.07302	−0.536511	+	0.843894i	$0.680258\pi$
$812$	6.41153e13i	5.17558i
$813$	7.89693e12i	0.633944i
$814$	1.62607e13	1.29816
$815$	0	0
$816$	−1.67950e12	−0.132610
$817$	− 3.61763e12i	− 0.284070i
$818$	− 5.90963e12i	− 0.461498i
$819$	9.04209e12	0.702249
$820$	0	0
$821$	−1.15652e13	−0.888398	−0.444199	−	0.895928i	$-0.646512\pi$
$821$	−1.15652e13	−0.888398	−0.444199	+	0.895928i	$0.646512\pi$
$822$	− 1.14113e12i	− 0.0871793i
$823$	9.35914e12i	0.711110i	0.934655	+	0.355555i	$0.115708\pi$
$823$	9.35914e12i	0.711110i	−0.934655	+	0.355555i	$0.884292\pi$
$824$	−2.17307e13	−1.64211
$825$	0	0
$826$	−5.66448e13	−4.23399
$827$	2.25652e13i	1.67751i	0.544512	+	0.838753i	$0.316715\pi$
$827$	2.25652e13i	1.67751i	−0.544512	+	0.838753i	$0.683285\pi$
$828$	1.58962e12i	0.117532i
$829$	−1.22484e13	−0.900705	−0.450353	−	0.892851i	$-0.648702\pi$
$829$	−1.22484e13	−0.900705	−0.450353	+	0.892851i	$0.648702\pi$
$830$	0	0
$831$	−1.15988e13	−0.843742
$832$	− 1.76392e13i	− 1.27622i
$833$	1.06541e13i	0.766681i
$834$	1.43129e13	1.02442
$835$	0	0
$836$	1.18582e13	0.839638
$837$	9.74963e11i	0.0686631i
$838$	− 3.52887e13i	− 2.47194i
$839$	−4.67277e12	−0.325571	−0.162786	−	0.986661i	$-0.552048\pi$
$839$	−4.67277e12	−0.325571	−0.162786	+	0.986661i	$0.552048\pi$
$840$	0	0
$841$	1.32090e13	0.910516
$842$	− 3.83414e13i	− 2.62883i
$843$	− 5.27537e12i	− 0.359773i
$844$	3.53551e13	2.39834
$845$	0	0
$846$	7.65876e12	0.514034
$847$	− 2.43550e13i	− 1.62597i
$848$	− 5.52094e11i	− 0.0366633i
$849$	−1.33999e13	−0.885149
$850$	0	0
$851$	1.55323e12	0.101520
$852$	− 5.62314e10i	− 0.00365595i
$853$	4.04678e12i	0.261721i	0.991401	+	0.130861i	$0.0417740\pi$
$853$	4.04678e12i	0.261721i	−0.991401	+	0.130861i	$0.958226\pi$
$854$	−9.18067e13	−5.90628
$855$	0	0
$856$	−3.20895e13	−2.04282
$857$	2.35372e13i	1.49053i	0.666766	+	0.745267i	$0.267678\pi$
$857$	2.35372e13i	1.49053i	−0.666766	+	0.745267i	$0.732322\pi$
$858$	− 2.32495e13i	− 1.46460i
$859$	−2.19727e13	−1.37694	−0.688470	−	0.725265i	$-0.741717\pi$
$859$	−2.19727e13	−1.37694	−0.688470	+	0.725265i	$0.741717\pi$
$860$	0	0
$861$	−1.56175e12	−0.0968494
$862$	− 7.88441e12i	− 0.486392i
$863$	− 2.06939e13i	− 1.26997i	−0.772525	−	0.634984i	$-0.781007\pi$
$863$	− 2.06939e13i	− 1.26997i	0.772525	−	0.634984i	$-0.218993\pi$
$864$	−6.46921e11	−0.0394947
$865$	0	0
$866$	−8.17796e12	−0.494099
$867$	− 8.84922e12i	− 0.531887i
$868$	2.23423e13i	1.33595i
$869$	2.84155e13	1.69031
$870$	0	0
$871$	1.34977e13	0.794652
$872$	− 3.88416e13i	− 2.27496i
$873$	3.75689e12i	0.218909i
$874$	1.71711e12	0.0995400
$875$	0	0
$876$	7.16437e12	0.411064
$877$	8.18344e12i	0.467130i	0.972341	+	0.233565i	$0.0750392\pi$
$877$	8.18344e12i	0.467130i	−0.972341	+	0.233565i	$0.924961\pi$
$878$	8.19991e12i	0.465676i
$879$	4.57052e12	0.258235
$880$	0	0
$881$	2.43747e13	1.36316	0.681581	−	0.731743i	$-0.261293\pi$
$881$	2.43747e13	1.36316	0.681581	+	0.731743i	$0.261293\pi$
$882$	− 2.80564e13i	− 1.56107i
$883$	− 1.17064e13i	− 0.648039i	−0.946050	−	0.324019i	$-0.894966\pi$
$883$	− 1.17064e13i	− 0.648039i	0.946050	−	0.324019i	$-0.105034\pi$
$884$	1.07693e13	0.593133
$885$	0	0
$886$	5.64407e13	3.07709
$887$	− 2.83247e13i	− 1.53642i	−0.640198	−	0.768210i	$-0.721148\pi$
$887$	− 2.83247e13i	− 1.53642i	0.640198	−	0.768210i	$-0.278852\pi$
$888$	− 9.60134e12i	− 0.518171i
$889$	4.60098e13	2.47055
$890$	0	0
$891$	−2.83669e12	−0.150786
$892$	3.39040e13i	1.79312i
$893$	− 5.45738e12i	− 0.287179i
$894$	2.76415e13	1.44725
$895$	0	0
$896$	−6.71163e13	−3.47890
$897$	− 2.22081e12i	− 0.114537i
$898$	− 8.51244e12i	− 0.436828i
$899$	9.65827e12	0.493152
$900$	0	0
$901$	−2.48647e11	−0.0125696
$902$	4.01565e12i	0.201988i
$903$	1.98315e13i	0.992569i
$904$	3.39091e13	1.68872
$905$	0	0
$906$	8.50462e11	0.0419351
$907$	− 5.36313e12i	− 0.263139i	−0.991307	−	0.131570i	$-0.957998\pi$
$907$	− 5.36313e12i	− 0.263139i	0.991307	−	0.131570i	$-0.0420017\pi$
$908$	3.62153e13i	1.76809i
$909$	−1.17078e13	−0.568771
$910$	0	0
$911$	3.43721e13	1.65338	0.826691	−	0.562656i	$-0.190220\pi$
$911$	3.43721e13	1.65338	0.826691	+	0.562656i	$0.190220\pi$
$912$	− 3.15153e12i	− 0.150850i
$913$	1.11869e12i	0.0532833i
$914$	−2.87335e13	−1.36185
$915$	0	0
$916$	3.84492e13	1.80450
$917$	2.41268e13i	1.12678i
$918$	− 1.99189e12i	− 0.0925708i
$919$	2.98037e13	1.37832	0.689160	−	0.724609i	$-0.257980\pi$
$919$	2.98037e13	1.37832	0.689160	+	0.724609i	$0.257980\pi$
$920$	0	0
$921$	−1.45282e12	−0.0665339
$922$	− 1.08668e13i	− 0.495234i
$923$	7.85592e10i	0.00356278i
$924$	−6.50057e13	−2.93378
$925$	0	0
$926$	−1.96682e12	−0.0879053
$927$	− 7.65221e12i	− 0.340352i
$928$	6.40859e12i	0.283659i
$929$	2.03150e13	0.894843	0.447421	−	0.894323i	$-0.352342\pi$
$929$	2.03150e13	0.894843	0.447421	+	0.894323i	$0.352342\pi$
$930$	0	0
$931$	−1.99921e13	−0.872136
$932$	2.66668e13i	1.15771i
$933$	− 2.59162e13i	− 1.11970i
$934$	−6.87399e13	−2.95562
$935$	0	0
$936$	−1.37280e13	−0.584609
$937$	− 2.73553e13i	− 1.15935i	−0.814848	−	0.579674i	$-0.803180\pi$
$937$	− 2.73553e13i	− 1.15935i	0.814848	−	0.579674i	$-0.196820\pi$
$938$	− 5.72107e13i	− 2.41304i
$939$	−2.56759e13	−1.07778
$940$	0	0
$941$	−4.24123e13	−1.76335	−0.881675	−	0.471857i	$-0.843584\pi$
$941$	−4.24123e13	−1.76335	−0.881675	+	0.471857i	$0.843584\pi$
$942$	3.05761e13i	1.26518i
$943$	3.83578e11i	0.0157961i
$944$	2.55344e13	1.04653
$945$	0	0
$946$	5.09918e13	2.07009
$947$	− 9.23741e12i	− 0.373229i	−0.982433	−	0.186614i	$-0.940248\pi$
$947$	− 9.23741e12i	− 0.373229i	0.982433	−	0.186614i	$-0.0597515\pi$
$948$	− 3.46613e13i	− 1.39382i
$949$	−1.00091e13	−0.400589
$950$	0	0
$951$	2.49607e13	0.989566
$952$	− 2.20958e13i	− 0.871855i
$953$	1.11343e13i	0.437265i	0.975807	+	0.218633i	$0.0701596\pi$
$953$	1.11343e13i	0.437265i	−0.975807	+	0.218633i	$0.929840\pi$
$954$	6.54784e11	0.0255936
$955$	0	0
$956$	1.33684e13	0.517629
$957$	2.81011e13i	1.08298i
$958$	− 3.02360e13i	− 1.15979i
$959$	4.45752e12	0.170180
$960$	0	0
$961$	−2.30740e13	−0.872705
$962$	2.77106e13i	1.04318i
$963$	− 1.12999e13i	− 0.423406i
$964$	1.84442e13	0.687882
$965$	0	0
$966$	−9.41304e12	−0.347803
$967$	5.48630e12i	0.201772i	0.994898	+	0.100886i	$0.0321677\pi$
$967$	5.48630e12i	0.201772i	−0.994898	+	0.100886i	$0.967832\pi$
$968$	3.69766e13i	1.35359i
$969$	−1.41936e12	−0.0517172
$970$	0	0
$971$	−2.07887e13	−0.750484	−0.375242	−	0.926927i	$-0.622440\pi$
$971$	−2.07887e13	−0.750484	−0.375242	+	0.926927i	$0.622440\pi$
$972$	3.46019e12i	0.124338i
$973$	5.59093e13i	1.99975i
$974$	5.19572e13	1.84982
$975$	0	0
$976$	4.13847e13	1.45987
$977$	− 2.25372e13i	− 0.791362i	−0.918388	−	0.395681i	$-0.870509\pi$
$977$	− 2.25372e13i	− 0.791362i	0.918388	−	0.395681i	$-0.129491\pi$
$978$	− 2.44053e13i	− 0.853022i
$979$	−2.04193e11	−0.00710427
$980$	0	0
$981$	1.36776e13	0.471519
$982$	3.78689e13i	1.29952i
$983$	− 2.20727e13i	− 0.753989i	−0.926216	−	0.376994i	$-0.876958\pi$
$983$	− 2.20727e13i	− 0.753989i	0.926216	−	0.376994i	$-0.123042\pi$
$984$	2.37110e12	0.0806253
$985$	0	0
$986$	−1.97323e13	−0.664861
$987$	2.99168e13i	1.00343i
$988$	2.02082e13i	0.674717i
$989$	4.87077e12	0.161888
$990$	0	0
$991$	−5.27788e13	−1.73831	−0.869157	−	0.494536i	$-0.835338\pi$
$991$	−5.27788e13	−1.73831	−0.869157	+	0.494536i	$0.835338\pi$
$992$	2.23321e12i	0.0732195i
$993$	1.45139e13i	0.473710i
$994$	3.32978e11	0.0108188
$995$	0	0
$996$	1.36458e12	0.0439371
$997$	4.19157e13i	1.34353i	0.740763	+	0.671767i	$0.234464\pi$
$997$	4.19157e13i	1.34353i	−0.740763	+	0.671767i	$0.765536\pi$
$998$	5.12199e13i	1.63437i
$999$	3.38099e12	0.107399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.b.f.49.1		4
3.2	odd	2		225.10.b.i.199.4		4
5.2	odd	4		15.10.a.d.1.2	✓	2
5.3	odd	4		75.10.a.f.1.1		2
5.4	even	2	inner	75.10.b.f.49.4		4
15.2	even	4		45.10.a.d.1.1		2
15.8	even	4		225.10.a.k.1.2		2
15.14	odd	2		225.10.b.i.199.1		4
20.7	even	4		240.10.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.d.1.2	✓	2	5.2	odd	4
45.10.a.d.1.1		2	15.2	even	4
75.10.a.f.1.1		2	5.3	odd	4
75.10.b.f.49.1		4	1.1	even	1	trivial
75.10.b.f.49.4		4	5.4	even	2	inner
225.10.a.k.1.2		2	15.8	even	4
225.10.b.i.199.1		4	15.14	odd	2
225.10.b.i.199.4		4	3.2	odd	2
240.10.a.r.1.1		2	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-38.7863i q^{2} -81.0000i q^{3} -992.374 q^{4} -3141.69 q^{6} -12272.1i q^{7} +18631.9i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-38.7863i q^{2} -81.0000i q^{3} -992.374 q^{4} -3141.69 q^{6} -12272.1i q^{7} +18631.9i q^{8} -6561.00 q^{9} -65897.9 q^{11} +80382.3i q^{12} -112300. i q^{13} -475990. q^{14} +214567. q^{16} -96634.7i q^{17} +254477. i q^{18} +181332. q^{19} -994042. q^{21} +2.55593e6i q^{22} +244145. i q^{23} +1.50919e6 q^{24} -4.35569e6 q^{26} +531441. i q^{27} +1.21785e7i q^{28} +5.26461e6 q^{29} +1.83457e6 q^{31} +1.21730e6i q^{32} +5.33773e6i q^{33} -3.74810e6 q^{34} +6.51097e6 q^{36} -6.36194e6i q^{37} -7.03318e6i q^{38} -9.09628e6 q^{39} +1.57111e6 q^{41} +3.85552e7i q^{42} -1.99504e7i q^{43} +6.53953e7 q^{44} +9.46946e6 q^{46} -3.00961e7i q^{47} -1.73799e7i q^{48} -1.10251e8 q^{49} -7.82741e6 q^{51} +1.11443e8i q^{52} -2.57306e6i q^{53} +2.06126e7 q^{54} +2.28653e8 q^{56} -1.46879e7i q^{57} -2.04195e8i q^{58} +1.19004e8 q^{59} +1.92875e8 q^{61} -7.11559e7i q^{62} +8.05174e7i q^{63} +1.57073e8 q^{64} +2.07030e8 q^{66} +1.20193e8i q^{67} +9.58978e7i q^{68} +1.97757e7 q^{69} -699549. q^{71} -1.22244e8i q^{72} -8.91287e7i q^{73} -2.46756e8 q^{74} -1.79949e8 q^{76} +8.08707e8i q^{77} +3.52811e8i q^{78} -4.31205e8 q^{79} +4.30467e7 q^{81} -6.09375e7i q^{82} -1.69761e7i q^{83} +9.86461e8 q^{84} -7.73800e8 q^{86} -4.26433e8i q^{87} -1.22780e9i q^{88} +3.09863e6 q^{89} -1.37816e9 q^{91} -2.42283e8i q^{92} -1.48600e8i q^{93} -1.16732e9 q^{94} +9.86009e7 q^{96} -5.72609e8i q^{97} +4.27624e9i q^{98} +4.32356e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1082 q^{4} - 5022 q^{6} - 26244 q^{9}+O(q^{10}) \) 4 * q - 1082 * q^4 - 5022 * q^6 - 26244 * q^9	\( 4 q - 1082 q^{4} - 5022 q^{6} - 26244 q^{9} - 43024 q^{11} - 923328 q^{14} + 774530 q^{16} + 191792 q^{19} - 2286144 q^{21} + 4233546 q^{24} - 10838332 q^{26} + 5356424 q^{29} + 21564864 q^{31} - 11445244 q^{34} + 7099002 q^{36} + 3934008 q^{39} + 52120744 q^{41} + 170859944 q^{44} + 34190784 q^{46} - 146565860 q^{49} + 25426872 q^{51} + 32949342 q^{54} + 484908480 q^{56} + 70989328 q^{59} + 682994680 q^{61} + 410240942 q^{64} + 470048184 q^{66} - 119112768 q^{69} + 420572128 q^{71} - 250480468 q^{74} - 437024728 q^{76} + 49510080 q^{79} + 172186884 q^{81} + 1838386368 q^{84} - 1746292744 q^{86} + 855278232 q^{89} - 2253718656 q^{91} - 3295087792 q^{94} + 1037208726 q^{96} + 282280464 q^{99}+O(q^{100}) \) 4 * q - 1082 * q^4 - 5022 * q^6 - 26244 * q^9 - 43024 * q^11 - 923328 * q^14 + 774530 * q^16 + 191792 * q^19 - 2286144 * q^21 + 4233546 * q^24 - 10838332 * q^26 + 5356424 * q^29 + 21564864 * q^31 - 11445244 * q^34 + 7099002 * q^36 + 3934008 * q^39 + 52120744 * q^41 + 170859944 * q^44 + 34190784 * q^46 - 146565860 * q^49 + 25426872 * q^51 + 32949342 * q^54 + 484908480 * q^56 + 70989328 * q^59 + 682994680 * q^61 + 410240942 * q^64 + 470048184 * q^66 - 119112768 * q^69 + 420572128 * q^71 - 250480468 * q^74 - 437024728 * q^76 + 49510080 * q^79 + 172186884 * q^81 + 1838386368 * q^84 - 1746292744 * q^86 + 855278232 * q^89 - 2253718656 * q^91 - 3295087792 * q^94 + 1037208726 * q^96 + 282280464 * q^99

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